Social Choice Theory

In the framework of ethical social choice theory, sustainability is justified by Efficiency and Equity as ethical axioms. These axioms correspond to the Suppes-Sen Grading principle. In technologies that are productive in a certain sense, the set of Suppes-Sen maximal utility paths is shown to equal the set of non-decreasing and efficient paths. Since any such path is sustainable, Efficiency and Equity can thus be used to deem any unsustainable path as ethically unacceptable. This finding is contrasted with results that seem to indicate that an infinite number of generations cannot be treated equally.

This paper provides a general framework to explore the possibility of agenda manipulationproof and proper consensus-based preference aggregation rules, so powerfully called in doubt by a disputable if widely shared understanding of Arrow's 'general possibility theorem'. We consider two alternative versions of agenda manipulation-proofness for social welfare functions, that are distinguished by 'parallel' vs. 'sequential' execution of agenda formation and preference elicitation, respectively. Under the 'parallel' version, it is shown that a large class of anonymous and idempotent social welfare functions that satisfy both agenda manipulation-proofness and strategy-proofness on a natural domain of single-peaked 'meta-preferences' induced by arbitrary total preference preorders are indeed available. It is only under the second, 'sequential' version that agenda manipulation-proofness on the same natural domain of single-peaked 'meta-preferences' is in fact shown to be tightly related to the classic Arrowian 'independence of irrelevant alternatives' (IIA) for social welfare functions. In particular, it is shown that using IIA to secure such 'sequential' version of agenda manipulation-proofness and combining it with a very minimal requirement of distributed responsiveness results in a characterization of the 'global stalemate' social welfare function, the constant function which invariably selects universal social indifference. It is also argued that, altogether, the foregoing results provide new significant insights concerning the actual content and the constructive implications of Arrow's 'general possibility theorem' from a mechanism-design perspective.

This note is to inform about a mistake in my paper . In that paper, I characterized strategy-proof, individually rational, budget-balancing, non-exploitative and non-bossy social choice functions for economies with one public good and one private good. I established as Theorem 3 (page 507) that a social choice function is strategy-proof, individually rational with respect to endowment, budget-balancing, nonexploitative and non-bossy if and only if it is a scheme of "semi-convex cost sharing determined by the minimum demand principle". I also exposed one example (Example 2, page 507) in order to emphasize that non-bossiness is indispensable for this characterization. I claimed that the social choice function in that example satisfies the above axioms except for non-bossiness, and is not a scheme of semi-convex cost sharing. However, the social choice function in the example is actually not strategy-proof, as shown in the simple discussion below. Therefore it is an open question whether or not a similar characterization theorem holds without non-bossiness.

Following Barberà, Sonnenschein, and Zhou (1991, Econometrica 59, 595-609), we study rules (or social choice functions) through which agents select a subset from a set of objects. We investigate domains on which there exist nontrivial strategy-proof rules. We establish that the set of separable preferences is a maximal domain for the existence of rules satisfying strategyproofness and no-vetoer.

This paper develops a unified physical framework for free will within the Information–Cognitive Compression Field (ICCF) paradigm. By integrating thermodynamic principles, the action-based formulation of physical laws, and informational inertia, we argue that free will can be rigorously defined as an emergent yet physically grounded property. Our model demonstrates that the exercise of free will is constrained by entropy exchange limits and scaling laws, leading to identifiable critical thresholds in both biological and civilizational systems. Using comparative anthropological data, cosmological energy bounds, and illustrative numerical estimates, we show that free will horizons can be mathematically formalized in analogy with causal horizons in physics. The theory suggests that while free will is not illusory, it is bounded by universal scaling constraints that govern all self-organizing structures. We conclude by proposing a set of testable predictions and outlining how this framework reshapes the dialogue between physics, philosophy, and the social sciences.

Proponents of Condorcet voting face the question of what to do in the rare case when no Condorcet winner exists. Recent work provides compelling arguments for the rule that should be applied in three-candidate elections, but already with four candidates, many rules appear reasonable. In this paper, we consider a recent proposal of a simple Condorcet voting method for Final Four political elections. Our question is what normative principles could support this simple form of Condorcet voting. When there is no Condorcet winner, one natural principle is to pick the candidate who is closest to being a Condorcet winner. Yet there are multiple plausible ways to define closeness, leading to different results. Here we take the following approach: identify a relatively uncontroversial sufficient condition for one candidate to be closer than another to being a Condorcet winner; then use other principles to help settle who wins in cases when that condition alone does not. We prove that our principles uniquely characterize the simple Condorcet voting method for Final Four elections. This analysis also points to a new way of extending the method to elections with five or more candidates that is simpler than an extension previously considered. The new proposal is to elect the candidate with the most head-to-head wins, and if multiple candidates tie for the most wins, then elect the one who has the smallest head-to-head loss. We provide additional principles sufficient to characterize this simple method for Final Five elections.

