Social Choice Theory

I aim to explain why majority voting can be assumed to have an epistemic edge over lottery voting. This would provide support for majority voting as the appropriate decision mechanism for deliberative epistemic accounts of democracy. To argue my point, I first recall the usual arguments for majority voting: maximal decisiveness, fairness as anonymity, and minimal decisiveness. I then show how these arguments are over inclusive as they also support lottery voting. I then present a framework to measure accuracy so (...) as to compare the two decision mechanisms. I go over four arguments for lottery voting and three arguments for majority voting that support their respective accuracy. Lottery voting is then shown to have, compared to majority voting, a decreased probability of discrimination. That is, I argue that with lottery voting it is less probable under conditions of normal politics that if the procedure selects X, X is reasonable. I then provide two case scenarios for each voting mechanism that illustrate my point. (shrink)

A dichotomous decision-making context in committees is considered where potential partisan members with predetermined votes can generate inefficient decisions and buy neutral votes. The optimal voting rule minimizing the expected costs of inefficient decisions for the case of a three-member committee is analyzed. It is shown that the optimal voting rule can be non-monotonic with respect to side-transfers: in the symmetric case, majority voting is optimal under either zero, mild or full side-transfer possibilities, whereas unanimity voting may be optimal under (...) an intermediate side-transfer possibility. The side-transfer possibilities depend on the power of partisans (their ability or willingness to pay for neutral votes) relative to the corruptibility of neutral members (personal cost of deliberately casting a `wrong' vote). (shrink)

In certain judgmental situations where a “correct” decision is presumed to exist, optimal decision making requires evaluation of the decision-makers’ capabilities and the selection of the appropriate aggregation rule. The major and so far unresolved difficulty is the former necessity. This article presents the optimal aggregation rule that simultaneously satisfies these two interdependent necessary requirements. In our setting, some record of the voters’ past decisions is available, but the correct decisions are not known. We observe that any arbitrary evaluation of (...) the decision-makers’ capabilities as probabilities yields some optimal aggregation rule that, in turn, yields a maximum-likelihood estimation of decisional skills. Thus, a skill-evaluation equilibrium can be defined as an evaluation of decisional skills that yields itself as a maximum-likelihood estimation of decisional skills. We show that such equilibrium exists and offer a procedure for finding one. The obtained equilibrium is locally optimal and is shown empirically to generally be globally optimal in terms of the correctness of the resulting collective decisions. Interestingly, under minimally competent (almost symmetric) skill distributions that allow unskilled decision makers, the optimal rule considerably outperforms the common simple majority rule (SMR). Furthermore, a sufficient record of past decisions ensures that the collective probability of making a correct decision converges to 1, as opposed to accuracy of about 0.7 under SMR. Our proposed optimal voting procedure relaxes the fundamental (and sometimes unrealistic) assumptions in Condorcet’s celebrated theorem and its extensions, such as sufficiently high decision-making quality, skill homogeneity or existence of a sufficiently large group of decision makers. (shrink)

An impossibility result for completely abstract social aggregation rules is presented. It is shown that non-imposition and a new no-veto property (two properties in the spirit of the Pareto principle and non-dictatorship respectively) are incompatible with an inter-profile consistency condition formulated in terms of proximity preservation.

The paper axiomatises a generalised utilitarian aggregation rule, under which different weights are assigned to utilities depending on the different rights involved. The relationship between actions, rights and the evaluation of utilities is investigated. Application is made to a famous example, Edwin-Angelina-the Judge, which appears in the social choice literature.

