A minimax procedure for electing committees (original) (raw)
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Journal of Economics, 2012
We analyze the voting behavior of a small committee that has to approve or reject a project proposal whose return is uncertain. Members have diverse preferences: some of them want to maximize the expected value, while others have a bias towards project approval and ignore their information on the project value. We focus on the most efficient use of scarce information when members cannot communicate prior to voting, and we provide insights on the optimal composition of the committee. Our main result is that the presence of biased members can improve the voting outcome, by simplifying the strategies of unbiased members. Thus, committees with diverse members perform as well as homogeneous committees, and even better in some cases. In particular, when value-maximizing members outnumber biased members by one vote, the optimal equilibrium becomes unique.
2004
Measuring Power in At-Large Representation Paul Edelman This talk presents a formal analysis of a voting game inspired by a common type of local legislature: a legislative body in which some of the seats are allocated by majority vote in equipopulous districts, and some of the seats are elected by an at-large majority vote. Such legislatures are common in city councils of large metropolitan areas and county boards. For instance, the Metropolitan Council of Nashville and Davidson County in the state of Tennessee consists of 40 members, 5 of whom are at-large and the remaining 35 are elected from separate districts. The motivation for this study is the question of how to decide how many of each type of representative is optimal, given a fixed total number of representatives. The analysis will follow in the tradition of Banzhaf [1]. The legislature will be modelled by a weighted voting game and I will compute the power of an individual voter by using the composition of this weighted vo...
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.
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.
Committee Voting Under Alternative Procedures and Preferences: An Experimental Analysis
This paper reports on four series of experiments in a five-person committee voting under majority rule. Each of two voting procedures was paired with each of two types of preference sets. The types were characterized as high or low intensity. Every set of preferences had a Condorcet point and that point was the best alternative for one (and only one) voter. When the high intensity preferences were used, committees operating under either voting procedure selected the Condorcet point more than 90% of the time; when low intensity payoffs were used, the success rate was less than 51%. A theory is suggested which predicts which preference sets should successfully induce selection of the Condorcet point and which should not; in the latter case, the same theory predicts that the choice will be confined to a certain collection of the other points. Our observations are consistent with this theory. .
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.
Influence in Weighted Committees
2019
A committee's decisions on more than two alternatives much depend on the adopted voting method, and so does the distribution of power among the committee members. We investigate how different aggregation methods such as plurality runoff, Borda count, or Copeland rule map asymmetric numbers of seats, shares, voting weights, etc. to influence on outcomes when preferences vary. A generalization of the Penrose-Banzhaf power index is proposed and applied to the IMF Executive Board's election of a Managing Director, extending a priori voting power analysis from binary simple voting games to choice in weighted committees.
Evaluating Committees for Representative Democracies: the Distortion and Beyond
2020
We study a model where a group of representatives is elected to make a series of decisions on behalf of voters. The quality of such a representative committee is judged based on the extent to which the decisions it makes are consistent with the voters’ preferences. We assume the set of issues on which the committee will make the decisions is unknown—a committee is elected based on the preferences of the voters over the candidates, which only reflect how similar are the preferences of the voters and candidates regarding the issues. In this model we theoretically and experimentally assess qualities of various multiwinner election rules.
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.