Manipulation in elections with uncertain preferences

In a large electorate it is natural to consider voters’ preference profiles as frequency distributions over the set of all possible preferences. We assume coherence in voters’ preferences resulting in accumulation of voters preferences. We show that such distributions can be studied via superpositions of simpler so called unimodal distributions. At these, it is shown that all well-known rules choose the mode as the outcome. We provide a set of sufficient conditions for a rule to have this trait of choosing the mode under unimodal distributions. Further we show that Condorcet consistent rules, Borda rule, plurality rule are robust under tail-perturbations of unimodal distributions.

This paper studies coalitional strategy-proofness of social choice correspondences that map preference profiles into sets of alternatives. In particular, we focus on the Pareto rule, which associates the set of Pareto optimal alternatives with each preference profile, and examine whether or not there is a necessary connection between coalitional strategy-proofness and Pareto optimality. The definition of coalitional strategy-proofness is given on the basis of a max–min criterion. We show that the Pareto rule is coalitionally strategy-proof in this sense. Moreover, we prove that given an arbitrary social choice correspondence satisfying the coalitional strategy-proofness and nonimposition, all alternatives selected by the correspondence are Pareto optimal. These two results imply that the Pareto rule is the maximal correspondence in the class of coalitionally strategy-proof and nonimposed social choice correspondences.

We introduce a new criterion, order symmetry, for assignment mechanisms that match n objects to n agents having ordinal preferences over the objects. An assignment mechanism is order-symmetric with respect to a given probability measure over preference profiles if every agent has equal probability of receiving their favorite object, equal probability of receiving their second favorite, and so on. Crucially, and unlike other fairness notions such as anonymity or envy-freeness, order symmetry can be satisfied by discrete assignment mechanisms when associated with a sufficiently symmetric probability measure. It can also be interpreted as a criterion of procedural fairness or fairness under uncertainty. Furthermore, it can be achieved without sacrificing other desirable axiomatic properties satisfied by existing mechanisms. In particular, we show that it can be achieved in conjunction with strategyproofness and efficiency by the Top Trading Cycles mechanism, but not by Serial Dictatorship. We also use the lens of order symmetry to improve the fairness of existing mechanisms with no loss in social welfare, focusing on the widely used family of Boston mechanisms. In addition to theoretical results, we present simulations using data from the Mallows distribution over its full range of parameters, which show an improvement in fairness even on probability measures for which full order symmetry is impossible.

Leading theories of transitions from single-party dominant systems begin with economic crisis, the party's loss of patronage resources, and elite-level defections. The multiparty elections that are then held exert no independent effect, but instead register neutrally the party's decline and the democratization of politics. This article, however, shifts attention from the dominant party to citizens and elections in noncrisis conditions. It argues that citizens assess on key dimensions the dominant party's legitimacy or worthiness of support. Further, where they grow critical of its policy outputs, they scrutinize more closely its conformity to procedures. And as they anticipate that their voting preferences will be thwarted by electoral manipulations, they vote in protest, perhaps producing a “liberalizing electoral outcome.” Elections, then, do not simply indicate the dominant party's decline. By deepening alienation, they help citizens to cause it. Analysis is set in Malaysia, long an exemplar of single-party dominance, but recently a case in which the government was dealt a striking electoral setback.

Distance-based and ad hoc consensus models in ordinal preference ranking

This article considers social welfare functions for which the set of alternatives is the two-dimensional nonnegative orthant and for which individuals can have any strictly monotonic, linear preference ordering. A Paretian generalized median social welfare function is defined by augmenting the n individuals in society with n — 1 phantom individuals each of whom has a fixed weakly monotonic, linear ordering and, for each profile of preferences, choosing the social preference to be the linear preference with slope equal to the median of all 2n — 1 individual slopes. Bossert and Weymark (1992) showed that the class of Paretian generalized median social welfare functions is characterized by anonymity, weak Pareto, and binary independence of irrelevant alternatives if the social preferences are restricted to be strictly monotonic, linear orderings. In this article we show that the monotonicity and linearity assumptions on social preferences can be weakened to continuity if we add an intra-profile neutrality condition.

We extend the single-crossing property to tree networks to facilitate its application in network games. It is equivalent to intermediate preferences and order restriction (also extended to networks). Moreover, to facilitate broader applications in real world cases and simulations, we develop algorithms that answer the following two questions. Given a preference profile, can we construct a tree graph that supports single-crossing? Given a set of alternatives, can we generate single-crossing preference profiles with associated tree graphs?

Limits of acyclic voting

If is a set of social alternatives, a social choice rule (SCR) assigns a subset of A to each potential profile of individuals' preferences over A, where the subset is interpreted as the set of 'welfare optima.' A game form (or 'mechanism') implements the social choice rule if, for any potential profile of preferences, (1) any welfare optimum can arise as a Nash equilibrium of the game form (implying, in particular, that a Nash equilibrium exists) and, (2) all Nash equilibria are welfare optimal. The main result of this paper establishes that any SCR that satisfies two properties - monotonicity and no veto power--can be implemented by a game form if there are three or more individuals. The proof is constructive.

