Strategy-proof consensus rules for committee elections (original) (raw)

Attainable results in committee elections

Mathematical and Computer Modelling, 1999

The committee election problem is to choose from a finite set S of candidates a nonempty subset T of committee members as the consequence of an election in which each voter expresses a preference for a candidate in S. Solutions of this problem can be modelled by functions which map each partition of 1 (i.e., normalized vote tallies of candidates who have been ordered canonically by tally) into a nonempty subset of positive integers (i.e., sizes of committees). To solve this problem, we recently described a parameterized voting scheme, the ratio-of-sums or rasp consensus rule, in which p controls the degree to which votes must be concentrated in elected committees. It is desirable to identify the attainable results of such rules so as to understand their properties and to facilitate their comparison. For all p, we characterize the attainable rasp results in the general csse where the partition's parts are real, and in the special case where p as well as its parts are rational.

Mqite Working paper series WP # 14-05 A Consensual Committee Using Approval Balloting

2014

A new voting rule for electing committees is described. Specifically, we use approval balloting and propose a voting procedure guaranteeing that if a committee representing (in a determined proportion) all voters exists, then the selected committee has to represent all voters at least in the same proportion. This condition is a generalization of the unanimity property and the usual voting procedures in this context do not satisfy it.

A Representative Committee by Approval Balloting

Group Decision and Negotiation

A new voting rule for electing committees is described. Specifically, we use approval balloting and propose a new voting procedure that guarantees that if there is a committee that represents (with a given proportion of representatives) all of the existing voters, then the selected committee has to represent all of voters in at least the same proportion. This property is a way of selecting a committee that represents completely all of voters when such a committee exists. The usual voting rules in this context do not satisfy this condition.

Stable voting procedures for committees in economic environments

2001

A strong representation of a committee, formalized as a simple game, on a convex and closed set of alternatives is a game form with the members of the committee as players such that (i) the winning coalitions of the simple game are exactly those coalitions, which can get any given alternative independent of the strategies of the complement, and (ii) for any profile of continuous and convex preferences, the resulting game has a strong Nash equilibrium. In the paper, it is investigated whether committees have representations on convex and compact subsets of R m . This is shown to be the case if there are vetoers; for committees with no vetoers the existence of strong representations depends on the structure of the alternative set as well as on that of the committee (its Nakamura-number). Thus, if A is strictly convex, compact, and has smooth boundary, then no committee can have a strong representation on A. On the other hand, if A has non-smooth boundary, representations may exist depending on the Nakamura-number (if it is at least 7). JEL No. D71, C71.

A minimax procedure for electing committees

Public Choice, 2007

A new voting procedure for electing committees, called the minimax procedure, is described. Based on approval voting (AV), it chooses the committee that minimizes the maximum "Hamming distance" to all voters (minimax outcome). Such an outcome may be diametrically opposed to the outcome obtained from aggregating votes in the usual manner, which minimizes the sum of the Hamming distances to all voters (minisum outcome). Computer simulation is used to assess how much minimax and minisum outcomes tend to diverge. The manipulability of the minimax procedure is also investigated.

Axiomatic characterization of committee scoring rules

Journal of Economic Theory, 2019

Committee scoring rules form a rich class of aggregators of voters' preferences for the purpose of selecting subsets of objects with desired properties, e.g., a shortlist of candidates for an interview, a representative collective body such as a parliament, or a set of locations for a set of public facilities. In the spirit of celebrated Young's characterization result that axiomatizes single-winner scoring rules, we provide an axiomatic characterization of multiwinner committee scoring rules. We show that committee scoring rules-despite forming a remarkably general class of rules-are characterized by the set of four standard axioms, anonymity, neutrality, consistency and continuity, and by one axiom specific to multiwinner rules which we call committee dominance. In the course of our proof, we develop several new notions and techniques. In particular, we introduce and axiomatically characterize multiwinner decision scoring rules, a class of rules that broadly generalizes the well-known majority relation.

Extensions of the Simpson voting rule to the committee selection setting

Public Choice, 2019

Committee selection rules are procedures selecting sets of candidates of a given size on the basis of the preferences of the voters. There are in the literature two natural extensions of the well-known singlewinner Simpson voting rule to the multiwinner setting. The first method gives a ranking of candidates according to their minimum number of wins against the other candidates. Then, if a fixed number k of candidates are to be elected, the k best ranked candidates are chosen as the overall winners. The second method gives a ranking of committees according to the minimum number of wins of committee members against committee nonmembers. Accordingly, the committee of size k with the highest score is chosen as the winner. We propose an in-depth analysis of those committee selection rules, assessing and comparing them with respect to several desirable properties among which unanimity, fixed majority, nonimposition, stability, local stability, Condorcet consistency, some kinds of monotonicity, resolvability and consensus committee. We also investigate the probability that the two methods are resolute and suffer the reversal bias, the Condorcet loser paradox and the leaving member paradox. We compare the results obtained with the ones related to further well-known committee selection rules. The probability assumption on which our results are based is the widely used Impartial Anonymous Culture.