I. INTRODUCTION

The information voters possess about candidates' positions (1) is crucial in deciding how to cast their ballot. We consider two-candidate elections and analyze, both theoretically and experimentally, differences in voter behavior between cases where voters know that political advertising is truthful and when they know there is a chance that candidates make false or deceptive statements about their own attributes. In both our theoretical and empirical work, we examine voter behavior (and the associated consequences for electoral outcomes) in both truthful and deceptive advertising environments. In all cases, voting is voluntary and costless.

More precisely, we study how voter turnout and voter decisions differ between truthful and deceptive advertising campaigns. We study both (informed) voters exposed to advertisements as well as (uninformed) voters without such exposure. In addition, we investigate whether deceptive advertising influences which candidate is elected, and in particular whether deception influences the chance that the candidate who generates the highest welfare for voters wins the election. In doing so, we hope to shed some light on possible welfare consequences of deceptive political advertising. (2)

We focus on positive advertising in the sense that truthful (deceptive) advertising implies that candidates make true (false) statements about their own ability or other attributes. We do not consider direct statements about the opponent's attributes (negative advertising). (3) Further, we do not consider strategic candidate advertising, because it would complicate participants' decision problems and make it more difficult to disentangle the effects of deception on voting behavior.

Our laboratory experiment compares voting decisions between environments where advertising is always truthful and environments where false advertising occurs. False advertising accounts for only a small fraction of overall advertising. While our theory predicts that the efficiency of outcomes is similar in truthful and deceptive campaigns, a goal of our empirical analysis is to examine whether the presence of deception leads voters to make suboptimal voting choices. Despite deceptive advertising being relatively uncommon in our experiment, we find that its presence has substantial effects on both behavior and efficiency.

More precisely, our theory implies several equilibria. All equilibria predict that voters should either vote for the candidate who sent them the potentially deceptive advertisement or abstain. No equilibrium predicts that a rational informed voter should vote for the candidate from whom she did not receive an advertisement. A main finding from our experiment is that, in relation to campaigns with only true information, informed voters in deceptive campaigns are much more likely to abstain or act suboptimally. That is, they vote for the opposition candidate from whom they did not receive an advertisement. This has a strong detrimental effect on electoral efficiency: introducing a small amount of false information leads to an economically and statistically significantly greater likelihood of electing a suboptimal candidate. This large reduction in efficiency stands in sharp contrast to our theoretical prediction.

Our study is motivated by the observation that, in naturally occurring elections, candidates often provide false information. This phenomenon is so prevalent that it has launched multiple websites aimed at pointing out false statements in candidate speeches and campaign advertisements. One example is www.factcheck.org, which operated during the 2008 presidential race to point out falsehoods in the campaigns of Senators Clinton, McCain, and Obama. (4) A well-known false statement during the 2008 Democratic primary occurred when Senator Clinton, apparently trying to bolster her foreign policy credentials, incorrectly claimed that she witnessed an attack during her visit to Bosnia in 1996.

While factcheck.org provides a list of false statements and deceptions to voters during the campaign, sometimes the validity of a statement (e.g., whether a candidate intends to keep a promise) can only be assessed after the election has been decided. A famous example is George Bush Sr.'s "Read My Lips: No New Taxes" (eventually broken) promise made during his nomination acceptance speech at the 1988 Republican National Convention. Our theoretical model and experiments capture this latter type of false information, which is revealed as false only after the election.

While false information in elections seems to be prevalent, to our knowledge, there is little theoretical work studying the effect of false information on abstention and voting decisions. (5) Further, no work on this topic has tested theoretical implications in the laboratory. Our paper takes a step toward filling these gaps by providing a framework in which to study and perform laboratory tests on false candidate advertising.

Truthful and correct information about candidate positions underpins much of the theoretical literature on voting. The voting literature, beginning with Downs (1957), has assumed that candidates truthfully represent their positions. More recent significant contributions allow for voter uncertainty about candidate positions, but continue to assume truthful representation of candidate positions. These include works by Matsusaka (1995) and Feddersen and Pesendorfer (1996), who show that more information about candidate positions and a higher probability of being informed, respectively, increases voter turnout. (6,7) A related literature, starting with Shepsle (1972) considers the consequences of ambiguity in (truthful) political advertisement. Shepsle identifies conditions when candidate ambiguity increases and decreases the appeal of a candidate. A subsequent literature has built on Shepsle's model both theoretically and empirically. (8)

Recent empirical studies examining the effect of information on voter behavior either assume truthful advertising (Houser, Morton, and Stratmann 2011) or assume that voters receive signals that either provide them with perfect information or are fully uninformative (Battaglini, Morton, and Palfrey 2008, 2010). (9)

Starting with Banks (1990), models of spatial electoral competition allow candidates to strategically misrepresent their policy intentions, though in doing so they might incur some cost of lying (see, e.g., Callander and Wilkie 2007 and Kartik and McAfee 2007). In these models some voters benefit and others lose from lying, depending on their positions, and no voter can abstain from voting. In contrast, here we investigate the possibility that false information can negatively affect the welfare of all voters, and in addition we allow for voters to abstain.

Corazzini et al. (2014) performed related experimental work examining nonbinding candidate promises. They found that promises are positively correlated with candidates' actions and that voters take such promises into account in their vote choice rather than writing them off as cheap talk.

A recent study by Nyhan and Reifler (2014) also considers misinformation in elections but, in contrast with our focus on voting decisions, they focus on the behavior politicians. In particular, they conduct a field experiment that finds fact-checking deters the spread of misinformation.

There is a large, related literature in political science analyzing the effects of negative political campaigning (negative advertising), and also the effects on voter turnout with respect to this type of advertising (for meta-analyses see Lau et al. 1999 and Lau, Sigelman, and Rovener 2007). The empirical evidence for effects on turnout is mixed. (10) A negative advertisement directly conveys information on competing candidates. Candidates often attack opponents by

stressing negative attributes of them or their policies, to manipulate the impression voters have about their opponents. There are two differences between negative and deceptive advertisements. First, deceptive advertisements convey false information about the candidate who sends the ad, to make him appear more appealing than he actually is. These are direct lies about own attributes ("I am the better candidate"), but do not contain a direct lie about the opponent, as voters have to infer that the ad implies that the opponent is worse. Second, negative advertisements can in some cases be truthful while deceptive advertisements by definition cannot.

Our study of deceptive advertising also differs from the literature on negative advertising in that we focus on the question whether and how voters' awareness of the fact that an ad may contain false information affects their behavior. The negative advertising literature concentrates on the impact and effectiveness of negative campaigning.

There is also a strand of literature on the effects of campaign advertising on voting, where advertising takes the form of campaign expenditures. However, this literature does not address the effect of informative advertising. (11)

II. MODEL

We consider two-candidate elections, with one candidate belonging to the Circle party (*) and the other one to the Triangle party ([DELTA]). Candidates have fixed ideologies that reflect their parties' positions. Candidates, in addition to their party affiliation, are also characterized by their types or qualities, which are either "high" (H) or "low" (L). (12)

The population consists of N (potential) voters, where N is even. Voting is voluntary and costless. All voters are swing voters, with half leaning toward the Circle party, and the other half leaning toward the Triangle party. With respect to candidate quality, all voters' preferences are homogenous. They all prefer a high-quality candidate to a low-quality candidate, irrespective of the candidate's party affiliation. As shown in Table 1, Panel A, voters' payoffs are [x.sub.H] or [x.sub.L] if their own-party high- or low-quality candidate is elected, respectively, and those same respective amounts, less [epsilon], if the other party's high- or low-quality candidate is elected, where [x.sub.H] - [x.sup.L] > [epsilon] [greater than or equal to] 0. This assumption ensures that voters prefer a high-quality candidate from the other party to a low-quality candidate from their own party. A voter can cast her ballot for her own party's candidate, the other party's candidate, or abstain. (13)

At the beginning of each campaign, voters are unaware of the true quality of a specific candidate. They do know, however, that each election will have exactly one high-quality candidate and one low-quality candidate, and that each party is equally likely to have the low-quality candidate. (14) We consider a first-past-the-post voting system where ties are broken randomly. Voters are rational, in the sense that they are motivated by the possibility that their ballot will be pivotal. A pivotal vote occurs if, absent that ballot, either candidate leads by exactly one vote or the election is tied.

A. Truthful Campaigns

Consider first the case in which advertising is only truthful. Candidates engage in campaign advertising to signal that they are of high quality. Advertising is truthful ("truthful campaign"), meaning that candidates cannot lie about their quality. Hence, only high-quality candidates should send advertisements. Candidates always advertise but voters do not necessarily receive the advertisement: each voter receives an advertisement with probability p (independent draws for each voter), where 0 < p < 1. A voter receiving an advertisement knows which party's candidate sent it. A voter can at most receive one advertisement. If a voter receives an advertisement, the advertisement truthfully reveals which candidate is of high quality; therefore, it also reveals that the other candidate is of low quality (as types are perfectly negatively correlated). Figure 1 shows the timing of the game. First, candidates send advertisements. Then each voter either receives or does not receive an advertisement. Next, voters cast their ballots. Finally, the winner is announced and payoffs realized.

Since advertising is exogenous, the voting game that we analyze is static. We consider the symmetric Bayesian Nash equilibria of this game. Voters form beliefs about the true state conditional on any advertisement they receive and also condition their ballots on the same ads. Note that the restriction to symmetric equilibria rules out an (asymmetric) equilibrium in which all voters vote for either the Circle or the Triangle candidate. This is ruled out because such voting behavior implies that some voters vote for the candidate from their own party and some vote for the candidate from the other party.

