The relevance of the voting paradox: a restatement

Journal of Economic Theory, 1997

Proceedings of TARK 2019, 2019

Much of the theoretical work on strategic voting makes strong assumptions about what voters know about the voting situation. A strategizing voter is typically assumed to know how other voters will vote and to know the rules of the voting method. A growing body of literature explores strategic voting when there is uncertainty about how others will vote. In this paper, we study strategic voting when there is uncertainty about the voting method. We introduce three notions of manipulability for a set of voting methods: sure, safe, and expected manipulability. With the help of a computer program, we identify voting scenarios in which uncertainty about the voting method may reduce or even eliminate a voter's incentive to misrepresent her preferences. Thus, it may be in the interest of an election designer who wishes to reduce strategic voting to leave voters uncertain about which of several reasonable voting methods will be used to determine the winners of an election.

Journal of Economic Interaction and …, 2011

Social choice models usually assume that choice is among exogenously given and non decomposable alternatives. Often, on the contrary, choice is among objects that are constructed by individuals or institutions as complex bundles made of many interdependent components. In this paper we present a model of object construction in majority voting and show that, in general, by appropriate changes of such bundles, different social outcomes may be obtained, depending upon initial conditions and agenda, intransitive cycles and median voter dominance may be made appear or disappear, and that, finally, decidability may be ensured by increasing manipulability or viceversa.

Group Decision and Negotiation, 2000

Many, if not most, problems in group decision making can be translated into MCDM problems by substituting criteria for voters. Yet, there has been very little discussion about the implications of various types of voting paradoxes to MCDM. The classic voting paradoxes, viz. Borda's and Condorcet's, have obvious implications for certain MCDM situations. The latter implies that the notion of the best alternative, given a set of criteria and information about the ordinal ranking of the alternatives on those criteria, can be essentially arbitrary. The former, in turn, demonstrates a particularly clear case of conflict between reasonable intuitions. Completely unexplored are implications of compound majority paradoxes to MCDM. The paper deals with Ostrogorski's and Anscombe's paradoxes which result from non-bisymmetry and non-associativity of the majority relation. Moreover, we shall discuss the implications of paradox of multiple elections which is a situation where the result of multiple-item election may be a policy alternative that nobody voted for.

J Math Econ, 2008

A decision scheme ) is a function mapping profiles of strict preferences over a set of social alternatives to lotteries over the social alternatives. Motivated by conditions typically prevailing in elections with many voters, we say that a decision scheme is weakly strategy-proof if it is never possible for a voter to increase expected utility (for some vNM utility function consistent with her true preferences) by misrepresenting her preferences when her belief about the preferences of other voters is generated by a model in which the other voters are i.i.d. draws from a distribution over possible preferences. We show that if there are at least three alternatives, a decision scheme is necessarily a random dictatorship if it is weakly strategy-proof, never assigns positive probability to Pareto dominated alternatives, and is anonymous in the sense of being unaffected by permutations of the components of the profile. This result is established in two settings: a) a model with a fixed set of voters; b) the Poisson voting model of Meyerson (Abstract A decision scheme (Gibbard ) is a function mapping profiles of strict preferences over a set of social alternatives to lotteries over the social alternatives. Motivated by conditions typically prevailing in elections with many voters, we say that a decision scheme is weakly strategy-proof if it is never possible for a voter to increase expected utility (for some vNM utility function consistent with her true preferences) by misrepresenting her preferences when her belief about the preferences of other voters is generated by a model in which the other voters are i.i.d. draws from a distribution over possible preferences. We show that if there are at least three alternatives, a decision scheme is necessarily a random dictatorship if it is weakly strategy-proof, never assigns positive probability to Pareto dominated alternatives, and is anonymous in the sense of being unaffected by permutations of the components of the profile. This result is established in two settings: a) a model with a fixed set of voters; b) the Poisson voting model of

2006

Whether made explicit or implicit, knowledge theoretic properties such as common knowledge of rationality are important in understanding and modeling game-theoretic, or strategic, situations. There is a large literature devoted to exploring these and other issues related to the epistemic foundations of game theory. Much of the literature focuses on what the agents need to know about the other agents' strategies, rationality or knowledge in order to guarantee that a particular solution concept, such as the Nash equilibrium, is realized. This paper, which is based on two recent papers 1 [7] and [16], develops a framework that looks at similar issues relevant to the field of voting theory. Our analysis suggests that an agent must possess information about the other agents' preferences in order for the agent to decide to vote strategically. In a sense, our claim is that the agents need a certain amount of information in order for the Gibbard-Satterthwaite theorem to be "effective".

