Results In Social Choice Theory Research Articles

IMPLICITLY RACIST EPISTEMOLOGY

This essay explores why examples of mainstream philosophy of cognition and applied phenomenology demonstrate the implicit bias that they treat as their subject matter, whether the authors of these works intend or approve of their doing so. It is shown why egalitarian intuitions, which form the basis for ideal models of justice appealing to elites in racially stratified societies, provide an inadequate framework for illuminating and dismantling the mechanics of racial discrimination. Recently developed results in social choice theory are applied here to cases where racial bias is perpetuated through institutionally orchestrated collective decision making. The “discursive dilemma” theorem suggests why the analysis of subliminal attitudes is irrelevant to correcting the racial injustices presumed to follow from implicit bias in societies where negative racial stereotypes, ostensibly and explicitly deplored, are covertly and illicitly reinforced.

Logics for Modelling Collective Attitudes

We introduce a number of logics to reason about collective propositional attitudes that are defined by means of the majority rule. It is well known that majoritarian aggregation is subject to irrationality, as the results in social choice theory and judgment aggregation show. The proposed logics for modelling collective attitudes are based on a substructural propositional logic that allows for circumventing inconsistent outcomes. Individual and collective propositional attitudes, such as beliefs, desires, obligations, are then modelled by means of minimal modalities to ensure a number of basic principles. In this way, a viable consistent modelling of collective attitudes is obtained.

Natural Deduction for Modal Logic of Judgment Aggregation

We can formalize judgments as (consistent sets of) logical formulas. Judgment aggregation deals with judgments of several agents, which need to be aggregated to a collective judgment. There are several logical formalizations of judgment aggregation. This paper focuses on a modal formalization which nicely expresses classical properties of judgment aggregation rules and famous results of social choice theory, like Arrow's impossibility theorem. A natural deduction system for modal logic of judgment aggregation is presented in this paper. The system is sound and complete. As an example of derivation, a formal proof of Arrow's impossibility theorem is given.

A Discernable and Manageable Standard for Partisan Gerrymandering

Abstract The case of Vieth v. Jubelirer (2004) challenges us to find a standard for partisan gerrymandering that is judicially discernable and manageable. Without such a standard even the most egregious partisan gerrymanders cannot be effectively challenged. However, we argue that the way to find a suitable standard is not to embark on a quest for a “new” standard. Rather it is to take the existing valid measures that science gives us, and show that these can be grounded in constitutionally protected rights. Using recent results in social choice theory, we show that the existing partisan symmetry standard can be derived from an individual right to equal protection. We also show that the existing technology for measuring partisan symmetry can provide a judicially manageable test for partisan bias.

Positional rules and q-Condorcet consistency

A well-known result in social choice theory is the following: every scoring rule (positional rules) violates Condorcet consistency. A rule is Condorcet consistent when it selects the alternative that is preferred to every other alternative by a majority of individuals. In this paper, we investigate some limits of this negative result. We expose the relationship between a weaker version of the Condorcet consistency principle and the scoring rules. Our main objective is then to study the condition on the quota that ensure that positional rules (simple and sequential) satisfy this principle.

Welfare, preferences and the reconstruction of desires

Purpose– The purpose of this paper is to propose a model that relates the desire for justice with welfare.Design/methodology/approach– The point of departure, elaborated in the first part of the paper, is the observation that we have no sense-organs for experiencing welfare and the experiences of happiness being, in general, transient if they emerge at all. Desires drive our behavior and motivate our decisions. The author will analyze conditions so that desires can be related to welfare, making use of results of social choice theory. There is some (technical) similarity between aggregating individual preferences and editing (“reconstruction”) desires.Findings– In special cases, desires are well ordered and can be represented by preference orderings, ready for deriving “rational choices.” However, desires may be circular. Then, of course, the satisfaction of a particular desire will never trigger happiness because there is always a “higher valued” (or “more prominent”) desire unsatisfied. In these cases, desires and welfare cannot be matched. However, there are social desires, such as the desire for justice (as fairness), that can have welfare-enhancing consequences if satisfied even when private desires are circular, as desires for justice contain a social component.Originality/value– This issue will be elaborated in the second part of the paper using a formal model, borrowed from Fehr and Schmidt (1999), in order to illustrate the underlying reasoning.