Informed Voters' Behavior. If a voter receives an advertisement, she knows perfectly which candidate is high- and low-quality. Table 1, Panel A describes our assumed structure of voter preferences. Given this structure, informed voters have a dominant strategy to vote for the high-quality candidate. Hence, if a voter receives an advertisement from the own (other) party's candidate she always votes for the own (other) party's candidate.

Uninformed Voters' Behavior. If a voter does not receive an advertisement, she cannot update her beliefs and thus believes it is equally likely that (1) the Triangle candidate is of high quality, while the Circle candidate is of low quality; or (2) the Triangle candidate is of low quality, while the Circle candidate is of high quality. Given that informed voters always vote for the high-quality candidate, two symmetric pure strategy equilibria exist. We derive these equilibria in Appendix S2.1.

In the first equilibrium, all uninformed voters abstain ("Abstention equilibrium"). This equilibrium exists if p [greater than or equal to] 2[epsilon]/[2[epsilon] + ([x.sub.H] - [x.sub.L] - [epsilon])(N - 1)]; that is, when the probability of receiving an advertisement is sufficiently high. Intuitively, the reason is that an uninformed voter who believes other uninformed voters will abstain also recognizes that an uninformed vote may cancel out an informed vote. Since all informed voters vote for the high-quality candidate, the uninformed voter finds it optimal to abstain so long as the probability of an informed vote is sufficiently large. This is similar to the swing voters curse result in Feddersen and Pesendorfer (1996).

In the second equilibrium, uninformed voters vote for their own party's candidate ("All vote equilibrium"). This equilibrium exists if p [less than or equal to] 2[epsilon]/([x.sub.H] - [x.sub.L] - [epsilon]); that is, the probability of receiving an advertisement is sufficiently low. Intuitively, when the probability of receiving an advertisement is small and when all uninformed voters vote for their own Circle (Triangle) party, then an uninformed vote is more likely to cancel out an uninformed vote for the Triangle (Circle) party than an informed vote. In this case, an uninformed voter's utility is higher if she votes for her own party's candidate rather than abstaining.

Because the threshold for the probability of receiving an advertisement is lower for the first equilibrium than for the second, there is a range of p in which both equilibria exist (see Figure 2). The parameterization for our experiment {N = 22, [x.sub.H] = 7.5, [x.sub.L] = 4.5, [epsilon] =.5, p = .2) is such that both equilibria exist. In our experiment, the likelihood of receiving an advertisement, p, takes the value of .2, while the range p where both equilibria exist goes from .0187 up to .286 (Figure 2).

Uninformed voters may also use a mixed strategy, in which they either mix between two or all three pure strategies. Concerning (symmetric) mixed strategy equilibria, we restrict the analysis to our experimental parameterization. When considering mixed strategies, the Pivot-probabilities become rather complicated. Therefore, we use Monte Carlo simulations to determine the Pivot-probabilities and then derive the mixed strategy equilibrium (cf. Appendix S3). We find that a mixed-strategy equilibrium exists, in which the uninformed voters mix between voting for the own candidate and abstaining (the probability of abstaining being approximately .75) and the informed voters vote for the high-quality candidate.

Efficiency of Electoral Outcome: Truthful Campaigns. We now compare the level of efficiency that is reached in equilibrium assuming truthful advertising relative to the first best, i.e., the situation where the high-quality candidate always wins. (15) This occurs when the state of the world is common knowledge among voters. We assign an efficiency value of "1" to an election in which the high-quality candidate wins and a value of "0" when the low-quality candidate wins. When there is a tie, the winning candidate is chosen at random; thus, we assign an efficiency value of .5.

First, we compute the expected efficiency reached in the Abstention equilibrium. According to our model, informed voters always vote for the high-quality candidate. If at least one voter is informed and all uninformed voters abstain, then the high-quality candidate wins the election. The probability that at least one voter is informed is 1 - [(1 - p).sup.N]. If no voter receives an ad, the outcome is a tie. Therefore the expected efficiency in the Abstention equilibrium is 1-.5[(1 - p).sup.N] . For our parameter values, N = 22 and p = .2, expected efficiency equals .996.

Next we compute the expected efficiency of the All vote equilibrium, in which uninformed voters cast their ballot for their own party's candidate. This implies that in each state of the world at least half of all voters vote for the high-quality candidate. To see this, suppose the Circle candidate is of high quality, and thus only the Circle candidate can send ads. In this case, all voters leaning toward the Circle party will vote for the Circle candidate, irrespective of whether they receive an advertisement. Voters leaning toward the Triangle party will vote for the Triangle candidate unless they receive an advertisement from the high-quality Circle candidate. Because half of the voters lean toward the Circle and Triangle parties, at least half of them will vote for the high-quality candidate. Hence, either the high-quality candidate wins or a tie results. A tie results if exactly none of the Triangle voters receives an advertisement, which occurs with probability [(1 - p).sup.N/2]. The same logic applies when the Triangle candidate is of high quality. Expected efficiency is in the All vote equilibrium; thus, 1 - .5[(1 - p).sup.N/2], which equals .957 for the experimental parameters.

Note that expected efficiency is lower when uninformed voters vote their own party's candidate than when they abstain. The reason is that the informed voter from the high-quality candidate's party has a lower probability of causing the pivotal vote. Expected efficiency of the mixed-strategy equilibrium therefore lies in between the values for the two pure strategy equilibria and equals .995 for our parameterization. (16)

B. Deceptive Campaigns

In deceptive campaigns, advertising need not be truthful. Both high-quality and low-quality candidates advertise, and each candidate claims to be high-quality. Hence, we define advertising as deceptive when a low-quality candidate advertises that she is of high quality. Consequently, advertisements from high-quality candidates are truthful while advertisements from low-quality candidates are false. Like the truthful campaigns described in the previous section, we assume that candidates advertise and that each voter receives an advertisement from the high-quality candidate with probability p. In addition she now receives an advertisement from the low-quality candidate with probability q. (17) We consider only cases where 0 < q < p < 1. (18)

Given this design, each voter receives either zero, one, or two advertisements (in the latter case, she receives one advertisement from each candidate). Voters who receive one advertisement know which party's candidate sent it. Further, voters who receive two ads and voters who receive zero ads both believe that the two states of the world (whether their own candidate or the other party's candidate is of high quality) are equally likely. This implies that voters who receive two advertisements are uninformed, as are voters who receive no advertisements. (19)

In our model, the probability of receiving an advertisement with correct information is the same in both the deceptive and the true campaigns. The deceptive campaigns differ from the true campaigns in that false information is added to the environment. In particular, the total advertisement frequency in true campaigns is "p," while it is "p + q" in deceptive campaigns. (20) Both types of campaigns also differ in another important way--voters who receive exactly one advertisement in the true campaigns know the truth about candidate qualities, while voters who receive exactly one advertisement in the deceptive campaigns are uncertain about the true underlying state. For example, a rational Bayesian in a true campaign who receives an advertisement indicating that a particular candidate is high-quality knows with probability one that this is the case, and that the other candidate is low-quality. In a deceptive campaign the same information leads a rational Bayesian to conclude that the candidate is high-quality with probability t = [(1 - q)/q]/[(1/q + 1/p - 2)], where again we consider only the case where 0 < q < p, which implies t > 1/2.

Following the same approach that we took for truthful campaigns, we consider symmetric Bayesian Nash equilibria of the voting game. In equilibrium, both voters who receive zero advertisements and voters who receive two ads (one from each candidate) use the same strategy (see Appendix S2.2). Hence, when we refer to uninformed voters in the discussion below, we refer to voters who receive zero or two ads.

We have several predictions based on the equilibrium played, and others that hold regardless of the equilibrium played. Given p > q > 0, the latter predictions hold independent of the parameters of the game as long as e is sufficiently small compared with [x.sub.H] - [x.sub.L] and the informativeness (f) of an ad, i.e., if 0 [less than or equal to] [epsilon] [less than or equal to] (2t - 1)([x.sub.H] - [x.sub.L]). (21) The equilibria we discuss below, however, may not exist for parameters other than those used in the experiment.

We start with the results that hold regardless of the equilibrium played. In Appendix S2.2 and S3.2 (Results 3, 4, 7, 14-16), we show that in equilibrium:

1. It is never the case that informed voters who receive an advertisement from the own (other) candidate vote with positive probability for the other (own) candidate;

2. It is never the case that informed voters who receive an advertisement from the own (other) candidate abstain with positive probability while at the same time uninformed voters vote for the own (other) candidate with positive probability.

Moreover, there exists no equilibrium in which all informed and uninformed voters abstain (see Result 10, Appendix S2.2).

Rephrasing these results, we predict that when an informed voter receives a potentially false advertisement from her own party's candidate, she will not vote for the other candidate. Similarly, when the voter receives a potentially deceptive advertisement from the opposing candidate, she will not choose to vote for her own candidate. In both cases, the theory predicts that if the voter casts a ballot, she will vote for the candidate from whom she received the potentially deceptive advertisement. This is because the voter knows that the advertisement is more likely to be true than deceptive. It can however be optimal for some informed voters to abstain (see below).

We derive three pure-strategy equilibria in deceptive campaigns (see Appendix S2.2) for the parameters (N = 22, [x.sub.H] - 7.5, [x.sub.L] = 4.5, [epsilon] =.5, p = .2, q = .05) that we use in the experiment. One of these equilibria is the Abstention equilibrium that we found for truthful campaigns. In this equilibrium, uninformed voters abstain and informed voters vote according to the advertisement they received. Similar to truthful campaigns, the intuition for this equilibrium behavior is that uninformed voters do not want to cancel an informed vote because the probability of informed votes is, with our parameters, sufficiently high. At the same time, ads are sufficiently informative to ensure that informed voters are not better off by voting for their own candidate.