2003

This paper analyses the effects played by rules within a coordination game. The starting point is constituted by the wide field of Public Choice theories. More precisely the focus of the research is on the stability of the voting process. The experiment is build on a game played through computers and the experimental subjects must perform some choices that can led to different individual and collective solutions. The game that they play is based on a set of rules that must be voted by the players themselves before a new session of the experiment will be run. The idea is to verify the degree of stability of the collective choices (logrolling phenomena).

Quality and Quantity, 1980

We theoretically and experimentally study voter behavior in a setting characterized by plurality rule and mandatory voting, where voters choose from three options. We are interested in the occurrence of strategic voting in an environment where Condorcet cycles may occur. In particular, we focus on how information about the distribution of preferences affects strategic behavior. We also vary the relative importance of the second preferred option to investigate how this affects the strategic vote. Quantal response equilibrium analysis is used to analyze the game and proves to be a good predictor for the experimental data. Our results indeed show that strategic voting arises, the extent of which depends on (i) the availability of information; (ii) the relative importance of the intermediate candidate; (iii) the electorate‟s relative support for one‟s preferred candidate; and (iv) the relative position of the majoritary-supported candidate in a voter‟s preference ordering. Our results show that information serves as a coordination device where strategic voting does not harm the majority-preferred candidate‟s chances of winning.

2009

In this paper, we expose the results of a voting experiment realised in 2007, during the French Presidential election. This experiment aimed at confronting the Single Transferable vote (SVT) procedure to two criteria : simplicity and the selection of a Condorcet-winner. Building on our electoral sample's preferences, we show that this voting procedure can design a different winner, depending on the vote counting process. With the vote counting process advocated by Hare, the winner is Nicolas Sarkozy, while the Coombs vote counting process has François Bayrou as winner. For these two vote counting processes, the details of the experiment are the same and it is shown that the simplicity criterion is respected. However, with regard to the Condorcet-winner criterion, the Coombs methods is the only one to elect the Condorcet-winner, i.e. François Bayrou.

adaptive agents and multi agents systems, 2017

Various voting rules (or social choice procedures) have been proposed to select a winner from the preferences of an entire population: Plurality, veto, Borda, Minimax, Copeland, etc. Although in theory, these rules may yield drastically different outcomes, for real-world datasets, behavioral social choice analyses have found that the rules are often in perfect agreement with each other! This work attempts to give a mathematical explanation of this phenomenon. We quantify the gap between the outcomes of two voting rules by the pairwise margin between their winners. We show that for many common voting rules, the gap between them can be almost as large as 1 when the votes are unrestricted. As a counter, we study the behavior of voting rules when the vote distribution is a uniform mixture of a small number of multinomial logit distributions. This scenario corresponds to a population consisting of a small number of groups, each voting according to a latent preference ranking. We show that for any such voting profile on g groups, at least 1/2g fraction of the population prefers the winner of a Borda election to any other candidate.

Studies in Choice and Welfare, 2009

Information on the rankings and information on the approval of candidates in an election, though related, are fundamentally different-one cannot be derived from the other. Both kinds of information are important in the determination of social choices. We propose a way of combining them in two hybrid voting systems, preference approval voting (PAV) and fallback voting (FV), that satisfy several desirable properties, including monotonicity. Both systems may give different winners from standard ranking and nonranking voting systems. PAV, especially, encourages candidates to take coherent majoritarian positions, but it is more information-demanding than FV. PAV and FV are manipulable through voters' contracting or expanding their approval sets, but a 3-candidate dynamic poll model suggests that Condorcet winners, and candidates ranked first or second by the most voters if there is no Condorcet winner, will be favored, though not necessarily in equilibrium.

