Abstract: The main purpose of the paper is to provide a unified framework within which normatively significant equality indices can be derived from social welfare orderings. The paper contains a functional representation of the class of social evaluation functions generating relative equality indices.

Abstract: By changing the choice of a positional voting method, different election rankings can result from a fixed profile. A geometric theory is developed to explain why this occurs, to completely characterize all possible sets of rankings that can arise in this manner, to determine the number of rankings and other properties of these sets of rankings, to design profiles that cause the different conclusions, to develop elementary tools to analyze actual data, and to compare new types of social choice solutions that are based on the set of rankings admitted by a profile. A secondary theme is to indicate how results for voting theory can be obtained with (relative) ease when they are analyzed with a geometric approach.

Abstract: This paper consideres the problem of designing “better” mechanisms whose Nash allocations coincide with constrained Walrasian allocations for non-neoclassical economies under the minimal possible assumptions. We show that no assumprions on preferences are needed for feasible and continuous implementation of the constrained Walraisan correspondence. Further, under the monotonicity assumption, we present a mechanism that is completely feasible and continuous. Hence, no continuity and convexity assumptions on preferences are required, and preferences may be nontotal or nontransitive. Thus, this paper gives a somewhat positive answer to the question raised in the literature by showing that, even for non-neoclassical economies, there are “incentive-compatible”, “privacy preserving”, and “well-behaved” mechanisms which yield Pareto-efficient and individually rational allocations at Nash equilibria.

Abstract: In this paper we describe a simple model of individual voting behavior and present its implications for the candidate positioning problem under both vote and plurality maximization. Under our assumptions, some voters at the extremes of the ideological spectrum typically will not vote because they are alienated by the equilibrium location of candidates. There will also be some voters in the middle of the ideological spectrum who will not vote because they are indifferent between the equilibrium locations of the candidates. Both the abstention from alienation and from indifference arise explicitly from utility maximization. Once we allow for alienation and indifference, the two alternative candidate objective functions (vote maximization and plurality maximization) yield different outcomes. In particular, we show that under vote maximization the Median Voter (or Minimum Differentiation) outcome will not arise. On the other hand, under plurality maximization, the Median Voter outcome may or may not hold, depending on the distribution of voter preferences.

Abstract: Existence theorems for envy-free and efficient allocations are derived for economies with public goods. For economies with an arbitrary but finite number of private and public goods, an adaptation of the existence proof of Svensson for private good economies is used. For economies with one private and one public good, a case often studied in theory and applications, two more direct proofs are given, using different conditions and taking advantage of the particularly simple structure of the set of envy-free allocations in this case. These proofs are also shown to apply to the case of excludable public goods with congestion.

Abstract: This paper develops a Coase-like solution of the problem of inducing Pareto optimal behavior in the presence of reciprocal externalities. In place of Coasean direct compensation between the parties to an externality problem, actors strategically match each other's externality-producing activity, and thus induce counterparts to internalize the external benefits or costs of their actions. The analysis suggests a general framework for analyzing social interactions in the presence of reciprocal externalities. As an application of the theory, a solution of the duopoly problem is noted.

Abstract: The objective of this paper is to consider the following question. Does the presence of increasing returns introduce a fundamental trade-off between equity and efficiency objectives? We show that if the no-envy notion of Foley (1967) is taken as the equity criterion and Pareto optimality as the efficiency criterion, then the answer is yes; there exist economies with increasing returns and well-behaved preferences (and no agent-specific inputs) in which there do not exist any envy-free and Pareto optimal allocations. We also propose a weakening of the no-envy criterion and prove that this weaker equity notion is compatible with Pareto optimality in general non-convex economies.

Abstract: This paper deals with the topological approach to social choice theory initiated by Chichilnisky. We study several issues concerning the existence and uniqueness of Chichilnisky rules defined on preference spaces. We show that on topological vector spaces the only additive, anonymous, and unanimous aggregation n-rule is the convex mean. We study the case of infinite agents and show that an infinite Chichilnisky rule might be considered as the limit of rules for finitely many agents. Finally, we show that under some restrictions on the preference space, the existence of a Chichilnisky rule for every finite case implies the existence of a weak Chichilnisky rule for the infinite case.

Abstract: The yolk, an important concept in the spatial model of voting, is defined in two dimensions as the smallest circle intersecting all median lines. In the literature one finds the assumption that the limiting median lines, i.e., those that pass through two voter ideal points, suffice to determine the yolk. Counterex-amples are given here which invalidate this assumption.

