Aggregation of dichotomic preferences

Social Choice and Welfare, 1999

An Excess-Voting Function relative to a pro®le p assigns to each pair of alternatives xY y, the number of voters who prefer x to y minus the number of voters who prefer y to x. It is shown that any non-binary separable Excess-Voting Function can be achieved from a preferences pro®le when individuals are endowed with separable preferences. This result is an extension of Hollard and Le Breton (1996). Soc Choice Welfare (1999) 16: 159±167 Many thanks are due to Jean-FrancË ois Laslier and to two referees for their valuable remarks to improve this paper. I would like to thank Basudeb Chaudhuri for his careful reading.

2003

I present a general theorem on preference aggregation. This theorem implies, as corollaries, Arrow's Impossibility Theorem, Wilson's extension of Arrow's to non-Paretian aggregation rules, the Gibbard-Satterthwaite Theorem and Sen's result on the Impossibility of a Paretian Liberal.

Arthaniti: Journal Of Economic Theory And Practice, 2018

In this paper, we show that there does not exist any triple acyclic preference aggregation rule that satisfies Majority property, weak Pareto criterion and a version of a property due to Alan Taylor. We also show that there are non-dictatorial preference aggregation rules and in particular non-dictatorial social welfare functions which satisfy the weak Pareto criterion and Taylor's Independence of Irrelevant Alternatives. Further, we are able to obtain analogous results for preference aggregation functionals by suitably adjusting the desired properties to fit into a framework which uses individual utility functions rather than individual preference orderings. Our final result is a modest generalisation of Sen's version of Arrow's impossibility theorem which is shown to hold under our mild domain restriction.

Fuzzy Sets and Systems, 2005

In this paper we have analyzed the accomplishment of several consistency conditions in a real decision case. A group of students showed their intensities of preference among the alternatives by means of linguistic labels represented by real numbers. The absolute and relative fulfillments of some kinds of fuzzy transitivity properties have been studied for individual and collective preferences. Collective preferences have been obtained by means of a wide class of neutral and stable for translations aggregation rules, which transports reciprocity from individual preferences to the collective preference. We notice that, in the real case studied, the aggregate preferences reach higher consistency properties than individual preferences.

Journal of Mathematical Psychology, 2003

We study the topological properties of aggregation maps combining individuals' preferences over n alternatives, with preference expressed by a real-valued, n-dimensional utility vector u defined on an interval scale. Since any such utility vector is specified only up to arbitrary affine transformations, the space of utility vectors R n may be partitioned into equivalence classes of the form fau þ b1 j aAR þ 0 ; bARg: The quotient space, denoted T; is shown to be the union of the n À 2-dimensional sphere S ¼ S nÀ2 with the singleton f0g; which corresponds to indifference or null preference. The topology of T is non-Hausdorff, placing it outside the scope of most existing theory (e.g., J. Econom. Theory 31 (1983) 68). We then investigate the existence and nature of continuous aggregation maps under the four scenarios of allowing or disallowing null preference both in individual and in social choice, i.e. maps f : P Â ? Â P-Q with P; QAfT; Sg: We show that there exist continuous, anonymous, unanimous aggregation maps iff the outcome space includes the null point ðQ ¼ TÞ; and provide a simple well-behaved example for the case f : S Â ? Â S-T: Similar examples exist for f : T Â ? Â T-T; but these and all other maps have a property of always either over-or under-allocating influence to each voter (in a specific manner). We conclude that there exist acceptable aggregation rules if and only if null preference is allowed for the society but not for the individual. r

2015

We consider a decision maker that holds multiple preferences simultaneously, each with different strengths described by a probability distribution. Faced with a subset of available alternatives, the preferences held by the individual can be in conflict. Choice results from an aggregation of these preferences. We assume that the aggregation method is monotonic: improvements in the position of alternative x cannot displace x if it were originally the choice. We show that choices made in this manner can be represented by context-dependent utility functions that are monotonic with respect to a measure of the strength of each alternative among those available. Using this representation we show that any generic monotonic rule can generate an arbitrary choice function as we vary the distribution of preferences. Domain restrictions on the set of preferences (e.g. dual motivation models) or consistency restrictions on the aggregator across choice sets reduce the set of admissible behaviors. Applications to positive models of individual decision making with context effects and social choice are discussed.

We discuss the problem of preference aggregation when the reasons supporting a preference for x wrt to y and the ones against are distinct and have to be considered independently. We show how it is possible to generalise the concordance/discordance principle in preference aggregation and we apply it to the problem of aggregating preferences expressed under intervals.

Journal of Economic Theory, 2008

We provide a general impossibility theorem on the aggregation of preferences under uncertainty. We axiomatize in the Anscombe-Aumann setting a wide class of preferences, called rank-dependent additive preferences that includes most known models of decision under uncertainty as well as state-dependent versions of these models. We prove that aggregation is possible and necessarily linear if and only if (society's) preferences are uncertainty neutral. The latter means that society cannot have a non-neutral attitude toward uncertainty on a subclass of acts. A corollary to our theorem is that it is not possible to aggregate multiple prior agents, even when they all have the same set of priors. A number of extensions are considered.

Autonomous Agents and Multi-Agent Systems, 2011

Agents that must reach agreements with other agents need to reason about how their preferences, judgments, and beliefs might be aggregated with those of others by the social choice mechanisms that govern their interactions. The emerging field of judgment aggregation studies aggregation from a logical perspective, and considers how multiple sets of logical formulae can be aggregated to a single consistent set. As a special case, judgment aggregation can be seen to subsume classical preference aggregation. We present a modal logic that is intended to support reasoning about judgment aggregation scenarios (and hence, as a special case, about preference aggregation): the logical language is interpreted directly in judgment aggregation rules. We present a sound and complete axiomatisation. We show that the logic can express aggregation rules such as majority voting; rule properties such as independence; and results such as the discursive paradox, Arrow's theorem and Condorcet's paradox-which are derivable as formal theorems of the logic. The logic is parameterised in such a way that it can be used as a general framework for comparing the logical properties of different types of aggregation-including classical preference aggregation. As a case study we present a logical study of, including a formal proof of, the neutrality lemma, the main ingredient in a well-known proof of Arrow's theorem.

2016

A statistical criterion for evaluating the appropriateness of preference aggregation functions for a fixed group of persons is introduced. Specifically, we propose a method comparing aggregation procedures by relying on probabilistic information on the homogeneity structure of the group members’ preferences. For utilizing the available information, we give a minimal axiomatization as well as a proposal for measuring homogeneity and discuss related work. Based on our measure, the group specific probability governing the constitution of preference profiles is approximated, either relying on maximum entropy or imprecise probabilities. Finally, we investigate our framework by comparing aggregation rules in a small study.