This is a contribution to thesociology and social epistemology of knowledgeproduction in Russian social sciences today. Inthe initial section, the epistemic status andsocial function of Soviet social scientificdiscourse are characterized in terms of textualforms and their modes of (re-)production. Theremaining sections detail the course of therestructuration of social scientific discoursesince the fall of the Soviet Union and draw onextant empirical sources, in particular studiesof bibliographical rubrics, thematicrepertoires, and current textual formsthroughout the public sphere and the academicestablishment in Russia. An underlying (...) concernis the shifting status of the intellectual inthe wider socio-cultural context as reflectedin language usage and its textualembodiments. (shrink)

We completely characterize the simple majority weighted voting game achievable hierarchies, and, in doing so, show that a problem about representative government, noted by J. Banzhaf [Rutgers Law Review 58, 317–343 (1965)] cannot be resolved using the simple majority quota. We also demonstrate that all hierarchies achievable by any quota can be achieved if the simple majority quota is simply incremented by one.

Is there a rationale for an electoral college system or do these voting systems always waste useful information? This paper studies this question in a setup in which voting is supposed to aggregate decentralized information about individual preferences for two candidates. Individual perceptions may be affected by regional information. When such regional information plays a major role, an electoral college system may be superior to simple majority voting.

The voting power of a voter—the extent to which she can affect the outcome of a collective decision—is often quantified in terms of the probability that she is critical. This measure is extended to a series of power measures of different ranks. The measures quantify the extent to which a voter can be part of a group that can jointly make a difference as to whether a bill passes or not. It is argued that the series of these measures allow (...) for a more appropriate assessment of voting power, particularly of a posteriori voting power in case the votes are stochastically dependent. Also, the new measures discriminate between voting games that cannot be distinguished in terms of the probability of only criticality. (shrink)

We develop a utilitarian framework to assess different decision rules for the European Council of Ministers. The proposals to be decided on are conceptualized as utility vectors and a probability distribution is assumed over the utilities. We first show what decision rules yield the highest expected utilities for different means of the probability distri- bution. For proposals with high mean utility, simple bench- mark rules (such as majority voting with proportional weights) tend to outperform rules that have been proposed in (...) the political arena. For proposals with low mean utility, it is the other way round. We then compare the expected utilities for smaller and larger countries and look for Pareto- dominance relations. Finally, we provide an extension of the model, discuss its restrictions, and compare our approach with assessments of decision rules that are based on the Penrose measure of voting power. (shrink)

The choice of a social decision rule for a federal assembly affects the welfare distribution within the federation. But which decision rules can be recommended on welfarist grounds? In this paper, we focus on two welfarist desiderata, viz. (i) maximizing the expected utility of the whole federation and (ii) equalizing the expected utilities of people from different states in the federation. We consider the European Union as an example, set up a probabilistic model of decision making and explore how different (...) decision rules fare with regard to the desiderata. We start with a default model, where the interests, and therefore the votes of the different states are not correlated. This default model is then abandoned in favor of models with correlations. We perform computer simulations and find that decision rules with a low acceptance threshold do generally better in terms of desideratum (i), whereas the rules presented in the Accession Treaty and in the (still unratified) Constitution of the European Union tend to do better in terms of desideratum (ii). The ranking obtained regarding desideratum (i) is fairly stable across different correlation patterns. (shrink)

The Condorcet jury theorem (CJT) is based on the assumption of homogeneous voters who imperfectly know the correct policy. We reassess the validity of the CJT when voters are homogeneous and each knows the correct decision with an average probability of more than a half.

The classical theory of rational choice is built on several important internal consistency conditions. In recent years, the reasonableness of those internal consistency conditions has been questioned and criticized, and several responses to accommodate such criticisms have been proposed in the literature. This paper develops a general framework to accommodate the issues raised by the criticisms of classical rational choice theory, and examines the broad impact of these criticisms from both normative and positive points of view.

The term “rationality” is applied to many different things, from beliefs and preferences to decisions and choices, actions and behaviors, people, collectivities, andinstitutions. Therefore this paper will limit its considerations only to social preferences and choices in order to clarify the role of rationality in social explanation. The paper will focus on degrees of rationality, calling upon the concept of transitivity for help.