With regard to the other two equilibria, it is necessary to distinguish between informed voters who receive an advertisement from their own party's candidate and those who receive an advertisement from the other party's candidate. In these two equilibria, one group of informed voters votes according to the advertising received, while one group of informed voters abstains. All uninformed voters vote. (22) Specifically, an informed voter who receives an advertisement from her own (other) candidate votes for her own (other) candidate. Likewise, an informed voter who receives an advertisement from the other (own) candidate abstains, and an uninformed voter votes for their own (other) candidate.

The intuition for why uninformed voters vote rather than abstain when one group of informed voters abstains is that it becomes less likely to cancel an informed vote and more likely to cancel another uninformed vote since not all informed voters vote. The reasoning is quite similar to the All-vote equilibrium in truthful campaigns where the probability to receive an advertisement must be sufficiently small.

The intuition underlying why some informed voters abstain is common to both equilibria. Consider, for example, the equilibrium in which informed voters who receive an advertisement from the other candidate abstain. Why would it not pay to vote for the other candidate? Consider the state of the world when the Circle candidate is of low quality and a voter leaning toward the Triangle party receives an advertisement from the Circle candidate. Since the Circle candidate is of low quality, Triangle ads are more likely. Thus, it is more likely that Circle-type voters will abstain and less likely that the Circle candidate will win. Consequently, voting for the Circle candidate rather than abstaining creates a relatively high chance of changing the outcome in favor of the low-quality Circle candidate. In the other state of the world, where the Circle candidate is of high quality, the logic is similar. Voters are more likely to receive ads from the high-quality Circle candidate; thus, Triangle-type voters are more likely to abstain and the Circle candidate is more likely to win. By voting for the Circle candidate, the chance of changing the outcome in favor of the high-quality Circle candidate is rather low. Since both states of the world are equally likely, it is better to abstain than to vote for the Circle candidate. (23)

Moreover, we show the existence of two mixed-strategy equilibria. In the first one, the informed voters vote according to the advertisement they received, and the uninformed voters mix between voting the own candidate and abstaining (the probability of abstention being approximately .84). In the second, the informed voters, who receive an advertisement from the own candidate, mix between voting the own candidate and abstaining (the probability of abstention being approximately .91), while the informed voters with an advertisement from the other candidate as well as the uninformed voters vote for the other candidate.

In addition, we show that for the parameters in the experiment, the "All vote equilibrium" that existed for truthful campaigns no longer exists in deceptive campaigns (see Appendix S2.2). The intuition is that, since some votes are based on false information (implying that both candidates receive votes and thus the election is closer than under truthful advertising), the likelihood of an uninformed vote changing the outcome to the low-quality candidate is sufficiently high to deter uninformed voting.

As mentioned in the introduction, the research closest to ours is that of Feddersen and Pesendorfer (1999), who considered the effect of a noisy signal on voter behavior when the size of the electorate is uncertain. In contrast with our results, they found two types of voters: one type votes for the own candidate irrespective of the signal received, and the other type votes for candidate A as long as she does not receive information from candidate B. If the voter receives information from candidate B, Feddersen and Pesendorfer's voter abstains while our voter switches to candidate B.

Efficiency of Electoral Outcome: Deceptive Campaigns. Again we consider the level of efficiency that is reached in equilibrium in the collective decision process relative to the first best. Compared to the case of truthful advertising, expected efficiency is lower in deceptive campaigns. The reason is that informed voting according to the received advertisement results in votes for the low-quality candidate (since some of the ads are false). This increases the probability of electing the low-quality candidate. For the parameters N = 22, p = .2 and q = .05 used in the experiment, we simulated the probabilities for the high-quality candidate winning the election and for a tie. In the Abstention equilibrium, the high-quality candidate wins with probability .91 and a tie results with probability .057. Thus, expected efficiency is about .938. In the mixed-strategy equilibrium, in which the uninformed mix between abstention and voting the own candidate, expected efficiency is only slightly lower with .93. In the two pure-strategy equilibria, where informed voters abstain but uninformed voters vote, efficiency is lower (because not all information is used and uninformed voters vote). Here, the high-quality candidate wins with probability .786 and a tie results with probability .158. Therefore, expected efficiency is about .865. Expected efficiency in the mixed-strategy equilibrium, in which informed voters mix if they receive an advertisement from the own candidate and the other informed and the uninformed voters vote for the other candidate is slightly lower with .835.

III. EXPERIMENT DESIGN

The experiment was implemented entirely on computers using software created specifically for election experiments with campaign advertising. Subjects were seated in the laboratory at individual computer terminals. They could not see other subjects' decisions. Once seated, subjects completed the computerized instructions, which included an interactive quiz. Instructions framed the game as an election with subjects playing the role of voters. A transcript of the instructions is given in Appendix S1. After all subjects successfully completed the instructions, they were acquainted with the software interface and the "mouse-over" technology. First, subjects were told that mouse-clicking was not necessary during the experiment but that all decisions could be executed by moving the cursor over the appropriate area on the screen ("mouse-over"). Subjects were required to acknowledge the receipt of an advertisement. Because of this technology, subjects could not hear whether other subjects received an advertisement. Subjects practiced two interactive campaigns. In the practice rounds no money was earned. After the practice rounds, paid rounds began.

The experiment included multiple rounds. Candidates and advertising were automated in our experiment. Thus, all subjects were voters. In each round, half of the subjects were randomly assigned to each party (the experiment was always conducted using an even number of subjects). Political parties were represented by Triangle or Circle. A party's (automated) candidate was assigned a pattern, Striped or Solid, which represented a candidate's quality or ideological position. (24) In each round, one party's candidate was randomly assigned as Striped and the other one as Solid. Voters knew the party of each candidate (Triangle or Circle) but not the candidate's quality (Striped or Solid). We set voters' incentives such that all voters were swing voters: they preferred Striped to Solid candidates, but within a quality, they preferred a candidate of their own party. Hence, a voter's payoff depended on her own party assignment as well as the party and shading (Striped or Solid) of the winning candidate. Our main focus lies on the quality dimension: we want to set incentives for the voters to elect the high quality candidate. The party assignment is rather meant to break the indifference between the two candidates within a quality. Thus, we consider a large difference in payoffs when a high or low quality candidate wins, whereas the difference when the own or the other party's candidate wins (for a given quality) is very small.

Table 1, Panel B shows the payoff of a voter. Payoffs are expressed in experimental dollars, which were converted at a known exchange rate (12 to 1) to US dollars at the end of the experiment. In addition, each subject received a $5 dollars show-up fee. A round proceeded as follows: At the beginning of each round, subjects were assigned a party affiliation. Then, in a one-minute campaign period, automated candidates sent ads claiming that they are Striped to the voters. Each voter received an advertisement with some probability as we describe below. After the campaign period, all subjects cast a vote for exactly one of the candidates or abstained from voting (each choice was an active choice). Voting was costless. The candidate receiving the majority of votes was declared the winner (ties were broken by a computerized random draw) and whether the winner was the Circle or Triangle candidate was announced to voters along with their personal earnings for the campaign. Note that this implies that subjects in deceptive campaigns can conclude whether an advertisement they received was true or false. Subjects were also told the cumulative amount that they had earned over the course of the experiment. Then a new round began.

We conducted two types of campaigns: truthful campaigns ("Treatment T") and deceptive campaigns ("Treatment D"). During truthful campaigns, Striped candidates sent advertisements to voters providing truthful information that the candidate's quality was Striped. During deceptive campaigns, Striped and Solid candidates sent advertisements. Advertisements sent by Striped candidates provided truthful information about the candidate's quality. Advertisements from Solid candidates, however, falsely claimed that the candidate was Striped. A voter can at most receive one advertisement in truthful campaigns and at most one advertisement from each candidate in deceptive campaigns.

In total, each of four sessions included between 39 and 42 campaigns and 22 potential voters. We used a within-subjects design, where campaign advertising treatments varied by round according to a predetermined (random) pattern. (25) Campaigns were split equally (or nearly equally in odd numbered campaign sessions) between the deceptive and truthful conditions. Subjects were not told how many campaigns were to be run in the experiment, nor the distribution of treatments. Before we began a campaign, we informed subjects about whether the campaign would be truthful or deceptive. In contrast to a between-subject design, the within-subject design allowed us to control for unobservable subject heterogeneity.

In truthful campaigns, the probability of receiving an advertisement from the Striped candidate was .2 for each voter. In deceptive campaigns, the probability of receiving an advertisement was .2 from the Striped candidate and .05 from the Solid candidate. We have chosen these values as on the one hand, we want to introduce a relatively small probability of deception. On the other hand, deception is salient in the sense that the updated probability that a candidate is high quality when a voter receives his advertisement is substantially smaller than 1 (here it is .826). Consequently, during any truthful campaign, some subjects might have seen one advertisement (from the Striped candidate) while others saw none. During any deceptive campaign, some subjects might have seen two advertisements (one advertisement from each candidate, occurring with probability pq = .01), some might have seen one advertisement (one advertisement from either the Striped or the Solid candidate, occurring with probability p(1 -q) + q(1 - p) =.23), and some might have seen none (with probability (1 - p)(1 - q) = .76). Comparing the two campaign advertising treatments enables us to analyze the effect of deceptive advertising on voter behavior, with particular attention to voter turnout, the identity of the elected candidate, and the efficiency of electoral outcomes.