Social Choice and Welfare, 1998

Assume that voters must choose between voting yes (Y) and voting no (N) on three propositions on a referendum. If the winning combination is NYY on the ®rst, second, and third propositions, respectively, the paradox of multiple elections is that NYY can receive the fewest votes of the 2 3 = 8 combinations. Several variants of this paradox are illustrated, and necessary and sucient conditions for its occurrence, related to the``incoherence'' of support, are given.

2012

Prima di cominciare la trattazione di questa tesi vorrei ringraziare il mio relatore Prof. Vito Fragnelli (o, più amichevolmente, Franco), per avermi dato l'opportunità di svolgere questo lavoro durante il di dottorato e per tutti gli argomenti interessanti che mi ha proposto. Ringrazio il Prof. Guido Ortona, con il quale ho avuto il piacere di discutere di alcuni degli argomenti trattati nella tesi e non solo, e il Dott. Stefano Gagliardo, mio compagno di avventura e collaboratore in questi tre anni di dottorato. Un grazie alla mia famiglia, ai miei genitori in primis, per tutto il sostegno che non mi hanno mai fatto mancare, a mia sorella Manu, a Luca e in particolare ad Alice, che mi fa capire come tutto questo lavoro sia modesto. Nel tempo che io ho impiegato a mettere insieme un po' di conti e di parole lei è riuscita a trasformarsi da un mucchietto di cellule in una personcina cantante, saltellante, amorevole e che conta fino a 20! Un grazie anche a mia cugina Joan Chessa Hollingsworth e a sua figlia Jo, per il loro prezioso aiuto. Grazie a tutti i miei amici, di cui non elenco i nomi perchè fortunatamente sono davvero tanti, ma che amo tutti quanti alla follia. Ognuno di loro conosce il proprio ruolo nella mia vita e le mille ragioni per cui una sola pagina di ringraziamenti comunque non basterebbe. Non posso però fare a meno di nominare almeno Chiara, Monica, Tania e Maura. Merci a toi, Arnaud, parce que tu seras pour moi unique au monde. Je serai pour toi unique au monde. Gennaio 2013, Michela CHESSA Preface My career as PhD student at University of Milan started 3 years ago, in January 2010. After a bachelor and a master thesis on Game Theory, I was really interested in continuing my research on this subject, when my PhD supervisor, Prof. Fragnelli, proposed me to start working on voting systems. I immediately found the topic actual and fascinating, particularly because of all the problems about the adopted electoral system and the political scenario my country, Italy, has in these years. It was a very convincing opportunity of working on Game Theory and on Game Practice in the same time, because of the concreteness of the problems I was going to deal with. Some of the results included in this thesis have been taken from some articles I previously published: the work presented in Chapter 3 contains some results included in "Chessa M., Fragnelli V., Embedding classical indices in the FP family, Czech Economic Review, vol.5, 2011, pp. 289-305", while the work in Chapter 4 has been presented as invited talk at the workshop "Models of Collusion, Games and Decisions for Applications to Judging, Selling and Voting" in Monte Isola (BS), Italy, on June 2012 with the title "The Bargaining Set for Sharing the Power ". Chapter 5 contains part of analysis presented in "Chessa M., Fragnelli V., A quantitative evaluation of veto power,

This paper studies the welfare consequences of strategic voting in plu- rality and runoff rules by comparing the utilitarian efficiencies obtained in simulated voting under two behavioural assumptions: expected util- ity maximising behaviour and sincere behaviour. Utilitarian efficiency is higher with expected utility maximising behaviour than with sincere voting behaviour in both voting rules under reasonable parameter values concerning the voters' preferences and beliefs. Strategic voting increases utilitarian efficiency especially when the distribution of preference intensi- ties correlates with voter types and when the voters have some information on the aggregate level preference intensities. (JEL classiÞcation numbers: D71, D81)