The paradox of multiple elections

Steven J. Brams, D. Marc Kilgour, William S. Zwicker

    Research output: Contribution to journalArticlepeer-review

    Abstract

    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 paradox of multiple elections is that NYY can receive the fewest votes of the 23 = 8 combinations. Several variants of this paradox are illustrated, and necessary and sufficient conditions for its occurrence, related to the "incoherence" of support, are given. The paradox is shown, via an isomorphism, to be a generalization of the well-known paradox of voting. One real-life example of the paradox involving voting on propositions in California, in which not a single voter voted on the winning side of all the propositions, is given. Several empirical examples of variants of the paradox that manifested themselves in federal 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 vote directly for combinations using approval voting or the Borda count, are discussed.

    Original languageEnglish (US)
    Pages (from-to)211-236
    Number of pages26
    JournalSocial Choice and Welfare
    Volume15
    Issue number2
    DOIs
    StatePublished - 1998

    ASJC Scopus subject areas

    • Social Sciences (miscellaneous)
    • Economics and Econometrics

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