Preferences, actions and voting rules

Cluster Computing, 2018

Multi-agent decision problems, in which independent agents have to agree on a joint plan of action or allocation of resources, are central to artificial intelligence. The main focus of paper is the analysis of dynamics of manipulation in voting rules like plurality and veto. An important technical issue that arises is manipulation of voting schemes: a voter may be able to improve the outcome (with respect to his own preferences) by reporting his preferences incorrectly. We consider scenarios where voters cannot coordinate their actions, but are allowed to change their vote after observing the current outcome, as is often the case both in offline committees and in online voting. Voters are allowed to change their votes if they can get their desirable results, we have worked on veto and plurality rule with the small number of candidates and voters. We also used different moves for analysing the dynamics of voting system and concluded different results based on different types of moves (both manipulative and non-manipulative). We also defined a new tie breaking rule ''Typicographical rule'' and according to our observation it works better than the lexicographical rule.

Studies in Fuzziness and Soft Computing, 2011

Consensus means general agreement among possibly di erent views, while dichotomus voting rules are a means of making decisions by using votes to settle di erences of view. How then can it often be the case that a committee whose only formal mechanism for decision-making is a dichotomus voting rule reaches a consensus? In this paper, based on a game-theoretic model developed in three previous papers, we provide an answer to this question.

Mathematical Social Sciences, 2012

By extending manipulability indices defined for single-valued social choice rules to the multi-valued case, we explore the degree of manipulability of seven multi-valued social choice rules. Our analysis is based on computational experiments.

Logics in Artificial Intelligence, 2004

Results in social choice theory such as the Arrow and Gibbard-Satterthwaite theorems constrain the existence of rational collective decision making procedures in groups of agents. The Gibbard-Satterthwaite theorem says that no voting procedure is strategy-proof. That is, there will always be situations in which it is in a voter's interest to misrepresent its true preferences i.e., vote strategically. We present some properties of strategic voting and then examine-via a bimodal logic utilizing epistemic and strategizing modalities-the knowledge-theoretic properties of voting situations and note that unless the voter knows that it should vote strategically, and how, i.e., knows what the other voters' preferences are and that it should vote a certain preference P , the voter will not strategize. Our results suggest that opinion polls in election situations effectively serve as the first n − 1 stages in an n stage election.

Handbook of Granular Computing

Decision making is one of the most crucial and omnipresent human activities. Its essence is to find a best alternative (option, variant,. . .) from among some feasible (relevant, available,. . .) ones. An universal relevance of decision making has clearly triggered an intensive research, in many fields of science, and from many diverse perspectives: behavioral, psychological, cognitive, social, mathematical, economic, etc. This chapter belongs to a formal, mathematical direction aimed at a mathematical formalization of the human rational behavior and how decisions are made. Decision making in real world usually proceeds under multiple criteria, decision makers, stages, etc. and we consider the case of multiperson decision making, more specifically of a group type, practically from the perspective of social choice and voting, under some fuzification of preferences and majority. We assume that there is a set of individuals who provide their testimonies assumed to be preferences over the set of alternatives. The problem is to find a solution, i.e., an alternative (or a set of alternatives) which is best acceptable by the group of individuals as a whole. For a different point of departure, involving choice sets or utility functions, we may refer the interested reader to, e.g., Kim [1], Salles [2], etc. Group decision making has been plagued since its inception by negative results in that no 'rational' choice procedure satisfies all 'natural,' or plausible, requirements; by far the best known negative result is the so-called Arrow's impossibility theorem (cf. Arrow [3] or Kelly [4]), negative results due to Gibbard and Satterthwaite, McKelvey, Schofield, etc.-cf. Nurmi [5]. Their essence is that no matter which group choice procedure is employed, it would satisfy some plausible conditions but other equally plausible

Public Choice, 2018

This paper studies the collective decision-making processes of voters who have heterogeneous levels of rationality. Specifically, we consider a voting body consisting of both rational and sincere voters. Rational voters vote strategically, correctly using both their private information and the information implicit in other voters' actions to make decisions; sincere voters vote according to their private information alone. We first characterize the conditions under which the presence of sincere voters increases, reduces, or does not alter the probabilities of making correct collective decisions. We also discuss how the probabilities change when the incidence of sincere voters in the population varies. We then characterize the necessary and sufficient condition under which informational efficiency can be achieved when sincere voters coexist with rational voters. We find that when sincere voters are present, supermajority rules with high consensus levels are not as desirable as they are in rational voting models, as informational efficiency fails under such voting rules.

Ratio juris, 2004

Public Choice, 1969

This paper is a study in the theory of committees and elections. By a committee we will mean any group of people who arrive at a decision by means of voting. By a voting scheme I we will mean any method by which individual voting decisions are aggregated into committee decisions. Given various voting schemes we shall examine three techniques by which members may seek to manipulate committee decisions to their advantage: a) additions or deletions to the alternatives to be considered b) deliberate distortions of one's own voting preferences c) manipulation of the order in .which alternatives are voted upon, and shall prove some theorems about rational voting behavior when preferences are unidimensionally scalable.

American Political Science Review, 2002

In pairwise voting, when a simple majority rule produces a winner, that winner is robust to the minority's 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 spe...

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".

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.

Decisions in Economics and Finance

Many classic social preference (multiwinner social choice) correspondences are resolute only when two alternatives and an odd number of individuals are considered. Thus, they generally admit several resolute refinements, each of them naturally interpreted as a tie-breaking rule. A tie-breaking rule is compulsory every time a single final decision is needed. Unfortunately, using a tie-breaking rule on some social preference (multiwinner social choice) correspondence can dramatically compromise its properties. In particular, very often, the arithmetic relation between the number of alternatives and the number of voters does not allow to maintain both anonymity and neutrality. In those cases, the only possibility is to look at suitable different forms of symmetry that are coherent with the decision context. We find out conditions which make a social preference (multiwinner social choice) correspondence admit a resolute refinement fulfilling some weak versions of the anonymity and neutr...

Social Choice and Welfare, 2012

The book 'Voting and Collective Decision Making' by A. Laruelle and F. Valenciano provides a critical revision of the theoretical foundations of collective yes-or-no decisions. It is a study of the theory of bargaining and voting power, revolving around a fundamental question: given a committee, what voting rule should be used?

Electoral Studies, 1988

Two models, one due to Farquharson and the other to Niemi-Frank, attempt to account for sophisticated voting behaviour when the voters' preference orderings are common knowledge and communication among voters is impossible. Having subjected these two models to experimental testing, we have found them lacking. Hence, we propose a new model of sophisticated voting for 3alternative n-person non-cooperative games under the plurality procedure, which can be extended to other voting procedures and more than three alternatives.

This dissertation consists of three related chapters. The first chapter, which is written jointly with Lones Smith presents a dynamic model of deliberation by two privately informed individuals. Even by assuming the coarsest possible language to communicate information among members, it is shown that the decision is `almost instantaneous' when individuals have identical objectives. Despite the coarse syntax, the model also predicts that information aggregation can be quite effective. The second chapter asks the question under what circumstances can a static voting mechanism aggregate dispersed information of committee members. I argue that whenever the voters are able to cast multiple votes, the quality of the joint decision increases. However, voting mechanisms are intrinsically additive ways of aggregating private information. This, naturally, is not a binding constraint if the private information is conditionally independent. However, if the `meaning' of the private infor...