The Idea of Justice

The Idea of Justice

Consistency of choice in nonparametric multiple comparisons

In this paper, we are interested in the inconsistencies that can arise in the context of rank-based multiple comparisons. It is well known that these inconsistencies exist, but we prove that every possible distribution-free rank-based multiple comparison procedure with certain reasonable properties is susceptible to these phenomena. The proof is based on a generalisation of Arrow's theorem, a fundamental result in social choice theory which states that when faced with three or more alternatives, it is impossible to rationally aggregate preference rankings subject to certain desirable properties. Applying this theorem to treatment rankings, we generalise a number of existing results in the literature and demonstrate that procedures that use rank sums cannot be improved. Finally, we show that the best possible procedures are based on the Friedman rank statistic and the k-sample sign statistic, in that these statistics minimise the potential for paradoxical results.

Social choice theory, belief merging, and strategy-proofness

Intelligent agents have to be able to merge informational inputs received from different sources in a coherent and rational way. Several proposals have been made for information merging in which it is possible to encode the preferences of sources [5,4,19,24,25,1]. Information merging has much in common with social choice theory, which aims to define operations reflecting the preferences of a society from the individual preferences of the members of the society. Given this connection, frameworks for information merging should provide satisfactory resolutions of problems raised in social choice theory. We investigate the link between the merging of epistemic states and some results in social choice theory. This is achieved by providing a consistent set of properties-akin to those used in Arrow's theorem [2]-for merging. It is shown that in this framework there is no Arrow-like impossibility result. By extending this to a consistent framework which includes properties corresponding to the notion of being strategy-proof, we show that results due to Gibbard and Satterthwaite [13,31,32] and others [6,3] do not hold in merging frameworks.

Choix social positionnel et principe majoritaire

A well-known result in Social Choice theory is the following: every scoring rule violates the majority principle as defined by Condorcet. In this paper, we investigate some limits of this negative result. Some weakened versions of Condorcet principle are introduced and we characterize those scoring rules which fulfill these conditions. Moreover, we evaluate the propensity of some scoring rules to violate these majority conditions.

Impossibility results for choice correspondences

One of the most important results in social choice theory is the Impossibility Theorem. Since 1951 when its first version was stated by K. Arrow, many other versions and extensions have been done. Although conditions differ, most results are concerned with relational aggregation rules which transform the individual preference relations into a social binary relation. The mixed case in which the social choice is defined in terms of choice functions while the individual opinions are represented by preference relations, also allows some interesting extensions of the original result. The study of the choice aggregation rules, when both individual and social choices are expressed in terms of choice functions, is well represented by the works of Aizerman and Aleskerov ( Mathematical Social Sciences, 1986, 11, 201–242). Our approach concerns this latter framework. We introduce new normative conditions under which impossibility results are derived. These results are not dependent upon rationality conditions and extend the Impossibility Theorem to general sets of voters and alternatives.

Social Choice in the Real World II: Cyclical Preferences and Strategic Voting in the Finnish Presidential Elections

The empirical relevance of the theoretical results of social choice theory is still unclear. The most radical thesis, put forth by William Riker, is that politics is a highly unstable process, characterized by preference cycles and strategic voting. This article ‐ a continuation of an earlier article published in this journal ‐ examines the Finnish presidential election in 1925, 1931, 1937 and 1982. The conclusion is that preference cycle and strategic voting have had a significant impact in the discussed cases. The relevancy of the social choice approach and its relation to historical research are discussed.