IV. THEORETICAL PREDICTIONS

In this section, we summarize the equilibrium predictions of our model for voter behavior and efficiency of the electoral outcome.

A. Voter Behavior

Given our parameterization in truthful campaigns, both the All vote and the Abstention equilibrium exist, and a mixed-strategy equilibrium in which the uninformed voters mix between abstaining and voting the own candidate and informed voters vote for the high-quality candidate. (26) We hypothesize, in line with the equilibrium predictions, that voters in truthful campaigns who receive an advertisement will vote for the candidate who sent the advertisement. We predict that those voters who do not receive an advertisement will either abstain from voting or vote for their own party's candidate.

According to our theoretical analysis and parameterization, several equilibria exist for deceptive campaigns, in particular, the Abstention equilibrium exists, but the All vote equilibrium does not. The central finding for deceptive campaigns that holds irrespective of the equilibrium played is that a voter who receives a potentially false advertisement makes a suboptimal choice when she votes for the other candidate. Consequently, we hypothesize that informed voters do not vote against the candidate sending the advertisement. Our experiments thus shed light on whether voters, when faced with the possibility that an advertisement is deceptive, follow this optimal strategy of not voting against the candidate who sent the advertisement.

We are aware that behavioral predictions in case of multiple equilibria are in general difficult. (27) Therefore, we focus on predictions that hold irrespective of the equilibrium played.

Nevertheless, one might expect that the equilibrium that leads to highest efficiency (the Abstention equilibrium) and at the same time highest voter payoffs forms a focal point and thus is more likely played. This would imply that uninformed voters mainly abstain in both types of campaigns, while in deceptive campaigns, informed voters do vote for the candidate who sent them an advertisement rather than abstain. Our experiment allows us to test whether this is indeed true. We can also test whether voting behavior over time approaches the most efficient equilibrium, which could be an indication of learning as subjects receive payoff-feedback after each campaign.

B. Efficiency of Electoral Outcomes

As derived in Section II, expected efficiency in truthful campaigns is between .957 and .996. In deceptive campaigns, expected efficiency is between .938 and .835. Thus, we hypothesize that efficiency in deceptive campaigns is lower.

V. RESULTS

All subjects were recruited from George Mason University's student population via an automated recruitment mechanism. Subjects were in the laboratory for about 1 hour. They were paid privately at the end of the experiment and earned about $25 on average. Overall, we conducted eight sessions including a total of 174 subjects and resulting in 7,198 voting decisions. For our baseline experiment, which we present first, we had four sessions each with 22 subjects, i.e., a total of 88 subjects. Subjects participated in 39 to 42 two-candidate elections (one session of 40, one of 39, and two of 42 elections). Overall, we have 3,586 voting decisions in the baseline experiment.

In Sections V.A and V.B, we analyze decisions of uninformed voters, and the decisions of informed voters. (28) We present descriptive statistics and cross-tabulations that indicate how voting decisions are influenced when voters receive an advertisement and when they do not receive an advertisement. In Section V.C, we analyze our data using a multinomial logit model and study the efficiency of the electoral outcome in Section V.D. Section V.E presents results from additional experiments which inform our baseline results.

A. Uninformed Voters

In truthful advertising campaigns 80% of all voters were uninformed. In deceptive campaigns, the number of uninformed voters, that is those who receive no advertisement or two advertisements, was 75%. (29) These empirical frequencies correspond closely with the theoretical values of 80% and 76%, respectively, which we implemented in our experiment design.

Columns 1 and 2 of Table 2 present cross-tabulations showing that voting and abstention decisions of uninformed voters are similar between treatments. The overall fractions of abstentions are 24% in the truthful and 23% in the deception treatments. Further, in these two treatments the chance of voting for one's own party's candidate is 66% and 64%. The likelihood of voting for the other party's candidate when uninformed is 10% when advertising is truthful, and 13% when advertisements might include deceptive information. Thus, uninformed voters do not mainly behave in a manner that is consistent with the most efficient equilibrium, but over 75% of these uninformed voters vote. In particular, uninformed voters tend to vote for their own party's candidate. For both campaigns, however, voting one's own party's candidate is consistent with the predicted behavior in one of the less efficient equilibria. A behavioral explanation for voting the own party might be that voters are influenced by their party affiliation because they psychologically identify with it. For example, Bassi, Morton, and Williams (2011) observe that choices are influenced by party identity in different voting experiments and Klor and Shayo (2010) find that social identification influences (experimental) voting behavior. We report statistical differences in voting behavior by treatment and voting decisions in Section V.C.

B. Informed Voters

Columns 2 and 4 of Table 2 summarize the decisions of informed voters in campaigns with true and deceptive advertisements. As predicted by theory, we find that there are almost no abstentions of informed voters in truthful campaigns. Also, in truthful campaigns roughly the same number of informed voters votes for their own candidate (52%) as for other party's candidate (46%), which was predicted by our model, because 50% of the voters lean toward each party). In campaigns with deceptive advertising, abstention rates of informed voters are substantially higher (14%) than in truthful campaigns (2%), while the likelihood of informed voters casting a ballot for the other party's candidate is twice as large in truthful campaigns than in deceptive campaigns (46% vs. 24%). Higher abstention rates of informed voters in deceptive campaigns are consistent with our three equilibria in which informed voters abstain. One surprising finding is that informed voters are almost three times as likely to vote for their own party's candidate in the deception treatment than for the opposition party candidate (Table 2, column 4). This finding suggests that informed voters make the suboptimal decision not to vote for the candidate from whom they received an advertisement.

A comparison between columns 1 and 3 of Table 2 shows that informed voters in truthful campaigns are nearly five times more likely to vote for the other party's candidate than uninformed voters (46% vs. 10%). In contrast, one observes smaller differences between informed and uninformed voters in deceptive campaigns. Twenty-four percent of informed voters vote for the other party's candidate while 13% of uninformed voters do. Also, abstention rates between informed and uninformed voters are more similar in the deception treatment, i.e., 23% versus 13% as opposed to 24% and 2% in the truthful treatment. Furthermore, in the deceptive campaigns, informed and uninformed voters are about equally likely to vote for their own party's candidate, that is 62% versus 64%.

Overall, informed voters' decisions in deceptive campaigns do not follow the patterns observed for truthful campaigns. In deceptive campaigns, informed voters are more likely to abstain and almost three times more likely to vote for their own candidate than the opposition candidate.

Our theory predicts that informed voters should never vote for the candidate who did not send an advertisement. Columns 5 to 8 in Table 2 shed light on the empirical validity of this prediction.

Columns 5 and 6 of Table 2 describe the decisions of informed voters after receiving an advertisement from the other party's candidate. Consistent with our theoretical predictions, we find that an informed voter in the truthful environment casts votes according to the information received. Specifically, 86% of the subjects who receive an advertisement from the other party's candidate vote for that candidate. In the deception treatment, however, only 41% of subjects vote for the other party's candidate upon receiving an advertisement from the other party's candidate. The remaining informed voters choose either to abstain (16%) or to vote for their own party (44%). The latter occurs in spite of the fact that our theory predicts that the optimal decision is to vote for the other party's candidate or to abstain. According to our theoretical prediction, voting for one's own party after receiving a potentially deceptive advertisement from the other party's candidate is the "wrong" choice. Thus, it appears that the presence of deceptive advertising leads to suboptimal decisions. (30)

Columns 7 and 8 of Table 2 present the choices of informed voters who receive an advertisement from their own party's candidate. Here, 96% of informed voters vote for their own party in the truthful treatment. Voting for the candidate from whom an advertisement was received was predicted by our theory. In the deception campaigns, only 81% of the voters cast a ballot for their own party when they receive an advertisement from their own candidate. As voters who receive advertisements from the other party's candidate (Table 2, columns 5 and 6), more own-party-informed voters make a suboptimal choice in the deception treatment than in the truthful treatment. In deception campaigns, the behavior of voters who receive an ad from the other party's candidate could be explained by their party affiliation: voters psychologically identify with the party to which they are assigned. Yet, party identity cannot explain why voters who receive an ad from their own candidate are reluctant to vote their own party. One explanation for voting against the candidate whose advertisement voters received in deceptive campaigns is that voters may not want to support a candidate whose advertising could turn out to be untruthful.

C. Multinomial Analysis of Voting Decisions

Next, we test our predictions within a multinomial logistic regression framework. Our dependent variable is the voter's choice; that is, whether the voter casts a ballot for the own party's candidate, for the other party's candidate, or abstains. In our first specification our independent variables include a treatment indicator, equaling zero for the truthful treatment and one for the deception treatment (Treatment D). We also include indicator variables for whether the voter received an advertisement from her own party's candidate or from the other party's candidate {Ad from own candidate, Ad from other candidate). We omit the "receiving no advertisements" category. We account for similarity of subjects' voting decisions by clustering standard errors by subject.

To test whether responses to advertising differ by treatment, in our second regression specification we also include an interaction variable between the type of treatment and whether the voter received an advertisement from the own party's candidate, and an additional interaction variable between the type of treatment and whether the voter received an advertisement from the other party's candidate. In the tables with regression results we denote these variables Treatment D*Ad from own party candidate and Treatment D*Ad from party other candidate. To control for temporal and campaign effects we include the campaign number {Campaign) among our independent variables.