Abstract: Beliefs in the impossibility of interpersonal comparison of welfare and the unacceptability of utilitarianism are based on a non-materialist solution to the theory of mind, i.e. on the existence of a soul. The compellingness of the theory of evolution and some discoveries in brain sciences render (philosophical) materialism very persuasive. The acceptance of materialism implies the negation of free will, non-significance of the self (no substantial reason to care much more about the welfare of one's own future self than the welfare of others), possibility of interpersonal comparison of welfare, compellingness of utilitarianism, and the possibility of conscious machines. Searle's argument on the impossibility of rigorous social sciences is however rejected.

Abstract: Motivated by certain paradoxa that have been discussed in the literature (Ostrogorski paradox), we prove an impossibility theorem for two-stage aggregation procedures for discrete data. We consider aggregation procedures of the following form: The whole population is partitioned into subgroups. First we aggregate over each subgroup, and in a second step we aggregate the subgroup aggregates to obtain a total aggregate. The data are either dichotomous (1 — 0; yes-no) or take values in a finite ordered set of possible attributes (e.g., exam grades A, B,...F). Examples are given by multistage voting procedures (indirect democracy, federalism), or by the forming of partial grades and overall grades in academic examinations and similar evaluation problems (sports competitions, consumer reports). It is well known from standard examples that the result of such a two-stage aggregation procedure depends, in general, not only on the distribution of attributes in the whole population, but also on how the attributes are distributed across the various subgroups (in other words: how the subgroups are defined). This dependence leads to certain “paradoxa”. The main result of the present paper is that these paradoxa are not due to the special aggregation rules employed in the examples, but are unavoidable in principle, provided the aggregators satisfy certain natural assumptions. More precisely: the only aggregator functions for which the result of a two-stage (a fortiori: multi-stage) aggregation does not depend on the partitioning are “degenerate” aggregators of the following form: there exists a partial order (“dominance”) on the set of possible attributes such that the aggregate over any collection of data is always equal to the supremum (w.r.t. dominance) of the attributes occurring in the data, regardless of the relative frequnencies of these occurrences. In the voting context, degeneracy corresponds to the unanimity principle. Our theorem is true for arbitrary partitionings of arbitrary (finite) sets and generalizes the results of Deb & Kelsey (for the matrix case with dichotomous variables and majority voting) to general two-stage aggregation procedures for attributes belonging to a finite ordered set. The general result is illustrated by some examples.

Abstract: This paper considers solutions to distribution problems defined on economic environments. It shows that there is a unique resource-egalitarian and symmetric solution that proposes always Pareto optimal allocations and satisfies Inidivual Restricted Monotonicity; this property requires the poor people of the society to be strictly better-off when social resources increase and the initial outcome is a welfare unequal position. That unique solution is the lexicographic extension of the maxmin criterion.

Abstract: Craven's conjecture says that 2n−1 is the maximum number of linear orders on {1, 2,...n} that simultaneously satisfy certain restrictions on three-element subsets of {1, 2,...n}. This is true for n=3, but the maximum exceeds 2n−1 for n≧4. There is a set of nine linear orders on {1, 2, 3, 4} that satisfy the restrictions. As n gets large, the ratio of the size of the maximum satisfying set to 2n−1 approaches infinity.

Abstract: In two-dimensional Euclidean spatial voting models the yolk is the smallest circle which intersects all median lines It has been assumed that limiting median lines, which intersect two voter ideal points, are sufficient to determine the yolk but recently counter examples have been reported This note describes the impact of those findings on the results of computation of the location and size of yolk

Abstract: This is the first of three papers introducing a theory for positional voting methods that determines all possible election rankings and relationships that ever could occur with a profile over all possible subsets of candidates for any specified choices of positional voting methods. As such, these results extend to all positional voting systems what was previously possible only for the Borda Count and the plurality voting systems. In this first part certain mathematical symmetries based on neutrality are used 1) to generalize the basic properties that cause the desired features of the Borda Count and 2) to describe classes of positional voting methods with new types of election relationships among the election outcomes. Some of these relationships generalize the well-known results about the positioning of a Condorcet winner/loser within a Borda ranking, but now it is possible for the Condorcet loser, rather than the winner, to have the advantage to win certain positional elections. Included among the results are axiomatic characterizations of many positional voting methods.