With her conception of epistemic injustice, Miranda Fricker has opened up new normative dimensions for epistemology; that is, the injustice of denying one?s status as a knower. While her analysis of the remedies for such injustices focuses on the epistemic virtues of agents, I argue for the normative superiority of adapting a broadly republican conception of epistemic injustice. This argument for a republican epistemology has three steps. First, I focus on methodological and explanatory issues of identifying epistemic injustice and argue, (...) against Fricker, that identity prejudice fails to provide a sufficient explanatory basis for the spread and maintenance of such systematic epistemic injustice. Second, this systemic basis can be found not so much in the psychological attitudes of individual knowers, but in the relations of domination among groups and individuals in a society. Third, if such a presence of domination plays a primary explanatory role in all forms of epistemic injustice, it is likely that those who suffer from epistemic injustice will also suffer other forms of injustice and loss of status via the exercise of other forms of power and exclusion. (shrink)

It is often assumed that democracies can make good use of the epistemic benefi ts of diversity among their citizenry, but difficult to show why this is the case. In a deliberative democracy, epistemically relevant diversity has three aspects: the diversity of opinions, values, and perspectives. Deliberative democrats generally argue for an epistemic form of Rawls' difference principle: that good deliberative practice ought to maximize deliberative inputs, whatever they are, so as to benefi t all deliberators, including the least eff (...) ective. The proper maximandum of such a principle is not the pool of reasons, but rather the availability of perspectives. Th is sort of diversity makes robustness across different perspectives the proper epistemic aim of deliberative processes. Robustness also offers a measure of success for those democratic practices of inquiry based on the deliberation of all citizens. (shrink)

This article illustrates how axiomatic social choice theory can be used in the evaluation of measures of group fitness for a biological hierarchy, thereby contributing to the dialogue between the philosophy of biology and social choice theory. It provides an axiomatic characterization of the ordering underlying the MichodSolariNedelcu index of group fitness for a multicellular organism. The MVSHN index has been used to analyse the germ-soma specialization and the fitness decoupling between the cell and organism levels that takes place during (...) the evolutionary transition to multicellularity. It is argued that some of the axioms satisfied by the MVSHN group fitness ordering are not appropriate for all stages in this transition. (shrink)

An allocation problem is a type of aggregation problem in which the values of individuals' opinions on some set of variables sum to a constant. This paper shows that for realistic allocation problems, namely ones in which the set of possible opinion values is finite, the only universal aggregation methods that satisfy two commonly invoked conditions are the dictatorial ones. The two conditions are, first, that the aggregate opinion on any variable depends only on the individuals' opinions on that variable (...) and not on their opinions on any other variable and, secondly, that the aggregate opinion minimally preserves unanimous individual opinion. Connections between this result and similar ones in the literature on judgment aggregation are explored and their significance assessed. (shrink)

Within the next few pages, we outline how the U.S. President might employ novel arrangements of human and technology elements to produce improved government efforts involving the collective insights of all government works to: (1) better serve the public, (2) protect our country, and (3) generate innovative solutions that both address present day problems and produce a better future for us all. We seek to discuss insights into collective intelligence in large organizations - which, for the most part, has not (...) been discussed with regard to the U.S. government - and translate the themes of these books to improve the Executive Branch. (shrink)

Should social preferences conform to the principles of rationality we normally expect of individuals? Should they, for instance, conform to the consistency axioms of expected utility theory? This article considers one fragment of this question.

Applying Weglorz' mode s of set theory without the axiom of choice, we investigate Arrow-type social we fare functions for infinite societies with restricted coalition algebras. We show that there is a reasonable, nondictatorial social welfare function satisfying “finite discrimination”, if and only if in Weglorz' mode there is a free ultrafilter on a set representing the individuals.

"Minimal liberalism", in Sen's strict definition, is impossible, because any 'social state', once chosen, freezes all of its components, thereby removing any prospect of further assignment of choice-making authority.