Table 3 shows the results from the multinomial logit regression. The first column contains no interaction. The second column contains the interactions between treatment and who sent the advertisement. Columns 3 and 4 add shared random effects to specifications 1 and 2, respectively. Under this specification point estimates tend to be larger (in absolute values) but otherwise remain very similar, so we only refer to the first two columns of Table 3.

The top panel of Table 3 shows the determinants of casting a ballot in favor of the other party's candidate. As predicted, receiving an advertisement from the own party's candidate reduces the probability that the subject will cast a ballot favoring the other party's candidate. Receiving an advertisement from the own-party (other-party) candidate decreases (increases) the likelihood of voting for the other-party candidate. Interestingly, relative to the truthful treatment the effect of messages in the deception treatment are muted. This is because the interaction terms are always of the opposite sign of the advertisements' effects.

The coefficients of the interaction variables between the deception campaign and who sent the advertisement indicate that voters make suboptimal choices in the presence of false information. Our theory predicts that the point estimates on both interaction variables should be zero, but they are not. For example, the coefficient of the interaction variable Treatment D*Ad from other party candidate is negative and statistically significant, indicating that subjects in the deception treatment who receive an advertisement from the other party's candidate are less likely to vote for the other party's candidate in the deception campaigns. Similarly, the estimation results indicate that in the deception treatment, the probability of voting for the own party's candidate is lower when receiving an advertisement from that candidate.

The bottom panel of Table 3 shows determinants of abstentions. In both specifications, the point estimates show that when voters receive an advertisement from their own candidate, the voter is less likely to abstain; the corresponding point estimate is negative and statistically significant. When receiving an advertisement from the other party's candidate the corresponding point estimate is also negative but is not statistically significant. This indicates that the likelihood of abstention does not decrease when receiving an advertisement from the candidate of the other party. Thus, information, when it comes from the other party's candidate, does not induce changes in abstention.

In the abstention equation, the interaction effect between the deception campaign and having seen an advertisement from the candidate of the voter's own party is positive and statistically significant (Table 3, column 2). This finding is consistent with two equilibria that we identified. This positive coefficient shows that the possibility of deception makes informed voters more likely to abstain. The coefficient on the interaction of the deception campaign with receiving advertising from the opposition party is also positive but is not statistically significant. The sum of the interaction and the direct effect shows that the effect of advertising in the deception treatment is to reduce the likelihood that uninformed voters abstain. That is, the deceptive advertising induces uninformed voters to move away from the most efficient equilibrium behavior, which is to abstain, toward voting for their own candidate.

Three of the four point estimates on Campaign are not statistically significant. Only in the second column of Table 3 is the coefficient on Campaign negative and statistically significant at the 10% level. These point estimates show little evidence suggesting that subjects systematically change their voting decision over the duration of the experiment to either abstain or to vote for the other party's candidate. Thus, we find little evidence for temporal effects.

The sum of our results in Table 3 shows that even a small probability of deception lowers the probability that informed voters will vote in elections. If voters with potentially false information decide to abstain due to the fact that they do not trust the information, this increases the likelihood that the low-payoff candidate is elected, and results in a reduction in welfare.

D. Efficiency of Electoral Outcomes

To assess the effect of information on efficiency of electoral outcomes, we first investigate the effect of information across our two treatments. Table 4 shows that informed voters cast their ballot for the high-quality candidate when advertising is truthful, but fail to do so when advertising is deceptive. We find that 91% of informed voters vote for the high-quality candidate in the true advertising environment, and only 53% of informed voters vote for the high-quality candidate in the deception treatment. This is despite the 4:1 odds that the political advertising information is accurate, and that the optimal decision, according to our model, is to vote for the candidate who sent the advertisement or to abstain. Table 4 also shows that in the deception treatment, informed voters are about five times more likely to cast a ballot for a low-quality candidate than in the truthful treatment, i.e., 48% versus 9%. These findings indicate that deceptive advertising leads to suboptimal choices and may lead to lower electoral outcome efficiency than was predicted.

Our theoretical model predicts that efficiency with true advertising is between .95 and .99, while predicted efficiency is slightly lower when advertising is deceptive, that is, between .84 and .94. To measure efficiency empirically, we assign an efficiency value of one to an election where the Striped candidate wins, a value of .5 if there is a tie, and zero if the Solid candidate wins.

The results of this computation show that the mean efficiencies are .88 for the truthful treatment and .55 for the deception treatment. This difference in efficiencies is statistically significant (t-test, p=.00, two-tailed). (31) This finding shows that campaigns with deceptive advertising are more likely to result in the election of a low-quality candidate than campaigns with truthful advertising. As there is an average efficiency of .5 if voters cast their votes randomly, the election outcome efficiency in the deception treatment is similar to the one if voters cast their votes randomly.

E. Additional Tests

In light of research findings by Battaglini, Morton, and Palfrey (2008, 2010) who report rational abstention by uninformed voters as predicted by the Swing Voter's Curse (Feddersen and Pesendorfer 1996), it is useful to examine what aspects of our experiment drive our results, which show less abstention of uninformed voters than the aforementioned work. As mentioned above, voting behavior in our experiment may be influenced by party affiliations. Bassi, Morton, and Williams (2011) provide evidence for the effect of party identity in a different voting setting (among others without abstentions). We therefore explore two aspects of our design: first, that there is a small payoff bonus when voters elect a candidate from their own party, holding candidate quality constant, and second, that our voters have party affiliations at all. (32)

In the first extension of our experiments, we remove the differential payment for electing a candidate of the same party as the voter's party, while maintaining voter assignment to a party. As before, voters receive a partisan identity in each campaign, but now are paid solely on whether the high- or low-quality candidate is elected (i.e., 7 E$ or 4 E$). All other aspects of the baseline experiment remained the same. We ran two sessions of 22 voters each for 42 separate elections per session, with the same mix of truthful and deceptive advertising campaigns as in the baseline experiments.

In our second extension, we not only remove the payoff differences based on partisan affiliation, but also remove voters' party affiliations. Candidates keep their party affiliation of Triangle or Circle, but voters no longer belong to either the Circle or Triangle party. Voters have no party affiliations in this second extension. For this extension, we ran two sessions, one with 20 voters, due to a lacking number of participants, and one with 22 voters. Each session had 42 elections, again with the same mix of truthful and deceptive advertising campaigns as in the baseline experiments. (33)

Tables 5-7 show the results from our first extension, and Tables 8-10 show the results from our second extension. Given that we added these experiments to study abstentions of uninformed voters, we will first focus on describing the results of uninformed voter abstention decisions.

The cross-tabulation results for the first extension (Table 5) show little change in abstentions relative to our baseline results (Table 2). However, we see a more than 50% increase in abstention of uninformed voters for our second extension (Table 8). When voters have no party affiliation and when there is no differential in payments depending on the party affiliation of candidates, we find an increase in abstention in the truthful treatment from 24% (Table 2, column 1) to 42% (Table 8, column 1), and a corresponding increase in abstention from 23% (Table 2, column 2) to 37% (Table 8, column 2) in the deception treatment. Hence, abstention rates by uninformed voters increase and become more similar to Battaglini, Morton, and Palfrey (2008, 2010) only when we remove party affiliations. Thus, party affiliations seem to play an important role even if no payoff differential exists.

Turning to informed voters, results show little change in the truthful treatments relative to the baseline (cf. Tables 2, 5, and 8). In the deception treatment associated with extension 1, we find that the fraction of informed voters voting for their own party decreases relative to the baseline treatment. Yet, voters are still very likely to cast votes that are not predicted by any of the equilibria. More precisely, we find that informed voters who receive an advertisement from the other party make better choices in the deception treatment when we remove the payoff differential between the two parties. Column 6 of Table 5 shows that now 32% of informed voters who receive an advertisement from the other party candidate voted (wrongly) for their own party, while the baseline experiment shows that 43% voted (wrongly) for their own party (Table 2, column 6). Next, comparing columns 8 of Tables 5 and 2, we find that informed voters who receive an ad from their own party also vote less often for their own candidate when the payoff differential is removed. However, these voters do not make better choices, as they more often vote for the other party's candidate (27%, cf. Table 5(4)).

The first observation could be explained by party identity effects even in the absence of financial incentives: voters still cast a ballot for their own candidate too often--though less often than with the payoff differential because the effect of party identity might be lower. The second observation, however, cannot be explained in a similar way, because not a sufficient number of voters casts a ballot for their own candidate. Thus, removing the financial aspect of the party affiliation reduces voting for the own candidate but does not improve choices.

Next, we analyze whether informed voters' choices improve when we eliminate party affiliations. Table 8, column 6, shows that when informed by a Circle candidate in the deception treatment, 61% vote for the Circle candidate and 23% for the Triangle candidate. And correspondingly, column 8 shows that when informed by a Triangle candidate, 67% vote for the Triangle candidate and 20% for the Circle candidate. So, in this second extension in the deception treatment informed voters vote less often against the candidate who sent the ad (23% and 20%, respectively) than in our first extension (32% and 27%, see Table 5) but are still likely to cast votes that do not use the available information optimally. (34)

The regression results in Table 6 (and Table 9) are consistent with our findings in the cross-tabulations. In the abstention regression equation, the point estimates on receiving an advertisement tend to get larger moving from the baseline to extension 1 to extension 2. For example, comparing the point estimate on Ad from own party candidate in Table 3, column 2 with the corresponding point estimate in Table 6, column 2, in Table 6 we find that the point estimate on that variable increases in absolute value by almost 50% from -2.7 to -3.9, indicating that voters' behavior is closer to the most efficient equilibrium and more consistent with the finding by Battaglini, Morton, and Palfrey (2008, 2010). (35)

With respect to efficiency, a comparison of Tables 5 and 7 shows that there is little difference between the baseline treatment and the first extension in terms of informed voters casting a ballot for the high-quality candidate versus low-quality candidate. However, we find that when also the party affiliation of the voter is removed, as in the second extension, more informed voters cast a ballot for the high-quality candidate in the deception treatment (see Tables 8-10 for the results of extension 2). Overall, we find that mean efficiency for the first extensions is .77 for the truthful treatment and .52 for the deception treatment, and this difference is statistically significant. For our second extension, we find that the corresponding mean efficiencies are .77 and .69 but the difference between these two is not statistically significant. Moreover, mean efficiency in the deception treatment of the second extension (.69) is much higher than in the first extension or in the baseline (.52 and .55). The higher efficiency in the second extension is explained by the fact that more informed voters cast a ballot for the high quality candidate (Tables 7 and 10).

