Real-world Choices Research Articles

Towards a theory of yes-no voting

The formal theory of majority-rule voting has dealt almost entirely with the unique selection of a single candidate(s) or motion(s) from a set of alternatives greater than two. The analysis presumes that there is only a single group or collective decision to be made, a single 'election,' or a single 'proposition.' This orthodox conceptual setting for collective choice is necessary to generate the possibility of the cyclically-rotating, and hence disequilibrium, set of outcomes on the one hand and for the median-voter dominated equilibrium outcome on the other. If the number of alternatives in the choice set is limited to two, simple majority rule voting yields unambiguous results provided only that we assume an odd number of voters with each voter assumed to have strictly ordered preferences. In the orthodox voting-model setting, few problems of analytical interest seem to arise in the single pairwise choice between two alternatives, for example, between approval and disapproval of a proposition. When the voting population is presented with a whole set of independent propositions, however, each one of which is to be resolved by simple 'yes-no,' 'up-down,' or 'approve-disapprove' majority voting, questions of considerable analytical interest do arise. To our knowledge no one has discussed or investigated the analogues and contrasts between yes-no voting and the conventional, multi-alternative, majority-rule voting. The relative neglect of the properties of yes-no voting under majority rule is itself puzzling since many real-world collective choice institutions formally operate in this way. Examples that come to mind include zoning boards, referenda and initiatives; in several states judges are re-elected on a yes-no basis.