We study the House Allocation problem (also known as the Assignment problem), i.e., the problem of allocating a set of objects among a set of agents, where each agent has ordinal preferences (possibly involving ties) over a subset of the objects. We focus on truthful mechanisms without monetary transfers for finding large Pareto optimal matchings. It is straightforward to show that no deterministic truthful mechanism can approximate a maximum cardinality Pareto optimal matching with ratio better than 2. We thus consider randomized mechanisms. We give a natural and explicit extension of the classical Random Serial Dictatorship Mechanism (RSDM) specifically for the House Allocation problem where preference lists can include ties. We thus obtain a universally truthful randomized mechanism for finding a Pareto optimal matching and show that it achieves an approximation ratio of eovere-1. The same bound holds even when agents have priorities (weights) and our goal is to find a maximum weight (as opposed to maximum cardinality) Pareto optimal matching. On the other hand we give a lower bound of 18 over 13 on the approximation ratio of any universally truthful Pareto optimal mechanism in settings with strict preferences. In the case that the mechanism must additionally be non-bossy, an improved lower bound of eovere-1 holds. This lower bound is tight given that RSDM for strict preference lists is non-bossy. We moreover interpret our problem in terms of the classical secretary problem and prove that our mechanism provides the best randomized strategy of the administrator who interviews the applicants.

Observational learning occurs when privately informed individuals sequentially choose among finitely many actions after seeing predecessors’ choices. We summarise the general theory of this paradigm: belief convergence forces action convergence; specifically, copycat ‘herds’ arise. Also, beliefs converge to a point mass on the truth exactly when the private information is not uniformly bounded. This subsumes two key findings of the original herding literature: With multinomial signals, cascades occur, where individuals rationally ignore their private signals, and incorrect herds start with positive probability. The framework is flexible – some individuals may be committed to an action, or individuals may have divergent cardinal or even ordinal preferences.

Philippine presidential elections have traditionally been characterized by the dominance of political popularity, populism, and financial interests, often marred by incidents of violence and electoral fraud. In this context, higher education is recognized as a pivotal tool for mitigating voter naivety and fostering informed political engagement. This study seeks to assess the preferences of voters, specifically 108 students from BiPSU (the research population), and to identify the significant sources of information that influence their decision-making about the election.

The theory of fuzzy sets has been applied to social choice primarily in the contexts where one is given a set of individual fuzzy preference relations and the aim is to find a non-fuzzy choice set of winners or best alternatives. We discuss the problem of composing multi-member deliberative bodies starting from a set of individual fuzzy preference relations. We outline methods of aggregating these relations into a measure of how well each candidate represents each voter in terms of the latter's preferences. Our main goal is to show how the considerations discussed in the context of individual non-fuzzy complete and transitive preference relations can be extended into the domain of fuzzy preference relations.

This paper develops a matrix-measure of multivariate risk aversion which is related to a notion of risk premium and states the restrictions that must be imposed upon the matrix-measures of two utility functions in order that one require a higher risk premium than another for every small multivariate risk. A necessary and sufficient condition for comparability of global attitude towards risk is that the local restrictions hold over the entire domain. The usefulness of the measures of risk aversion is discussed within the context of a multivariate risk-sharing problem. UNIVARIATE MEASURES OF ABSOLUTE and relative risk aversion were introduced in the seminal works of Pratt [8] and Arrow [1], and have since become indispensable tools for the analysis of risk bearing in situations involving unidimensional risks. Recent years witnessed numerous attempts to generalize various aspects of the Pratt-Arrow notions to the case of multivariate risk (Kihlstrom and Mirman [6], Keeney [5], Duncan [2], Paroush [7], and Stiglitz [9]). The univariate case is qualitatively different from the multivariate case in that the ordinal preferences of all decision makers are identical, whereas in the multivariate case the preference orderings may differ among decision makers. This fact has two important consequences. First, while the analysis of risk bearing in situations involving univariate risks turns out to depend solely upon the cardinal properties of the function representing the ordinal preferences of the decision makers involved, in situations involving multivariate risks, the ordinal preferences themselves play an important role in addition to that of the function representing them. Second, in the univariate case the local measure of absolute risk aversion permits a complete ordering of individuals according to the relation least as risk averse as, whereas in the multivariate case such ordering is not in general independent of the specific risk under consideration. Pratt [8] has shown that the univariate measure of absolute risk aversion satisfies a formal relation to a number which has the interpretation of risk premium. In this study I introduce a matrix measure of absolute multivariate risk aversion which satisfies a similar formal criterion. It should be noted at the outset, however, that in the multivariate case the risk premium may be regarded as a vector of commodities (see, for example, Duncan [2, 3]), and interpersonal comparison of risk aversion is not directional independent. I.e., the ranking of risk

2x2 games with uncertain ordinal preferences