Our findings suggest that assigning party affiliations to voters makes them develop an attachment to their parties and that this attachment impedes optimal decision making. There is plenty of evidence that group-identity induces people to act more favorably toward in-group members and that even arbitrary assignment of identity can elicit partisan behavior (see, e.g., Chen and Li 2009; Tajfel and Turner 1979, and for a survey Hewstone, Rubin, and Willis 2002). Nevertheless, partisan behavior cannot fully explain our findings. Facing the possibility of a small chance of deceptive advertising, voters appear to have difficulties making optimal choices. In particular, voters are likely to vote against the candidate who sent the ad--irrespective of party affiliations. As mentioned above, a possible explanation is that voters are reluctant to support a candidate whose advertisement could turn out to be untruthful, i.e., voters "punish" a potential liar. Such a behavior is similar to a "altruistic punishment" where individuals punish others who misbehave, although punishment is costly and yields no material gain (see, e.g., Fehr and Gachter 2002). Our findings regarding voter behavior might also be explained by voting decisions being influenced by anticipated regret, as in models of regret aversion (see, e.g., Zeelenberg et al. 1996). That is, voters anticipate that they would feel regret when having voted for a candidate who lied, and thus cast a vote opposing the candidate who had sent a potentially deceptive advertisement.

VI. CONCLUSION

It is widely accepted that candidates do not always tell the truth during electoral campaigns. This raises the question of how deception influences voter behavior, turnout, and the overall efficiency of elections. In this paper, we address this question using laboratory experiments in which campaign advertising is exogenous and is either truthful or possibly deceptive. In-line with previous studies that assume that advertising is truthful, we find that informative advertising leads to a higher turnout of informed voters. Yet voters make suboptimal choices when an advertisement has even a small chance of being deceptive. In particular, we find that voters are reluctant to vote for the other party's candidate when they know they received a potentially deceptive advertisement from that candidate.

These changes in behavior influence an election's outcome. The low pay-off candidate is more likely to be elected when deception is possible; consequently, the efficiency of the election outcome is lower in deceptive campaigns. Both (1) the decrease in efficiency; and (2) voters' reactions to a small probability of deception are much larger than predicted by our model that assumes rational behavior. Observed efficiency in deceptive campaigns is just as high as when voters cast their votes randomly.

To obtain further insights we modified our treatments such that we had one treatment in which there are no payoff differences by party affiliation of the voters, i.e., only the candidate's quality matters for a voter's payoff but not the candidate's party affiliation, and another treatment were there are no such payoff differences and in addition no party affiliations of the voters. Here we find that voters with no information act more consistently with previous work (Battaglini, Morton, and Palfrey 2008, 2010) when we remove party identity from the experiment. Also we find that the deception treatment efficiency in the no-party, no-bonus treatment is higher than in our other treatments. This finding suggests that voter attachment to parties is important in explaining some of the seemingly suboptimal voting decisions.

Our paper shows that the standard model of voting which incorporates the likelihood of false information cannot fully explain the behavior of voters. An important open question is why relatively large changes in behavior occur in environments with small amounts of false information. It would be profitable to explore this with future theoretical research in economics and psychology. Our study of deception is a small step along a rich path for inquiry in theoretical, experimental, and field research. Future studies might inform the role of strategic release of possibly deceptive information. Another study might examine negative advertising, where a candidate falsely advertises not only about his own attributes but about those of the opposition candidate.

doi: 10.1111/ecin.12236

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SUPPORTING INFORMATION

Additional Supporting Information may be found in the online version of this article:

Appendix S1. Instructions

Appendix S2. Pure-Strategy Equilibria in the Voting Game

Appendix S3. Mixed-Strategy Equilibria

Appendix S4. Equilibria in the Voting Game for the Case [epsilon] = 0

Appendix S5. Figures and Tables for Appendices S3 and S4

(1.) Candidates may differ with respect to their policy positions or with respect to valence criteria such as their qualities or attributes. In this paper we will use the positions, attributes, and qualities interchangeably.

(2.) In our model, candidates compete for election but these candidates are not incumbents running for reelection. We thus abstract from the possibility that voters can punish candidates when discovering false statements (since the election is already decided). In reality, such punishments might matter for many elections but it is also often the case that there is no incumbent, as for example in congressional open seat races in the United States. We chose our setting to exclude repeated game effects, which would further complicate the setting.

(3.) See, for example, the theoretical study by Polbom and Yi (2006) comparing truthful positive and negative advertising. In political science, there is a large empirical literature on the effects of negative advertising (see, e.g., Lau et al. 1999 and Lau, Sigelman, and Rovener 2007 for meta-analyses), which we discuss below.

(4.) http://www.factcheck.org/elections-2008/hillarys_ adventures_abroad.html and http://www.factcheck.org/ specialreports/our_disinformed_electorate.html, accessed January 2009.

(5.) Closest to our theoretical model is work by Feddersen and Pesendorfer (1999). In their model, the introduction of noisy information increases turnout of uninformed voters and decreases turnout of informed voters.

(6.) Empirical studies by Gentzkow (2006) and Lassen (2005) show that turnout is positively affected when voters have more sources of information, such as newspapers. Also, Coupe and Noury (2004), Palfrey and Poole (1987), and Wattenberg, McAllister, and Salvanto (2000) found a positive correlation between turnout and information levels.

(7.) There is also theoretical work with truthful advertising in an environment where parties can target campaigns on different groups (see Schultz 2007).

(8.) Page (1976) and Glazer (1990) build on Shepsle and contribute to the theoretical development of candidate ambiguity. They show that often it is in the candidates' interest to adopt an ambiguous policy position. Using a different theoretical framework, Alesina and Cukierman (1990) identify conditions when it is advantageous for politicians to take ambiguous policy positions. Also, within a game theoretical framework Aragones and Neeman (2000) analyze the role of candidate ambiguity in elections and come to similar conclusions regarding ambiguity as previous work. In an experimental setting Tomz and Van Houweling (2009) find that ambiguous policy positions do not reduce candidates' votes at the polls and may in fact increase their votes. Related to this is experimental evidence on how voters process information provided by candidates (Rahn 1993). Peterson (2009) emphasizes the importance of campaigns for election outcomes and shows that voter behavior in Presidential elections changes when their uncertainty about candidate positions changes.

(9.) These studies build on the swing voter's curse literature, e.g., Feddersen and Pesendorfer (1996).

(10.) While the study by Clinton and Lipinski (2004) and the meta-analyses by Lau et al. (1999) and Lau, Sigelman, and Rovener (2007) do not hint at systematic effects of negative advertising on turnout, other studies suggest that turnout is affected (see, e.g., Ansolabehere and Iyengar 1995 for negative effects on turnout, Goldstein and Freedman 2002 for positive effects and Krupnikov 2011 for specific conditions under which turnout might be affected).

(11.) Empirical works includes Levitt (1993), who analyzed the effect of campaign spending for repeat challengers, and Gerber (1998), who found that campaign spending positively affected election outcomes for the U.S. Senate. Theoretical work examining truthful strategic advertising and financing of campaigns includes Coate (2004a, 2004b). Potters, Sloof, and van Winden (1997) and Prat (2002) examined the consequences of indirect informative advertising, where voters are influenced by the amount of money that has been spent on advertising. For a recent overview of this literature see Stratmann (2005).

(12.) One interpretation of the candidates' pattern is that all voters prefer a moderate (high-quality) candidate of either party to an extreme (low-quality) one. Alternatively, we can think of any other valence criterion that all voters favor.

(13.) In our setting, there is no difference between abstention and turnout.

(14.) While we could generalize the theoretical model by relaxing the assumption that the quality of candidates is perfectly negatively correlated, the assumption makes the experiment more transparent as subjects only have to consider the two asymmetric states of the world where candidates are heterogeneous.

(15.) Here we consider allocative efficiency, because this allows us to determine which mechanism allocates winners with greatest probability in the different environments. An alternative measure of efficiency is informational efficiency which exists if all signals are publically revealed.

(16.) To obtain this value, we simulated the probabilities for the high-quality candidate winning the election and for a tie. We ran Monte Carlo simulations with 1 million draws to obtain these probabilities. The MATLAB programs for all simulations that we ran are available from the authors upon request.

(17.) This implies that a voter who receives an advertisement does not know for sure whether the information is correct or false before the election is decided. In principle, the environment could be modeled using noisy advertising. Our framework connects to the idea that one candidate is more likely to lie than the other.

(18.) In our setting, no costs are associated with deceptive advertising as candidates are not strategic players. Yet, as candidates always advertise either truthfully or deceptively, one potential cost of deception is that the advertising is less effective (since q < p).

