International Workshop on New Approaches to Voting and Social Choice
25-26 May 2009
Tilburg University,room DZ 3, Dante building, The Netherlands
Tilburg University,room DZ 3, Dante building, The Netherlands
Program
Monday, May 25
09:00 Michel Balinski: Majority Judgement: Overview
09:50 Rida Laraki: Majority Judgement: Basic Theory
10:45 - 11:15 Break
11:15 – 11:45 Steven Brams: Comparing Approval Voting (in single-winner elections) with Range Voting and the Balinski-Laraki System
11:45 – 12:15 Marc Kilgour: Using Approval Balloting in Multi-Winner Elections
This paper is a survey of ways to use approval balloting in multi-winner elections, an approach that seems natural because both the ballot and the election result are subsets of the candidates. The class of admissible, or potentially winning, subsets is considered to be a parameter of the election. Most approval methods for multi-winner elections are best understood as scoring systems, in which the subset with the highest total score wins, but some are better explained as threshold systems, which select the maximally representative subset, or centralization systems, which find an admissible subset that is "central" among the ballots. This survey is devoted mainly to the classification of the methods, but some comparative properties are mentioned, particularly with respect to admissibility.12:15 – 13:00 Steven J. Brams and D. Marc Kilgour: Satisfaction Approval Voting
We propose a new voting system, satisfaction approval voting (SAV), for multiwinner elections, in which voters can approve of as many parties or candidates as they like. A voter's satisfaction score is the fraction of his or her approved candidates who are elected. If k candidates are to be elected, SAV chooses the set of k candidates that maximizes the sum of all voters' satisfaction scores. We show that SAV guarantees the proportional representation of parties in a legislature if parties nominate, and their supporters vote for, a number of candidates roughly proportional to their strength in the electorate. Because voters can approve of coalitions of parties, parties will be encouraged to seek coalition partners, even before an election, that reflect their supporters' preferences. This incentive is reinforced by the fact that coalitions can always obtain at least as many seats as their constituent parties when voters approve of all their members. Other ways of aggregating approval votes that give representation to different interests in an electorate are shown to be wanting, including giving seats to parties directly in proportion to their approval votes (this gives parties an incentive to create clones to increase their vote proportions, whereas SAV does not).13:00 –13:30 Break: sandwiches, tea and coffee will be served
13:30 – 14:15 Ton Storcken and Ad van Deemen: Unimodular Cultures
The issue here is on anonymous collective desicion making in large populations. Based on the structure on linear orderings induced by the Kemeny distance we study culture, i.e. (frequency) distributions. In case of a so called unimodular culture it appears that many if not all reasonable and well-known decision rules yield the same outcome.14:15 – 15:00 Vincent Merlin: A Characterization of the Maximin Rule in the Context of Voting
In a voting context, when the preferences of voters are described by linear orderings over a finite set of alternatives, the Maximin rule orders the alternatives according to their minimal rank in the voters’ preferences. It is equivalent to the Fallback bargai-ning process described by Brams and Kilgour [4]. This paper proposes a characteriza-tion of the Maximin rule as a Social Welfare Function (SWF) based upon five conditi-ons: Neutrality, Duplication, Unanimity, Top Invariance, and Weak Separability. In a similar way, we obtain a characterization for the Maximax SWF by using Bottom In-variance instead of Top Invariance. Then, these results are compared with the axioma-tic characterizations of two famous scoring rules, the Plurality rule and the Antiplurality rule.15:00 – 15:45 Hans Peters: On the Manipulability of Approval Voting
One of the attractive properties of approval voting is its non-manipulability if preferences are dichotomous. In this presentation we consider the manipulability of approval voting if preferences are not dichotomous. To this end we characterize the manipulable profiles of preferences under several different extensions of preferences to sets of alternatives: comparing sets by considering their worst alternatives; their best alternatives; or stochastically: set B is preferred to set C if the lottery that assigns equal probabilities to the elements of B stochastically dominates the lottery that ssigns equal probabilities to the elements of C. It turns out that the number of manipulable profiles tends to increase under these different assumptions on preference extension and, indeed, is highest under the more refined notion of stochastic comparison, as compared to the other two notions. We also consider so-called k-approval voting, where voters approve of a fixed number k of alternatives. In general, k-approval voting offers less flexibility to voters to express their preferences than approval voting, but is also less vulnerable to manipulation. For k=1, we obtain plurality voting, which is sometimes (e.g., for two voters) not manipulable at all, but - indeed - takes only very little preference information into account. For k>1 we provide some results on the optimal value of k as far as immunity to manipulation is concerned. We conjecture that, if the number of voters is large then (even) among all scoring rules k-approval voting with k equal to half the number of alternatives is optimal, i.e., least manipulable. (This presentation is based on joint research with Ton Storcken and Souvik Roy.)15:45 – 16:15 Break
16:15 – 17:15 Donald Saari: Explaining all possible positional and pair wise voting inconsistencies and paradoxes
For over a couple of centuries, "voting paradoxes" of positional and majority votes over pairs have intrigued academics and frustrated voters. The issue is whether there exists a consistent way to examine and explain all of them; is there a way to identify which voting rule more accurately represents the views of the voters. A new approach has been developed to analyze these questions, and it will be described here.17:15 – 18:15 José Luis García-Lapresta and Miguel Martínez-Panero: A Compromise between Majority Judgement and Range Voting
In 2007, concerning the first round of French presidential elections, Balinski and Laraki held an experiment at Orsay under a recent median-based voting system: Majority Judgement. Using their data, in this contribution we test a new class of voting procedures (García-Lapresta, J.L., Martínez-Panero, M.: “Linguistic-based voting through centered OWA operators”, forthcoming in Fuzzy Optimization and Decision Making). The outcomes obtained allow us to think of a compromise between Majority Judgement and Range Voting, a mean-based voting system advocated by Smith. It is worth mentioning that our voting systems avoid some drawbacks of Majority Judgement and Range Voting when used in small electorates.19:00 Workshop dinner at Auberge du Bonheur
Tuesday, May 26
09:00 – 10:00 Donald Saari: Extending Arrow's Theorem to --- just about everything!