Referendum Design: An Exercise in Applied Social Choice Theory

The formal status of the referendum institution in democratic system varies from consultative and optional to mandatory and binding. Despit the formal status, it can be argued that in all systems the legislators can hardly ignore the referendum results. The article presents two arguments: (1) The results of social choice theory suggest that the number of alternatives in referenda should to be restricted to two in order to a void severe problems of interpretation and agenda manipulation. (2) The consultative referendum system may lead to quite dramatic norm conflicts for both legislators and voters. Taken together, these two arguments imply that referenda are appropriate only in cases where there is natural way to dichotomize the issue at hand. Moreover, whenever a referendum is called, its result should be binding.

A note on social choice theory without the Pareto principle

Although the Pareto principle is a very intuitive property, it has been observed that many results in social choice theory do not require it as an assumption. For example, Wilson [8] proved an impossibility theorem concerning the aggregation of individual preferences without the Pareto principle. Since Wilson's theorem implies as a corollary the Arrow impossibility theorem (Arrow [1]) when the Pareto principle is also assumed, it has been viewed by some as more fundamental than Arrow's theorem. However, most proofs of Wilson's theorem (in particular a recent ultrafilter approach proof by Campbell [3]) are so close to known proofs of Arrow's theorem that one might conjecture that these two results are essentially the same.

Preferences, choices, tournaments: Alternative foundations for the evaluation of voting schemes

The standard assumption underlying most of the negative results of the social choice theory is that the individuals have complete and transitive preference relations over the candidates. As an alternative to this assumption we consider the possibility that individuals can be characterized as possessing preference tournaments (i.e. asymmetric and complete relations) over the candidate set. We discuss the implications of the latter assumption to the negative results of social choice theory. Finally some solution concepts applicable in the individual preference tournament framework are outlined.

Social choice theory in the case of von Neumann-Morgenstern utilities

Part I of this paper offers a novel result in social choice theory by extending Harsanyi's well-known utilitarian theorem into a “multi-profile” context. Harsanyi was contented with showing that if the individuals' utilities ui are von Neumann-Morgenstern, and if the given utility u of the social planner is VNM as well, then the Pareto indifference rule implies that u is affine in terms of the ui. We provide a related conclusion by considering u as functionally dependent on the ui, through a suitably restricted “social welfare functional” (u1,...,un)→u=f(u1,...,un). We claim that this result is more in accordance with contemporary social choice theory than Harsanyi's “single-profile” theorem is. Besides, harsanyi's initial proof of the latter was faulty. Part II of this paper offers an alternative argument which is intended to be both general and simple enough, contrary to the recent proofs published by Fishburn and others. It finally investigates the affine independence problem on the ui discussed by Fishburn as a corollary to harsanyi's theorem.

Rights and Social Choice: Is There a Paretian Libertarian Paradox?

In 1970 Amartya Sen exposed an apparent antinomy that has come to be known as the Paradox of the Paretian Libertarian (Sen, 1970b, pp. 152–57). Sen introduced his paradox by establishing a simple but startling theorem. Roughly put, what he proved was that if a mechanism for selecting social choice functions satisfies two standard adequacy conditions, there are possible situations in which it will violate either the very weak libertarian precept that every individual has at least some rights or the seemingly innocuous Paretian principle that an option should be judged unacceptable if there is an available alternative that everyone prefers to it. Many economists and philosophers have proposed solutions to Sen's problem, but there is no general consensus on what solution (if any) is correct. In the present paper I argue that Sen's original theorem fails to establish the existence of any conflict between libertarianism and Paretianism. Furthermore, I contend that Sen has misinterpreted certain other theorems which he has used to defend the existence of a paradoxical conflict between these two doctrines. In general, I try to show that whenever Sen posits a Paretian-libertarian conflict to explain an apparently troubling result in social choice theory, the difficulty can be better dealt with either by claiming that the theorem in question imposes overly strong background constraints on the form of social choice functions or by claiming that it relies on an unacceptable construal of individual rights.