(19.) To keep the Bayesian updating in the experiment as simple as possible, we do not consider a setting in which voters can receive more than one ad from each candidate.

(20.) A small difference between truthful and deceptive campaigns will be that in truthful campaigns less voters will be informed since only the high-quality candidate sends ads: 20% of voters are informed and 80% uninformed in truthful campaigns, while in deceptive campaigns 23% are informed and 77% uninformed (76% receive zero ads, 1% two ads).

(21.) These conditions (which are satisfied for the parameters used in the experiment) rule out the trivial outcome that all voters (informed and uninformed) vote for their own candidate.

(22.) These two equilibria exist given the parameters that we use in our experiments.

(23.) The existence of the two equilibria seems to depend on the fact that we consider an equal number of voters that lean toward either party; for simulations that we ran with unequal numbers of voters affiliated with either party, the equilibria do not exist.

(24.) In the instructions we only refer to a candidate's pattern and do not use expressions like a candidate's quality.

(25.) This predetermined pattern also included the random choice of candidates' types which ensured they were high-quality in half (or, in 39 campaign sessions, nearly half) of campaigns.

(26.) An advantage of the parameters we used for "true campaigns" is that with these same values we are able to add deception in such a way that, as discussed above, it is not dominant yet is salient. A second advantage is that these parameters allow for equilibria in which uninformed voters both vote and abstain. Our experiment thus enables us to determine whether one of these two options is more likely to be chosen when both are reasonable, and whether that choice might vary with the presence of deceptive information.

(27.) Since in deceptive campaigns multiple equilibria exist, the turnout decision of voters might be affected by observing whether other people decided to vote or not. Grosser and Schram (2006) experimentally analyze the effect of observability of other people's decisions and find that this information increases turnout.

(28.) Uninformed voters are those who receive no advertisement and those who receive two advertisements in the deception treatment, Informed voters are those who receive a single advertisement.

(29.) In line with theory, testing whether voting decisions in deceptive campaigns differ between uninformed voters who received zero or two advertisements indicates no significant difference (p = .665, Fisher exact test). In our cross tabulation in Table 2 we classify those who have received two advertisements as uninformed. Receiving two advertisements in the deception treatment occurred 27 times, accounting for 1.5% of our observations.

(30.) One might ask whether our results are influenced by the fact that individuals often tend to overweigh small probabilities. However, even if subjects in our experiment suffer from such a bias, they should realize that the chance of receiving truthful information is four times as high as receiving false information.

(31.) When we exclude ties, results do not change (f-test, p = .00, two-tailed).

(32.) In Appendix S4 we consider the extensions theoretically; however we discuss the second extension only briefly due to the difference in the definition of strategies.

(33.) In these additional treatments, in .76% of the observations a voter received two advertisements in the deceptive campaign when we had no payoff differences by partisan identity but with voter partisan identities. And this event occurred for .57% of the observations in the treatment with no payoff differences by partisan identity and no partisan identities for voters.

(34.) Note that once we remove party affiliations, equilibria exist, where, for example, all voters vote for the Circle candidate (see Appendix S4.IV.3.). Consequently, we cannot say that the above choices are inconsistent with any equilibria. Nevertheless, such equilibria are not the efficiency-maximizing ones as available information is not used optimally.

(35.) We also tested whether uninformed voters are more likely to abstain over the course of the session that contains about 40 campaigns. We find no evidence of learning by uninformed voters in terms of being more likely to abstain in the latter campaigns in our baseline treatments. We also do not find evidence of learning by informed voters. However, for uninformed voters, we find evidence of learning in our two extensions. In both extensions, the more experience uninformed voters have with voting, the more likely they are to abstain.

Houser: Professor, Department of Economics, George Mason University, Fairfax, VA 22030. Phone 703-993-4856, Fax 703-993-4851, E-mail dhouser@gmu.edu

Ludwig: Professor, Department of Economics, University of Ulm, Ulm, Germany. Phone +49-731-5023549, Fax +49-731-5023737, E-mail sandra.ludwig@uni-ulm.de

Stratmann: Professor, Department of Economics, George Mason University, Fairfax, VA 22030. Phone 703-993-4920, E-mail tstratma@gmu.edu

TABLE 1
Voters' Payoffs

Panel A. Voters' Payoff Structure

                            Elected Candidate's Quality
Elected
Candidate's Party       High Quality           Low Quality

Own party                [x.sub.H]              [x.sub.L]
Other party         [x.sub.H]--[epsilon]   [x.sub.L]--[epsilon]

Panel B. Voters' Payoffs in Experiment

                            Elected Candidate's Quality
Elected
Candidate's Party       High Quality           Low Quality

Own party                   7.50                   4.50
Other party                 7.00                   4.00

TABLE 2
Cross Tabulations: Results from the Baseline Experiment

                     All Uninformed           All Informed
                         Voters                  Voters

                           (1)                     (2)

Decision/         Treatment   Treatment   Treatment   Treatment
Treatment             T           D           T           D

Abstain             24.02       22.81       1.99        13.71
Vote own            65.79       63.87       51.85       62.41
Vote other          10.19       13.32       46.15       23.88
Number of votes     1,453       1,359        351         423

                    Informed Voters:        Informed Voters:
                  Advertising received    Advertising received
                     from candidate          from candidate
                   of the other party       of the own party

                           (3)                     (4)

Decision/         Treatment   Treatment   Treatment   Treatment
Treatment             T           D           T           D

Abstain             1.60        15.94       2.44        11.57
Vote own            12.83       43.48       96.34       80.56
Vote other          85.56       40.58       1.22        7.87
Number of votes      187         207         164         216

Notes: In each of the four columns, the abbreviation T indicates
voting decisions associated with the truthful treatment and D with
the deception treatment. Results are based on 88 subjects.

TABLE 3
Explaining Vote Choices: Baseline Experiment

                                            (1)          (2)

Vote Choice: Vote Other Party
Campaign                                   -.008       -.007 *
                                          (.005)        (.004)
Treatment D                                -.166        319 **
                                          (.135)        (.149)
Advertisement from own candidate        -1.510 ***    -2.512 ***
                                          (.267)        (.645)
Treatment D*Advertisement from own                     1.466 **
  candidate                                             (.651)
Advertisement from other candidate       2.425 ***    3.767 ***
                                          (.225)        (.348)
Treatment D*Advertisement from other                  -2.361 ***
  candidate                                             (.305)
Constant                                -1.458 ***    -1.706 ***
                                          (.146)        (.178)

Vote Choice: Abstain
Campaign                                   .000          .000
                                          (.005)        (.005)
Treatment D                                .087         -.019
                                          (.135)        (.140)
Advertisement from own candidate        -1.325 ***    -2.668 ***
                                          (.272)        (.516)
Treatment D*Advertisement from own                    1.823 ***
  candidate                                             (.563)
Advertisement from other candidate         -.071        -1.072
                                          (.250)        (.745)
Treatment D*Advertisement from other                    1.136
  candidate                                             (.798)
Constant                                -1.065 ***    -1.010 ***
                                          (.245)        (.243)
Subject

Log likelihood                            -2,975        -2,911
N                                          3,586        3,586

                                            (3)          (4)

Vote Choice: Vote Other Party
Campaign                                   -.008        -.008
                                          (.007)        (.006)
Treatment D                                -.181        .365 *
                                          (.187)        (.206)
Advertisement from own candidate        -2.032 ***    -3.531 ***
                                          (.061)        (.759)
Treatment D*Advertisement from own                    2.182 ***
  candidate                                             (.773)
Advertisement from other candidate       3.229 ***    5.217 ***
                                          (.324)        (.480)
Treatment D*Advertisement from other                  -3.343 ***
  candidate                                             (.425)
Constant                                -1.729 ***    -2.053 ***
                                          (.210)        (.248)

Vote Choice: Abstain
Campaign                                   .000          .000
                                          (.007)        (.007)
Treatment D                                .080          .025
                                          (.192)        (.207)
Advertisement from own candidate        - 1.834 ***   -3.697 ***
                                          (.334)        (.645)
Treatment D*Advertisement from own                    2.552 ***
  candidate                                             (.676)
Advertisement from other candidate        729 ***        .375
                                          (.279)        (.777)
Treatment D*Advertisement from other                     .156
  candidate                                             (.826)
Constant                                -1.352 ***    -1.365 ***
                                          (.317)        (.330)
Subject                                  2.986 ***    3 427 ***
                                          (.539)        (.670)
Log likelihood                            -2,446        -2,362
N                                          3,586        3,586

Notes: The abbreviation D indicates voting decisions associated with
the deception treatment. The table reports point estimates and
standard errors in parenthesis, clustered by voters from a
multinomial logit regression. Column 1 shows specification 1 and
Column 2 shows specification 2, which adds interaction terms. Column
3 and Column 4 add shared random effects to specifications 1 and 2,
respectively. Base outcome in the regressions is "vote for own
party's candidate." Results are based on 88 subjects.

Statistically significant at the *** 1%, ** 5%, and * 10% level.

TABLE 4
Fraction of Informed Voters Voting for the
High-and Low-Quality Candidate: Baseline
Experiment

                    Treatment T   Treatment D

Vote high quality      90.60         52.48
Vote low quality       9.40          47.52
Number of votes         351           423

Notes: The abbreviation T indicates voting decisions
associated with the truthful treatment and D with the deception
treatment. Results are based on 88 subjects and 774 votes.