We think of Arrow's Theorem in terms of voting and social choice. As described, the ideas from Arrow's result extend to address questions coming from science, foreign policy, economics, engineering, nano-technology, and just about everything. Some of the consequences, such as "Dark Matter," as surprising.10:00 – 10:45 Hannu Nurmi: Alternatives to Ranking in the Theory of Voting
Since its re-birth in the 1950's the theory of voting has been based on the assumption that the voters are endowed with complete and transitive preference relations over the alternatives being voted upon. In this preliminary presentation I shall deal with a few alternative assumptions and assess their advantages and disadvantages. The alternatives looked at are individual choice functions, individual preference tournaments as well as assumptions akin to utility functions. The latter features in systems like range voting and majoritarian judgment.10:45 – 11:15 Break
11:15 – 12:00 Maurice Salles and Feng Zhang: Rights Revisited, and Limited
One of the most justly famous result of social choice theory is Sen's Theorem on the impossibility of a Paretian liberal. In two recent papers, Salles introduced the notion of limited rights both in an aggregation function framework and in a social choice function framework. He then proved Sen-type impossibility theorems. In the aggregation function framework an individual has a `right' if whenever she prefers an option (social state), say a, to another social state, say b, the social preference ranks a before b. Salles proposed to consider the following weakening. Rather than a being socially ranked before b, he suggests that b should not be ranked before a. In the social choice framework, a framework which was introduced later on and was thought to be more or less equivalent to the aggregation function framework, if the individual prefers a to b, b must not be chosen from any set to which a belongs. Salles's weakening amounts to say that if it happens that b be chosen, then a must be chosen too. In the present paper, we will describe from an intuitive point of view the technical results obtained by Salles in the light of the distinction between possibility and obligation, and we will present a research program based. on the use of tools borrowed from modal logic.12:00 – 13:00 Michel Grabisch and Agnieszka Rusinowska: Influence Functions, Followers, and Command Games.
We study a model of influence in a social network in which players are to make a certain acceptance/rejection decision. It is assumed that each player has an inclination to say YES or NO which, due to influence of other players, may be different from the decision of the player. We propose among other descriptive tools a definition of a (weighted) influence index of a coalition upon an individual. Moreover, we consider different influence functions representative of commonly encountered situations, and study their properties. The concept of a follower of a given coalition is also defined. The properties of the follower function are analyzed. We also study a relation between influence function and follower function. We deliver sufficient and necessary conditions for a function to be a follower function, and we describe the structure of the set of all influence functions that lead to a given follower function. Furthermore, we compare the model of influence with command games. In the command structure introduced by Hu and Shapley, for each player a simple game called the command game is built. One of the central concepts of this model is the concept of command function. We deliver sufficient and necessary conditions for a function to be a command function, and describe the minimal sets generating a normal command game. We also study the relation between command games and influence functions. A sufficient and necessary condition for the equivalence between an influence function and a normal command game is delivered.13:00 – 13:30 Break: sandwiches, tea and coffee will be served
13:30 – 14:15 Rohit Parikh : The Logic of Campaigning
In the US at least, the election campaign occupies a much longer period of time than the election itself, just as a typical courtship occupies a much longer period than the wedding itself. Nonetheless, while we have a well developed theory of elections going back more than two hundred years, we have a much less developed theory of campaigning. Clearly, during an election campaign, the candidates regard the voters as a more or less fixed entity with beliefs and preferences, and the objective of the candidates is to get more voters to vote for them and to get fewer voters to vote for their opponents. Thus the candidates are involved in actively changing the mental models of the voters, i.e., how the voters see themselves and their competitors, and it is quite interesting to see how theory and practice in this area correlate. Tools we can make use of here include Dynamic Epistemic Logic, the AGM theory of belief revision as well as the more recent developments in Cheap Talk. (Some of the results reported are joint with Walter Dean.)14:15 – 15:00 Remzi Sanver : Approval as an Intrinsic Part of Preference
15:00 – 15:45 Madeleine Hosli : Reforming the United Nations Security Council: Collective and Distributive Effects
Changing the composition, and possibly voting system, of the Security Council, in an effort to increase this institution's global legitimacy, is proving to be one of the most difficult hurdles to overcome for the global community of states as represented in the United Nations (UN). This paper demonstrates that due to institutional hurdles, it is considerably more difficult today to reach a winning coalition in the General Assembly as needed to secure Security Council reform than it was in the early years of the UN. In addition, the paper analyzes effects that adapted patterns of voting, as prescribed by recent reform proposals, would have on the distribution of power among UN member states in the Security Council. Our power and decision capacity computations are based on (modified) Penrose-Banzhaf-Coleman measures.15:45 – 16:15 Break
16:15 – 17:15 Rida Laraki: Majority Judgement: Objections Answered
17:15 – 18:15 Michel Balinski: Majority Judgement: Empirical Evidence
19:00 – 22:00 Joint dinner at restaurant Lucebert of the Theatre in Tilburg. Taxi’s will leave the university at 17:45 and bring
you back to the Auberge du Bonheur at 22:00
