Beyond Condorcet: optimal aggregation rules using voting records |
| |
Authors: | Eyal Baharad Jacob Goldberger Moshe Koppel Shmuel Nitzan |
| |
Institution: | 1.Department of Economics,Bar Ilan University,Ramat Gan,Israel;2.School of Engineering,Bar Ilan University,Ramat Gan,Israel;3.Department of Computer Sciences,Bar Ilan University,Ramat Gan,Israel |
| |
Abstract: | In certain judgmental situations where a “correct” decision is presumed to exist, optimal decision making requires evaluation
of the decision-makers’ capabilities and the selection of the appropriate aggregation rule. The major and so far unresolved
difficulty is the former necessity. This article presents the optimal aggregation rule that simultaneously satisfies these
two interdependent necessary requirements. In our setting, some record of the voters’ past decisions is available, but the
correct decisions are not known. We observe that any arbitrary evaluation of the decision-makers’ capabilities as probabilities
yields some optimal aggregation rule that, in turn, yields a maximum-likelihood estimation of decisional skills. Thus, a skill-evaluation equilibrium can be defined as an evaluation of decisional skills that yields itself as a maximum-likelihood estimation of decisional
skills. We show that such equilibrium exists and offer a procedure for finding one. The obtained equilibrium is locally optimal
and is shown empirically to generally be globally optimal in terms of the correctness of the resulting collective decisions.
Interestingly, under minimally competent (almost symmetric) skill distributions that allow unskilled decision makers, the
optimal rule considerably outperforms the common simple majority rule (SMR). Furthermore, a sufficient record of past decisions
ensures that the collective probability of making a correct decision converges to 1, as opposed to accuracy of about 0.7 under
SMR. Our proposed optimal voting procedure relaxes the fundamental (and sometimes unrealistic) assumptions in Condorcet’s
celebrated theorem and its extensions, such as sufficiently high decision-making quality, skill homogeneity or existence of
a sufficiently large group of decision makers. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|