Voting Records as Assessors of Premises Behind Collective Decisions

The question of how to maximize benefits from the accuracy of collective decisions by weighting votes has been examined for a single-issue agenda. This study generalizes the existing optimal weighting rule in the context of collective judgment on an agenda consisting of multiple logically interconnected issues. Specifically, it determines the best approach to weight each voter’s judgment on a proposition in order to estimate the states of premises behind the proposition, which maximize the expected collective benefit obtained from their correctness, when voters’ judgments for the proposition are available as a record, but their judgments for premises are not available. Although the optimal weight assigned to a vote for a single-issue agenda has been known to depend only on voters’ competences (i.e., probability of a voter making a correct decision), we found that the weight in the case of multiple connected issues further depends on the content of the voter’s judgment. This difference raises a new question. In the case of a single-issue agenda, if voters have overwhelmingly high competence, dictatorial or oligarchic situations arise, namely, the weights to those voters can be so large that the remaining voters’ decisions do not affect the collective decision. By contrast, in the case of multiple connected issues, we should define who would be dictatorial or oligarchic in terms of the contents of their decisions, not just their competence. We examine the conditions under which such cases are likely to arise.