We consider different choice procedures such as scoring rules, rules, using majority relation, value function and tournament matrix, which are used in social and multi-criteria choice problems. We focus on the study of the properties that show how the final choice is changed due to changes of preferences or a set of feasible alternatives. As a result a theorem is provided showing which normative properties (rationality, monotonicity, non-compensability) are satisfied for the given choice procedures.

In 1953, and extended over the following two decades, John Harsanyi published a theorem suggesting that Bayesian rationality postulates together with interpersonal utility comparisons entail an average utilitarian theory. This article summarizes critique on key assumptions of his account. First, irrational and antisocial preferences entail undesirable consequences. Second, the von Neumann-Morgenstern utility function is a cardinal theory of utility. Third, rational, self-interested, and impartial parties choose acceptable moral principles. Fourth, the observer assigns an equal probability to all positions in society. Fifth, different observers have uniform extended preferences and no personal preferences. This summary is followed by a discussion of model extensions that aim at making welfare interpersonally comparable. These accounts are either based on Harsanyi's original process of 'imaginative empathy' or a process of 'deep imaginative empathy', including a conceptualization based on life years in perfect utility.

Today, group decision making in our democratic society uses the non-ranked method. What we need is an improved method that allows decision makers to indicate not only their chosen alternative, but also their order of preference by which all alternatives will be placed. We classify this as a particular Social Choice Function, where choice is a group decision-making methodology in an ideal democratic society that gives the expression of the will of the majority. We use the Eigenvector Function to obtain individual priorities of preferences and Borda's Function to obtain the Ranking or otherwise, the Group Choice. Our conclusions give rise to new directions for pervasive democracy with an innovative degenerative quantum scale to allow even for strong to very strong preferences.

Today, group decision making in our democratic society uses the non-ranked method. What we need is an improved method that allows decision makers to indicate not only their chosen alternative, but also their order of preference by which all alternatives will be placed. We classify this as a particular Social Choice Function, where choice is a group decision-making methodology in an ideal democratic society that gives the expression of the will of the majority. We use the Eigenvector Function to obtain individual priorities of preferences and Borda's Function to obtain the Ranking or otherwise, the Group Choice. Our conclusions give rise to new directions for pervasive democracy with an innovative degenerative quantum scale to allow even for strong to very strong preferences.

We study the aggregation of a couple's preferences over their respective jobs when they enter a centralized labor market jointly, such as the market for assigning hospital residencies to medical students. Usually in such markets couples need to submit joint preferences over pairs of jobs. Starting from two individual preference orderings over jobs, we first study the Lexicographic and the Rank-Based Leximin aggregation rules, and then propose a family of aggregation rules, the k-Lexi-Pairing rules, and provide an axiomatic characterization of these rules. The parameter k indicates the degree of selfishness for one partner (and altruism for the other partner), with the least selfish Rank-Based Leximin rule at one extreme and the most selfish Lexicographic rule at the other extreme. Since couples care about geographic proximity, we also identify a simple parametric family of preference aggregation rules which build on the k-Lexi-Pairing rules and reflect the couple's preference for togetherness.

BY SZILVIA PAPAI 1 give a characterization of the set of group-strategyproof, Pareto-optimal, and reallocation-proof allocation rules for the assignment problem, where individuals are assigned at most one indivisible object, without any medium of exchange. Although there are no property rights in the model, the rules satisfying the above criteria imitate a trading procedure with individual endowments, in which individuals exchange objects from their hierarchically determined endowment sets in an iterative manner. In particular, these assignment rules generalize Gale's top trading cycle procedure, the classical rule for the model in which each individual owns an indivisible good.