The author submits that Popper's social philosophy rests on seven pillars: rationality (both conceptual and practical), individualism (ontological and methodological), libertarianism, the nonexistence of historical laws, negative utilitarianism ("Do no harm"), piecemeal social engineering, and a view on social order. The first six pillars are judged to be weak, and the seventh broken. In short, it is argued that Popper did not build a comprehensive, profound, or even consistent system of social philosophy on a par with his work in epistemology. (...) Still, he did make some important contributions to the field, such as unveiling the philosophical roots of totalitarianism and defending social engineering against both revolutionists and conservatives. (shrink)

Since the 1950s, Donald T. Campbell has been one of the most influential contributors to the methodology of the social sciences. A distinguished psychologist, he has published scores of widely cited journal articles, and two awards, in social psychology and in public policy, have been named in his honor. This book is the first to collect his most significant papers, and it demonstrates the breadth and originality of his work.

How is a person's freedom related to his or her preferences? Liberal theorists of negative freedom have generally taken the view that the desire of a person to do or not do something is irrelevant to the question of whether he is free to do it. Supporters of the “pure negative” conception of freedom have advocated this view in its starkest form: they maintain that a person is unfree to Φ if and only if he is prevented from Φ-ing by (...) the conduct or dispositions of some other person . This definition of freedom is value-neutral in the sense that no reference is made to preferences over options or indeed to any other indicators of the values of options, either in the characterization of “Φ-ing” itself or in the characterization of the way in which Φ-ing can be constrained. (shrink)

As the ongoing literature on the paradoxes of the Lottery and the Preface reminds us, the nature of the relation between probability and rational acceptability remains far from settled. This article provides a novel perspective on the matter by exploiting a recently noted structural parallel with the problem of judgment aggregation. After offering a number of general desiderata on the relation between finite probability models and sets of accepted sentences in a Boolean sentential language, it is noted that a number (...) of these constraints will be satisfied if and only if acceptable sentences are true under all valuations in a distinguished non-empty set W. Drawing inspiration from distance-based aggregation procedures, various scoring rule based membership conditions for W are discussed and a possible point of contact with ranking theory is considered. The paper closes with various suggestions for further research. (shrink)

In two recent papers, Christian List and Philip Pettit have argued that there is a problem in the aggregation of reasoned judgements that is akin to the aggregation of the preference problem in social choice theory. 1 Indeed, List and Pettit prove a new general impossibility theorem for the aggregation of judgements, and provide a propositional interpretation of the social choice problem that suggests it is a special case of their impossibility result. 2 Specifically, they show that no judgement aggregation (...) function for a group is possible if the group seeks to satisfy certain `minimal conditions' designed to ensure that the function is both responsive to the individually rational views of its members and collectively rational in the set of judgements it holds. In this article, I resist the List and Pettit claim that there is the same propensity for collective irrationality or incoherence in the aggregation of reasoned judgements as there is in the aggregation of preference. I argue that reason, because it has a logical structure that is lacking in mere preference, has the effect of giving priority to some aggregations over others, a priority that is not permitted by one of the conditions imposed by List and Pettit. This avoids the incoherence that would otherwise exist if these different aggregations, not consistent with one another, were to compete at the same level of priority. The priority of some aggregations is particularly apparent, I shall argue, if one views the aggregation of judgements through the lens of common law decision-making. Key Words: social choice • judgement • Condorcet jury theorem • collective rationality • public reason • doctrinal paradox • discursive dilemma. (shrink)

This paper examines a special kind of social preference, namely a preference to do one's part in a mixed-motive setting because the other party expects one to do so. I understand this expectation-based preference as a basic reactive attitude. Given this, and the fact that expectations in these circumstances are likely to be based on other people's preferences, I argue that in cooperation a special kind of equilibrium ensues, which I call a loop, with people's preferences and expectations mutually cross-referring. (...) As with a Lewis-norm, the loop can get started in a variety of ways. It is self-sustaining in the sense that people with social preferences have sufficient reason not to deviate. (shrink)

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