Eyal Baharad’s research while affiliated with Bar Ilan University and other places

This study identifies a new optimal decision rule in a general pairwise choice framework, taking into account behavioral aspects where subjective probabilities are assumed. The optimal rule under such a setting is compared to the one identified where behavioral considerations are not incorporated into the model.

We show that the inconsistency associated with judgment aggregation (the “doctrinal paradox”) is not a rare exception. When judgments express degrees of belief or conviction and thus belong to the entire interval [0,1] we show that for any typical proposition aggregator (mapping several opinions about different propositions into a single one), the set of individual opinion aggregators (mapping individual opinions about the same issue into a single one) that avoid the paradox is very small, i.e., is nowhere dense in the space of bounded functions. In addition, we offer several examples of judgement aggregation for which the paradox can be avoided.

This study shows that independence between voters’ skills and states of nature improves the majority voting efficiency relative to the case when such independence does not exist. This implies that specialization (state of nature wise) is not advantageous under the simple majority rule.

Under the unanimity rule, a single voter may alter a decision that is unanimously accepted by all other voters. Under the simple majority rule, the impact of such a voter diminishes. This paper examines the marginal effect of competence on the collective performance—the likelihood of reaching a correct decision. It is shown that adding an incompetent voter to the group is inferior (superior) to giving up an existing competent voter, when the decision mechanism is the unanimity (simple majority) rule. The negative impact of an incompetent voter cannot (can) always be balanced by adding a competent one under the unanimity (simple majority) rule. Moreover, improving a single voter’s competence may have a greater effect on the collective performance under the simple majority rule relative to the unanimity rule.

We determine the scoring rule that is most likely to select a high-ability candidate. A major result is that neither the widely used plurality rule nor the inverse-plurality rule are ever optimal, and that the Borda rule is hardly ever optimal. Furthermore, we show that only the almost-plurality, the almost-inverse-plurality, and the almost-Borda rule can be optimal. Which of the “almost” rules is optimal depends on the likelihood that a candidate has high ability and how likely committee members are to correctly identify the abilities of the different candidates.

The most well-known approaches to decision rules are inspired by “majority-based” and “ranking-based” utilitarianism. The long lasting discussion on the appropriate collective decision mechanism is based on the merits of the rules consistent with these two approaches. Focusing on conformity with qualified majority, we propose single-approval multiple-rejection (SAMR) as a plausible flexible scoring rule narrowing the gap between the two approaches. Given k alternatives, such a mechanism permits approval of a single alternative and rejection of at most (Formula presented.) alternatives allowing any relative significance of the approved vs. the rejected alternatives. SAMR is the unique type of rule that spans the whole spectrum of the qualified majority-based utilitarian rules, independent of k. Our first characterization result exposes the relationship between its consistency with any predetermined (Formula presented.)-majority based rule, (Formula presented.), and the best/worst (approval/rejection) relative weight p. Our second result establishes that the plurality rule is the unique scoring rule consistent with any (Formula presented.)-majority, (Formula presented.). These results imply the impossibility of universal scoring-rule consistency with any ideal or real (Formula presented.)-majority.

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. KeywordsSimple majority rule–Condorcet–Voting record–Optimal aggregation rule

Given the judgments of multiple voters regarding some issue, it is generally assumed that the best way to arrive at some collective judgment is by following the majority. We consider here the now common case in which each voter expresses some (binary) judgment regarding each of a multiplicity of independent issues and assume that each voter has some fixed (unknown) probability of making a correct judgment for any given issue. We leverage the fact that multiple votes by each voter are known in order to demonstrate, both analytically and empirically, that a method based on maximum likelihood estimation is superior to the simple majority rule for arriving at true collective judgments.