claims that another variant of her condition limiting arbitrage is necessary and su½cient for existence of equilibrium and nonemptiness of the core in an economy with short sales allowing half lines in indi¨erence surfaces. Her proof, however, is based on a proposition purporting to relate her notion of ``global cone'' (see for references) to the Page-Wooders ``increasing cone.'' In this paper, we present a counterexample showing that parts (i) and (ii) of Chichilnisky's proposition are false. Thus, Chichilnisky's claimed result is without proof. * The authors are grateful to Kenneth Arrow, Peter Hammond, and an anonymous referee for helpful comments. ** F. H. Page gratefully acknowledges ®nancial support from the RGC program at the University of Alabama. *** M. H. Wooders is indebted to the Social Sciences and Humanities Research Council of Canada for support. 1 Monteiro, Page, and Wooders (1997) discuss previous versions of her condition and, in particular, the global cones used in her previous conditions (see Sect. 1 below). 2 For example, her model does not allow an agent to have half lines in indi¨erence surfaces in some directions and no half lines in others.

Condorcet's voting method, as its extension known as the Kemeny-Young rule, is often seen as the incarnation of Rousseau's general will. But the Kemeny-Young rule has problems when cycles in the social ranking arise. In particular, it can lead to choose a "covered" alternative, i.e. one for which there are candidates with better performances in pairwise comparisons. On the other hand, the uncovered set, the set of all the alternatives that are not covered, puts limits to insincere votes of sophisticated voters under certain conditions. Basically, voting insincerelly for a non-preferred alternative in order to favor the actually preferred candidate would lead to the choice of an uncovered alternative. We argue that Rousseau's general will could be embodied in a different kind of rule than

We study a class of preference domains that satisfies the familiar properties of minimal richness, diversity and no-restoration. We show that a specific preference restriction, hybridness, has been embedded in these domains so that the preferences are single-peaked at the "extremes" and unrestricted in the "middle". We also study the structure of strategy-proof and unanimous Random Social Choice Functions on these domains. We show them to be special cases of probabilistic fixed ballot rules (introduced by Ehlers, ).

La presente investigación versa sobre cómo la noción de racionalidad, del individuo representativo de la teoría de la elección racional, que elige en un entorno administrativo, es incapaz de establecer generalizaciones de interacción social-solidaria: reflejados en la teoría de juegos y el teorema de imposibilidad de Arrow. Lo cual tiene explicación en el tipo de axiomas que debe cumplir un individuo racional, condición que trae consigo incompatibilidades entre estrategias competitivas y cooperativas. Que por el contrario, en un contexto culturalista si encuentra cabida la combinación de estrategias competitivas y cooperativas, llevando a acciones colectivas o de interacción social. Palabras clave: administración competitiva vs. administración solidaria, culturalismo, teoría de Juegos, teorema de imposibilidad de Arrow.

This paper presents a novel philosophical framework for addressing the persistent ontological incompatibility between General Relativity and Quantum Mechanics. Rather than pursuing the traditional unification approach, we propose a Contextual Stratification Model that reconceptualizes physical reality as a stratified structure where different theoretical frameworks operate within distinct ontological domains. This approach transforms the century-old conflict from an irreconcilable contradiction into a complementary plurality, offering a practical solution to what we term the "ontological crisis" in contemporary physics.

In this paper we develop on a geometric model of social choice among bundles of interdependent elements (objects). Social choice can be seen as a process of search for optima in a complex multidimensional space and objects determine a decomposition of such a space into subspaces. We present a series of numerical and probabilistic results which show that such decompositions in objects can greatly increase decidability, as new kind of optima (called local and u-local) are very likely to appear also in cases in which no generalized Condorcet winner exists in the original search space.

Marengo and the second author have developed in the last years a geometric model of social choice when this takes place among bundles of interdependent elements, showing that by bundling and unbundling the same set of constituent elements an authority has the power of determining the social outcome. In this paper we will tie the model above to tournament theory, solving some of the mathematical problems arising in their work and opening new questions which are interesting not only from a mathematical and a social choice point of view, but also from an economic and a genetic one. In particular, we will introduce the notion of u-local optima and we will study it from both a theoretical and a numerical/probabilistic point of view; we will also describe an algorithm that computes the universal basin of attraction of a social outcome in O(M 3 log M ) time (where M is the number of social outcomes).

Marengo and the second author have developed in the last years a geometric model of social choice when this takes place among bundles of interdependent elements, showing that by bundling and unbundling the same set of constituent elements an authority has the power of determining the social outcome. In this paper we will tie the model above to tournament theory, solving some of the mathematical problems arising in their work and opening new questions which are interesting not only from a mathematical and a social choice point of view, but also from an economic and a genetic one. In particular, we will introduce the notion of u-local optima and we will study it from both a theoretical and a numerical/probabilistic point of view; we will also describe an algorithm that computes the universal basin of attraction of a social outcome in O(M 3 log M ) time (where M is the number of social outcomes).