Abstract: Recent work shows that, in theory scoring methods are very sensitive to the scoring points used. I analyze the results of Most Valuable Player voting in baseball as a test of the practical relevance of this work. I find that Most Valuable Player rankings are indeed quite dependent on the particular scoring points in use.

Abstract: Place a voter v in the plane and scatter additional voters at random about v. What are v's chances of being undominated? When the number of voters, n, is even, this probability is known to be nonzero [5]. Here we prove that the exact probability is 2−(n−2).

Abstract: Given two players whose declarations about their private preferences are to be used in enforcing imputations, i.e. individually rational Pareto optima according to the declared preference profile, the Nash equilibria of the revelation game so defined always induce individually rational outcomes according to the true preferences, and for all such outcomes there is (and we construct) a Nash equilibrium declaration of preferences which induces precisely that outcome.

Abstract: It is well known that the transfer and advantageous reallocation paradoxes cannot occur at a Walrasian stable equilibrium in a two agent economy. In an influential recent paper Chichilnisky provided an example of the transfer paradox in the context of a globally Walrasian stable three agent economy. It is evident, though, that the paradoxes depend on the underlying data-tastes, preferences and net export positions-of the economy. This paper characterizes and generalizes the transfer and advantageous reallocation paradoxes: necessary and sufficient conditions on the underlying data of a globally Walrasian stable economy for the occurence of each of these paradoxes are established; the key role of the third agent in generating these paradoxes is clarified.

Abstract: When a group of decision makers with common interests faces a dichotomous choice, the task of deciding may be delegated to a committee consisting of a subset of the original group. This procedure is called a restricted majority decision rule. If each member of the original group is characterized by the probability of his deciding correctly, the expected utility from the decision is determined by which members are appointed to the committee. The conditions between enabling the comparison of alternative restricted majority rules are based on the voting profiles of the decision makers. The purpose of the current study is to propose an algorithm for identifying the optimal restricted majority rule amongst all restricted majority rules.

Abstract: We consider a social situation where individuals choose one or some alternative(s) from a set of feasible alternatives. When one alternative is socially chosen, each individual must share the cost for it according to an exogenously given sharing rule. Individuals are allowed to collude among themselves through money transfers. As the mechanism of choosing a social alternative, we consider the cost share equilibrium and a voting game. The cost share equilibrium is an allocation where each individual maximizes his/her utility independently and where unanimity is still maintained. We will show the equivalence between the set of all equilibrium allocations and the core of the voting game with compensation.

Abstract: A social welfare function satisfying Arrow's independence axiom is constant or authoritarian if it generates continuous and transitive social preferences over the space of allocations of public and private goods, and individual preferences have the classical economic properties. The social welfare function will be oligarchial if it generates continuous and quasitransitive social preferences and satisfies a weak version of the Pareto criterion in addition to the independence axiom.

Abstract: Following the results of Nakamura (1979) and Muto (1984), we derive, for a given proper voting game G, the upper bound on the size of the space of alternatives, which guarantees that the core constitutes a von Neumann-Morgenstern solution for any profile of voter's preferences. In particular, we show that if the space of alternatives consists of more than two elements, then, in general, the core is not a von Neumann-Morgenstern solution.

Abstract: An elementary proof of a theorem on two-person Nash implementable choice functions is provided.

Abstract: The Condorcet efficiency of Pairwise Proportional Lottery Rules (PPLR) is considered under various assumptions concerning the likelihood that given voters' preference profiles are observed on three alternatives. Representations are developed for the expected Condorcet efficiency under impartial culture, impartial anonymous culture, and a generalization to Polya-Eggenberger distributions. PPLR is shown to be equivalent to a random selection process in the limit of voters under impartial culture. However, relatively small increases in social homogeneity, as measured by Kendall's Coefficient of Concordance, cause significant increases in the Condorcet efficiency of PPLR.

Abstract: The Kemeny distance for preference orderings is used to determine individual rankings of social preferences. Based on this distance function, the strategy-proofness of social welfare functions is examined. Our main result is an impossibility theorem stating that no social welfare function can be strategy-proof, if some additional properties are required.

Abstract: This paper presents an extension of Borda's choice function to k-choice function (the k-choice set may be understood as the set of equally best “elites” of k alternatives). Young's axiomatic conditions are then generalized to k-choice functions and a simple combinatorial proof is exposed for the axiomatic characterization of Borda's k-choice function.