TABLE 5
Cross Tabulations: Results from the Experiment without Party Payoff
Differential

                     All Uninformed           All Informed
                         Voters                  Voters

                           (1)                     (2)

Decision/         Treatment   Treatment   Treatment   Treatment
Treatment             T           D           T           D

Abstain             25.90       22.33       2.02        12.32
Vote own            53.86       50.21       55.05       46.31
Vote other          20.25       27.46       42.93       41.38
Number of votes      726         721         198         203

                    Informed Voters:        Informed Voters:
                  Advertising received    Advertising received
                    from candidate of       from candidate of
                     the other party          the own party

                           (3)                     (4)

Decision/         Treatment   Treatment   Treatment   Treatment
Treatment             T           D           T           D

Abstain             3.13        12.62       0.98        12.00
Vote own            11.46       32.04       96.08       61.00
Vote other          85.42       55.34       2.94        27.00
Number of votes      96          103         102         100

Notes: In each of the four columns, the abbreviation T indicates
voting decisions associated with the truthful treatment and D with
the deception treatment. Results are based on 44 subjects.

TABLE 6
Explaining Vote Choices: Experiment without Party Payoff Differential

                                            (1)           (2)

Vote Choice: Vote Other Party
Campaign                                   .003          .003
Treatment D                               (.005)        (.005)
                                          299 **       .423 ***
                                          (.151)        (.158)
Advertisement from own candidate        -1.066 ***    -2.507 ***
                                          (.249)        (.824)
Treatment D*Advertisement from own                     2.074 **
  candidate                                             (.844)
Advertisement from other candidate       1.820 ***     2.99Q ***
                                          (.257)        (.375)
Treatment D*Advertisement from other                  -2.022 ***
  candidate                                             (.445)
                                         -.972 ***    -1.039 ***
                                          (.206)        (.231)

Vote Choice: Abstain
Campaign                                  Qj7 ***      .016 ***
                                          (.004)        (.004)
Treatment D                                .102          -.030
                                          (.134)        (.134)
Advertisement from own candidate        -.1.733 ***   -3.850 ***
                                          (.422)        (1.045)
Treatment D*Advertisement from own                     2.953 ***
  candidate                                             (1.004)
Advertisement from other candidate         -.263         -.551
                                          (.417)        (.842)
Treatment D*Advertisement from other                     .356
  candidate                                             (.888)
Constant                                -.1.189 ***   -1.108 ***
                                          (.316)        (.317)
Subject

Log likelihood                            -1,764        -1,730
N                                          1,848         1,848

                                            (3)           (4)

Vote Choice: Vote Other Party
Campaign                                   .006          .006
Treatment D                               (.007)        (.008)
                                          .424 **      .569 ***
                                          (.205)        (.216)
Advertisement from own candidate        -1.759 ***    -3.764 ***
                                          (.099)        (1.046)
Treatment D*Advertisement from own                     2.907 ***
  candidate                                             (1.077)
Advertisement from other candidate       2.519 ***     4.272 ***
                                          (.411)        (.513)
Treatment D*Advertisement from other                  -3.029 ***
  candidate                                             (.570)
                                        -1.166 ***    -1.236 ***
                                          (.295)        (.342)

Vote Choice: Abstain
Campaign                                  021 ***       019 ***
                                          (.006)        (.006)
Treatment D                                .235          .120
                                          (.183)        (.191)
Advertisement from own candidate        -2.410 ***    -5.077 ***
                                          (.469)        (1.247)
Treatment D*Advertisement from own                     3.757 ***
  candidate                                             (1.174)
Advertisement from other candidate         .430          .728
                                          (.454)        (.880)
Treatment D*Advertisement from other                     -.655
  candidate                                             (.962)
Constant                                -1.395 ***    -.1.311 ***
                                          (.387)        (.411)
Subject                                  3.049 ***     3.499 ***
                                          (.822)        (.966)
Log likelihood                            -1,485        -1,437
N                                          1,848         1,848

Notes: The abbreviation D indicates voting decisions associated with
the deception treatment. The table reports point estimates and
standard errors in parenthesis, clustered by voters from a
multinomial logit regression. Column 1 shows specification 1 and
Column 2 shows specification 2, which adds interaction terms. Column
3 and Column 4 add shared random effects to specifications 1 and 2,
respectively. Base outcome in the regressions is "vote for own
party's candidate." Results are based on 44 subjects.

Statistically significant at the ***1%, **5%, and *10% level.

TABLE 7
Fraction of Informed Voters Voting for the
High-and Low-Quality Candidate: Experiment
without Party Payoff Differential

                    Treatment T   Treatment D

Vote high quality      90.91         53.20
Vote low quality       9.09          46.80
Number of votes         198           203

Notes: The abbreviation T indicates voting decisions
associated with the truthful treatment and D with the deception
treatment. Results are based on 44 subjects and on 401 votes.

TABLE 8
Cross Tabulations: Results from the Experiment without Party Payoff
Differential and without Party Identification

                      AH Uninformed           All Informed
                         Voters                  Voters

                           (1)                     (2)

Decision/         Treatment   Treatment   Treatment   Treatment
Treatment             T           D           T           D

Abstain             41.74       36.69       4.44        14.75
Vote Circle         23.50       27.37       44.44       42.40
Vote Triangle       34.76       35.94       51.11       42.86
Number of votes      702         665         180         217

                    Informed Voters:        Informed Voters:
                  Advertising received    Advertising received
                    from candidate of       from candidate of
                      Circle party           Triangle party

                           (3)                     (4)

Decision/         Treatment   Treatment   Treatment   Treatment
Treatment             T           D           T           D

Abstain             3.45        16.10       5.38        13.13
Vote Circle         90.80       61.02       1.08        20.20
Vote Triangle       5.75        22.88       93.55       66.67
Number of votes      87          118         93          99

Notes: In each of the two columns, the abbreviation T indicates
voting decisions associated with the truthful treatment and D with
the deception treatment. Results are based on 42 subjects.

TABLE 9
Explaining Vote Choices: Experiment without Party Payoff Differential
and without Party Identity

                                              (1)          (2)

Vote Choice: Vote Triangle
Campaign                                      .006         .002
                                             (.004)       (.004)
Treatment D                                  -.062        -.131
                                             (.161)       (.185)
Advertisement from Circle candidate        -1.896 ***   -3.148 ***
                                             (.303)       (.627)
Treatment D*Advertisement from Circle                    1.913 **
  candidate                                               (.757)
Advertisement from Triangle candidate      1.775 ***    4.073 ***
                                             (.380)      (1.012)
Treatment D*Advertisement from Triangle                 -3.019 ***
  candidate                                              (1.070)
Constant                                      .223        .336 *
                                             (.191)       (.196)
Vote Choice: Abstain
Campaign                                     012 **        .009
                                             (.006)       (.006)
Treatment D                                  -.093       -.295 **
                                             (.121)       (.135)
Advertisement from Circle candidate        -2.250 ***   -3.834 ***
                                             (.427)       (.633)
Treatment D*Advertisement from Circle                   2.337 ***
  candidate                                               (.582)
Advertisement from Triangle candidate        -.311        1.029
                                             (.479)      (1.271)
Treatment D*Advertisement from Triangle                   -1.405
  candidate                                              (1.295)
Constant                                      .211         .374
                                             (.300)       (.314)
Subject

Log likelihood                               -1,761       -1,733
N                                            1,764        1,764

                                              (3)          (4)

Vote Choice: Vote Triangle
Campaign                                     .009 *        .005
                                             (.005)       (.005)
Treatment D                                  -.085        -.121
                                             (.200)       (.233)
Advertisement from Circle candidate        -2.712 ***   -4.150 ***
                                             (.066)       (.590)
Treatment D*Advertisement from Circle                   2.177 ***
  candidate                                               (.768)
Advertisement from Triangle candidate      1.955 ***    4.583 ***
                                             (.427)      (1.080)
Treatment D*Advertisement from Triangle                 -3.568 ***
  candidate                                              (1.119)
Constant                                    .581 **      .686 **
                                             (.251)       (.276)
Vote Choice: Abstain
Campaign                                    .015 **       .012 *
                                             (.007)       (.007)
Treatment D                                  -.109        -.287
                                             (.159)       (.183)
Advertisement from Circle candidate        -3.042 ***   -4.854 ***
                                             (.469)       (.786)
Treatment D*Advertisement from Circle                   2.648 ***
  candidate                                               (.635)
Advertisement from Triangle candidate        -.128        1.538
                                             (.495)      (1.298)
Treatment D*Advertisement from Triangle                   -1.951
  candidate                                              (1.318)
Constant                                      .558        .719 *
                                             (.375)       (.394)
Subject                                    1.894 ***    1.988 ***
                                             (.472)       (.535)
Log likelihood                               -1,619       -1,587
N                                            1,764        1,764

Notes: The abbreviation D indicates voting decisions associated with
the deception treatment. The table reports point estimates and
standard errors in parenthesis, clustered by voters from a
multinomial logit regression. Column 1 shows specification 1 and
Column 2 shows specification 2, which adds interaction terms. Column
3 and Column 4 add shared random effects to specifications 1 and 2,
respectively. Base outcome in the regressions is "vote for Circle."
Results are based on 42 subjects.

Statistically significant at the *** 1%, ** 5%, and * 10% level.

TABLE 10
Fraction of Informed Voters Voting for the
High-and Low-Quality Candidate: Experiment
without Party Payoff Differential and without
Party Identity

                    Treatment T   Treatment D

Vote high quality      92.22         56.22
Vote low quality       7.78          43.78
Number of votes         180           217

Notes: The abbreviation T indicates voting decisions
associated with the truthful treatment and D with the deception
treatment. Results are based on 42 subjects and on 397 votes.