In this paper we develop on a geometric model of social choice among bundles of interdependent elements (objects). Social choice can be seen as a process of search for optima in a complex multidimensional space and objects determine a decomposition of such a space into subspaces. We present a series of numerical and probabilistic results which show that such decompositions in objects can greatly increase decidability, as new kind of optima (called local and u-local) are very likely to appear also in cases in which no generalized Condorcet winner exists in the original search space.

Marengo and the second author have developed in the last years a geometric model of social choice when this takes place among bundles of interdependent elements, showing that by bundling and unbundling the same set of constituent elements an authority has the power of determining the social outcome. In this paper we will tie the model above to tournament theory, solving some of the mathematical problems arising in their work and opening new questions which are interesting not only from a mathematical and a social choice point of view, but also from an economic and a genetic one. In particular, we will introduce the notion of u-local optima and we will study it from both a theoretical and a numerical/probabilistic point of view; we will also describe an algorithm that computes the universal basin of attraction of a social outcome in O(M 3 log M ) time (where M is the number of social outcomes).

In [MP08] L. Marengo and C. Pasquali 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. In this paper we extend and generalize this approach ...

Social choice function or voting procedure is one of the crucial concepts in the domain of political sciences. It maps individuals' preferences over a set of candidates to some subset (possibly one-element) of the candidates who can be thought as the winners of an election procedure. The paper is aimed at applications of formal concept analysis methods to study of social choice functions. We will construct concept lattices over selected set of social choice functions characterized by possessing some properties deemed as important from the point of view of political sciences. We will discuss issues connected with reducibility of both objects and attributes, irreducibility of object concepts as well as attribute concepts and attribute implications. We will discuss also the shape of the constructed concept lattice of social choice functions which in some part is exceptionally regular from the perspective of the lattice theory.

We consider the problem of combining ranking results from various sources. In the context of the Web, the main applications include building meta-search engines, combining ranking functions, selecting documents based on multiple criteria, and improving search precision through word associations. We d e v elop a set of techniques for the rank aggregation problem and compare their performance to that of well-known methods. A primary goal of our work is to design rank aggregation techniques that can e ectively combat \spam," a serious problem in Web searches. Experiments show that our methods are simple, e cient, and e ective.

We report the results of elections conducted in a laboratory setting, modelled on a threecandidate example due to Borda. By paying subjects conditionally on election outcomes, we create electorates with (publicly) known preferences. We compare the results of experiments with and without non-binding pre-election polls under plurality rule, approval voting, and Borda rule. We also refer to a theory of voting "equilibria," which makes sharp predictions concerning individual voter behavior and election outcomes. We find that Condorcet losers occasionally win regardless of the voting rule or presence of polls. Duverger's law (which asserts the predominance of two candidates) appears to hold under plurality rule, but close three-way races often arise under approval voting and Borda rule. Voters appear to poll and vote strategically. In elections, voters usually cast votes that are consistent with some strategic equilibrium. By the end of an election series, most votes are consistent with a single equilibrium, although that equilibrium varies by experimental group and voting rule.

Cet article propose une refondation des mécanismes de décision collective à partir d'une approche computationnelle du vote, fondée non plus sur des préférences ordinales rigides, mais sur l'expression combinée du soutien et de l'approbation. En mobilisant les outils de la théorie du choix social, de l'économie du bien-être et du design procédural, nous proposons une méthode de fabrication de procédures de décisions collectives respectant les cinq critères d'Arrow et orientées vers la production du bien-être collectif. Du point de vue du marketing, cette recherche ouvre des perspectives concrètes pour le design d'interfaces de choix, la construction d'expériences participatives et l'optimisation des décisions en environnement incertain, qu'il s'agisse de plates-formes numériques, de panels consommateurs ou de dispositifs de gouvernance collective. Nous posons ainsi les fondements d'un paradigme décisionnel de l'intelligence collective, au croisement des sciences sociales, de la computation et de l'économie comportementale.

