摘要：Condorcet's paradox is one of the most prominent results in social choice theory. It says that there may not exist any alternative that a net majority prefers over every other alternative. When outcomes need not be deterministic alternatives, we show that a similar paradox still exists even if preferences are dichotomous. Thus relaxing the requirement of discrete alternatives does not help in circumventing Condorcet's paradox. On the other hand, we show that a fractional/randomized version of Black's Median Voter Theorem still holds for single-peaked preferences.
关键词：Social choice theory ; Condorcet's Paradox ; Median Voter Theorem ; Social decision function
