Eyal Baharad

Ameliorating Majority Decisiveness through Expression of Preference Intensity

In pairwise voting, when a simple majority rule produces a winner, that winner is robust to the minoritys preferences. The typical means of protecting the minority from the decisiveness of the majority is by increasing the required majority or by augmenting the simple majority rule with constitutional constraints. In the former case the required majority q becomes larger than one-half, and this implies that the q-majority rule becomes biased in favor of one of the alternatives, usually the status quo. In the latter case the augmented rule becomes biased in favor of the minority. The main issue examined in this paper is whether the amelioration of majority decisiveness can be attained by unbiased voting rules that allow some restricted expression of preference intensities. Our results clarify that the use of scoring rules provides a positive answer to the above question when voters resort to variable degrees of coordinated strategic voting. The results are illustrated in the special cases of the plurality and the Borda rules.

CONTEST EFFORTS IN LIGHT OF BEHAVIOURAL CONSIDERATIONS

This study shows that distortion of probabilities is a possible reason for rent under-dissipation in contests with relatively small number of participants. Such distortion may also result, however, in over-dissipation of the contested rent. Focusing on contests with homogeneous contestants and the commonly studied contest success function, our main results clarify under what circumstances (i) rents are more under-dissipated relative to the standard situation where probabilities are not distorted (ii) rents are under-dissipated, yet less intensely relative to the standard situation where probabilities are not distorted (iii) rents are over-dissipated and (iv) the contest does not possess a symmetric interior equilibrium in pure strategies.

The inverse plurality rule—an axiomatization

Under the ‘inverse plurality rule’, voters specify only their least preferred alternative. Our first result establishes that this rule is the only scoring rule that satisfies the minimal veto condition (MV). We then prove that the inverse plurality rule is characterized by MV and the four well known conditions that characterize scoring rules; namely, Anonymity (A), Neutrality (N), Reinforcement (RE) and Continuity (CO). Our new characterization result is related to the characterizations of approval voting and of the widely used plurality rule. We finally show how the axiomatization of the inverse plurality rule can be extended to the axiomatization of elementary scoring rules (vote for t-alternatives scoring rules).

Extended preferences and freedom of choice

Abstract. The common choice theory in economics is based on the assumption that an individual is defined in terms of a binary preference relation. This preference relation is defined over alternatives without taking into account menu dependence and, in particular, freedom of choice or, more generally, the set that contains the alternatives. In this study we clarify the nature and the significance of freedom of choice which may positively or negatively affect the individuals welfare. Our proposed extended preference relation of the individual takes into account both the particular alternative and the opportunity set that he faces. This extended relation does not induce ranking of opportunity sets. Its restriction to a particular opportunity set is the paradigmatic preference relation and it can capture the dependence of preferences on freedom of choice. Our main result establishes the inconsistency between dependence of extended preferences on freedom of choice and the existence of a utility that represents the paradigmatic preference relation and any of its restrictions.

Distilling the wisdom of crowds: weighted aggregation of decisions on multiple issues

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.

Beyond Condorcet: Optimal Aggregation Rules Using Voting Records

The difficulty of optimal decision making in uncertain dichotomous choice settings is that it requires information on the expertise of the decision makers (voters). This paper presents a method of optimally weighting voters even without testing them against questions with known right answers. The method is based on the realization that if we can see how voters vote on a variety of questions, it is possible to gauge their respective degrees of expertise by comparing their votes in a suitable fashion, even without knowing the right answers.

On the selection of the same winner by all scoring rules

Different scoring rules can result in the selection of any of the k competing candidates, given the same preference profile, (Saari DG 2001, Chaotic elections! A mathematician looks at voting. American Mathematical Society, Providence, R.I.). It is also possible that a candidate, and even a Condorcet winning candidate, cannot be selected by any scoring rule, (Saari DG 2000 Econ Theory 15:55–101). These findings are balanced by Saari’s result (Saari DG 1992 Soc Choice Welf 9(4):277–306) that specifies the necessary and sufficient condition for the selection of the same candidate by all scoring rules. This condition is, however, indirect. We provide a sufficient condition that is stated directly in terms of the preference profile; therefore, its testability does not require the verdict of any voting rule.

Is majority consistency possible

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

Robustness against inefficient manipulation

(k-2)