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Premise-based vs conclusion-based collective choice

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  • Masaki Miyashita

    (Yale University)

Abstract

Imagine a group of individuals faces a yes-no type question whose answer is logically determined by multiple premises. There are two salient types of procedures to aggregate individual judgments—the “premise-based way” (PBW) and the “conclusion-based way” (CBW). We derive necessary and sufficient conditions under which two procedures are universally ordered. If (and only if) a decision problem takes a “conjunctive” form, PBW derives a positive collective judgment (i.e., “yes”) whenever CBW does. Furthermore, if we replace “conjunctive” with “disjunctive” in the previous line, PBW derives a negative collective judgment (i.e., “no”) whenever PBW does. These observations highlight the fact that these two procedures are a mathematical dual of each another. Asymptotic properties are also studied. Under classical Condorcetian assumptions, PBW ensures the probability that the voting outcome is correct converges to one as the size of a group tends to infinity, whereas this holds for CBW only if an additional condition is satisfied.

Suggested Citation

  • Masaki Miyashita, 2021. "Premise-based vs conclusion-based collective choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(2), pages 361-385, August.
    • Handle: RePEc:spr:sochwe:v:57:y:2021:i:2:d:10.1007_s00355-021-01319-w
    DOI: 10.1007/s00355-021-01319-w
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    References listed on IDEAS

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    1. Aureli Alabert & Mercè Farré & Rubén Montes, 2023. "Optimal Decision Rules for the Discursive Dilemma," Group Decision and Negotiation, Springer, vol. 32(4), pages 889-923, August.

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