Table of Contents 1. Introduction 2. Literature Review: Theoretical and Empirical Perspectives 3. Data and Methodology 4. Analysis of Key Variables 5. Predictive Modeling Approach 6. Discussion on Electoral Success, Populism, and Radicalization 7. Policy Implications and Future Research Directions 8. Conclusion

Voters determine their preferences over alternatives based on cases (or arguments) that are raised in the public debate. Each voter is characterized by a matrix, measuring how much support each case lends to each alternative, and her ranking is additive in cases. We show that the majority vote in such a society can be any function from sets of cases to binary relations over alternatives. A similar result holds for voting with quota in the case of two alternatives.

In this paper, we study the strategy-proofness properties of the randomized Condorcet voting system (RCVS). Discovered at several occasions independently, the RCVS is arguably the natural extension of the Condorcet method to cases where a deterministic Condorcet winner does not exists. Indeed, it selects the always-existing and essentially unique Condorcet winner of lotteries over alternatives. Our main result is that, in a certain class of voting systems based on pairwise comparisons of alternatives, the RCVS is the only one to be Condorcet-proof. By Condorcet-proof, we mean that, when a Condorcet winner exists, it must be selected and no voter has incentives to misreport his preferences. We also prove two theorems about group-strategy-proofness. On one hand, we prove that there is no group-strategyproof voting system that always selects existing Condorcet winners. On the other hand, we prove that, when preferences have a one-dimensional structure, the RCVS is group-strategy-proof.

In this paper, we study the strategy-proofness properties of the randomized Condorcet voting system (RCVS). Discovered at several occasions independently, the RCVS is arguably the natural extension of the Condorcet method to cases where a deterministic Condorcet winner does not exists. Indeed, it selects the always-existing and essentially unique Condorcet winner of lotteries over alternatives. Our main result is that, in a certain class of voting systems based on pairwise comparisons of alternatives, the RCVS is the only one to be Condorcet-proof. By Condorcet-proof, we mean that, when a Condorcet winner exists, it must be selected and no voter has incentives to misreport his preferences. We also prove two theorems about group-strategyproofness. On one hand, we prove that there is no group-strategy-proof voting system that always selects existing Condorcet winners. On the other hand, we prove that, when preferences have a one-dimensional structure, the RCVS is group-strategy-proof.

The geometric median, an instrumental component of the secure machine learning toolbox, is known to be effective when robustly aggregating models (or gradients), gathered from potentially malicious (or strategic) users. What is less known is the extent to which the geometric median incentivizes dishonest behaviors. This paper addresses this fundamental question by quantifying its strategyproofness. While we observe that the geometric median is not even approximately strategyproof, we prove that it is asymptotically α-strategyproof : when the number of users is large enough, a user that misbehaves can gain at most a multiplicative factor α, which we compute as a function of the distribution followed by the users. We then generalize our results to the case where users actually care more about specific dimensions, determining how this impacts α. We also show how the skewed geometric medians can be used to improve strategyproofness.

Several rules for social choice are examined from a unifying point of view that looks at them as procedures for revising a system of degrees of belief in accordance with certain specified logical constraints. Belief is here a social attribute, its degrees being measured by the fraction of people who share a given opinion. Different known rules and some new ones are obtained depending on which particular constraints are assumed. These constraints allow to model different notions of choiceness. In particular, we give a new method to deal with approval-disapproval-preferential voting.

A method is given for quantitatively rating the social acceptance of different options which are the matter of a preferential vote. The proposed method is proved to satisfy certain desirable conditions, among which there is a majority principle, a property of clone consistency, and the continuity of the rates with respect to the data. One can view this method as a quantitative complement for a qualitative method introduced in 1997 by Markus Schulze. It is also related to certain methods of one-dimensional scaling or cluster analysis.

A recent study by Hammond (2007) delves into scoring methods in athletic events as a way of illuminating social choice problems. Hammond's study indicates, using data from a girls' high school cross-country meet in Michigan, that the current scoring method for high school cross-country is plagued by two problems related to inconsistency and ambiguity in the results -problems that can be characterized as violations of the principles of independence from irrelevant teams (IIT) and transitivity. Our note supports and extends Hammond's study by examining the results from both the 2008 and 2009 NCAA Division I men's cross-country championships, wherein the types of scoring problems found by Hammond are present. Unlike high school-level cross-country, however, we show that salaries, bonuses, and budgets at the collegiate level can be substantial, so that any inconsistencies and ambiguities in the scoring mechanism can be quite costly for individuals and institutions.

