THE PARADOX OF MULTIPLE ELECTIONS

Assume that voters must choose between voting yes (Y) and voting no (N ) on three propositions on a referendum. If the winning combination is NYY on the first, second, and third propositions, respectively, the p aradox of multiple elections is that NYY can receive the fewest votes of the 2(3) = 8 combinations. Several variants of this paradox are ill ustrated, and necessary and sufficient conditions for its occurrence, related to the ''incoherence'' of support, are given. The paradox is s hown, via an isomorphism, to be a generalization of the well-known par adox of voting. One real-life example of the paradox involving voting on propositions in California, in which not a single voter voted on th e winning side of all the propositions, is given. Several empirical ex amples of variants of the paradox that manifested themselves in federa l elections - one of which led to divided government - and legislative votes in the US House of Representatives, are also analyzed. Possible normative implications of the paradox, such as allowing voters to vot e directly for combinations using approval voting or the Borda count, are discussed.