Consider a divisible resource or cost that is to be fairly distributed among a group, and suppose that various members of the group have different opinions about what a fair distribution might be. We exhibit a class of mechanisms that aggregate individual opinions into a group opinion, and which have the property that no one can manipulate the size of his own share. There is a unique such mechanism that satisfies a variant of Arrow's conditions for social choice functions. We illustrate its application to distributing dues among the member countries of IIASA. Other potential applications include distributing shares in formerly state-owned enterprises, and in allocating voting power among different states or regions in a federal system of government.

Comparisons between utilities pose a pressing problem if, while incapable of being grounded, they are required in ethical deliberation. My aim is to consider whether there are epistemological impediments to implementing such ethical choices. Can we find ourselves being persuaded of the ethical need to compare utilities of different individuals, yet unable to do so because the comparisons cannot be warranted? I argue that the problem cannot arise; no plausible moral principle will invoke magnitudes which are inscrutable.

The problem of truth discovery, i.e., of trying to find the true facts concerning a number of objects based on reports from various information sources of unknown trustworthiness, has received increased attention recently. The problem is made interesting by the fact that the relative believability of facts depends on the trustworthiness of their sources, which in turn depends on the believability of the facts the sources report. Several algorithms for truth discovery have been proposed, but their evaluation has mainly been performed experimentally by computing accuracy against large datasets. Furthermore, it is often unclear how these algorithms behave on an intuitive level. In this paper we take steps towards a framework for truth discovery which allows comparison and evaluation of algorithms based instead on their theoretical properties. To do so we pose truth discovery as a social choice problem, and formulate various axioms that any reasonable algorithm should satisfy. Along the...

Ranking the participants of a tournament has applications in voting, paired comparisons analysis, sports and other domains. In this paper we introduce bipartite tournaments, which model situations in which two different kinds of entity compete indirectly via matches against players of the opposite kind; examples include education (students/exam questions) and solo sports (golfers/courses). In particular, we look to find rankings via chain graphs, which correspond to bipartite tournaments in which the sets of adversaries defeated by the players on one side are nested with respect to set inclusion. Tournaments of this form have a natural and appealing ranking associated with them. We apply chain editing – finding the minimum number of edge changes required to form a chain graph – as a new mechanism for tournament ranking. The properties of these rankings are investigated in a probabilistic setting, where they arise as maximum likelihood estimators, and through the axiomatic method of ...

Social choice theory addresses how to aggregate individual preferences, values, and welfare into collective decisions. It aims to answer the question of how to best represent a society's preferences based on the individual preferences of its members. Arrow's Impossibility Theorem stands as a critical milestone in social choice theory, illustrating the challenges and limitations in creating a fair and rational collective decision-making process.

We use Stein's method to prove a generalization of the Lindeberg-Feller CLT providing an upper and a lower bound for the superior limit of the Kolmogorov distance between a normally distributed random variable and the rowwise sums of a rowwise independent triangular array of random variables which is asymptotically negligible in the sense of Feller. A natural example shows that the upper bound is of optimal order. The lower bound improves a result by Andrew Barbour and Peter Hall.

We use Stein's method to prove a generalization of the Lindeberg-Feller CLT providing an upper and a lower bound for the superior limit of the Kolmogorov distance between a normally distributed random variable and the rowwise sums of a rowwise independent triangular array of random variables which is asymptotically negligible in the sense of Feller. A natural example shows that the upper bound is of optimal order. The lower bound improves a result by Andrew Barbour and Peter Hall.

What do we know? Data sources, simple tools. Analytical approaches and experiments Amiel and Cowell (1999), DeNavas-Walt et al. (2005), Kroll and Davidovitz (2003) 2 Welfare analysis of distribution Income, personal welfare, utility The basis for redistribution Risk and welfare

We study Random Social Choice Functions (or RSCFs) in a standard ordinal mechanism design model. We introduce a new preference domain called a hybrid domain which includes as special cases as the complete domain and the single-peaked domain. We characterize the class of unanimous and strategy-proof RSCFs on these domains and refer to them as Restricted Probabilistic Fixed Ballot Rules (or RPFBRs). These RSCFs are not necessarily decomposable, i.e., cannot be written as a convex combination of their deterministic counterparts. We identify a necessary and sufficient condition under which decomposability holds for anonymous RPFBRs. Finally, we provide an axiomatic justification of hybrid domains and show that every connected domain satisfying some mild conditions is a hybrid domain where the RPFBR characterization still prevails.

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