Social choice, the strong Pareto principle, and conditional decisiveness

This paper examines social choice theory with the strong Pareto principle. The notion of conditional decisiveness is introduced to clarify the underlying power structure behind strongly Paretian aggregation rules satisfying binary independence. We discuss the various degrees of social rationality: transitivity, semi-transitivity, the interval-order property, quasi-transitivity, and acyclicity.     

A Note On Impossibility Theorems and Seniority Rules

We characterize seniority rules, also known as lexical dictatorships, under weak consistency constraints on the groups choice function. These constraints are base triple-acyclicity in the case of binary choices and rationalizability (although not rationality) in the case of choices between an arbitrary number of alternatives. Existing results on these weakened constraints remain silent on the treatment of the groups most junior individuals and therefore do not yield a complete characterization of seniority rules. We also impose a universal domain, binary strict Pareto optimality, binary Pareto indifference, binary independence of irrelevant alternatives, and the newly introduced condition of conflict resolution. The latter condition requires a social choice rules not to remain indecisive between alternatives for which individuals have conflicting preferences.JEL CLASSIFICATIONS: D63, D71This revised version was published online in May 2005 with a corrected article title.     

The impossibility of the Paretian liberal and its relevance to welfare economics

The purpose of this study is to analyse the implications of Sen's impossibility result, the liberal paradox, for orthodox welfare economics. Because the rather special format of social choice theory makes it a little difficult to be sure of the relevance of this result, the whole dilemma is posed here in terms of a rather informal analysis of information al patterns.On the one hand, it is argued that the traditional approach to welfare economics, including both utilitarianism and Paretian ordinalism, contains severe informational constraints eliminating the use of all kinds of independent non-utility information in the social evaluation process. This property, called welfarism, is also present in the weak Pareto principle, which conflicts with even minimal requirements of personal liberty according to Sen's result.On the other hand, it is argued that there is in fact little to be resolved in this problem in spite of several attempts to circumvent the conflict. These studies are argued to be mainly ad hoc solutions to the formal problem and relevant only to the extent they indicate how severe restrictions are needed to avoid the paradox. The analogy with the prisoner's dilemma does not work either. Since liberal values are intrinsically non-welfaristic, the liberal paradox can be interpreted as only one, but a rather powerful, example of the informational deficiency of the orthodox approach.Finally, it is argued that the liberal paradox has striking implications for both the concept of preference and social optimum as well as empirical research on social welfare. This means that if the impossibility is to be taken seriously we need to revalue both the status of utility information and the role of the Pareto principle in social welfare analysis.The author is grateful to Professor Amartya Sen and Matti Tuomala for helpful comments and suggestions.     

Preference aggregation and statistical estimation

This paper deals with various connections that are found to exist between statistical estimation methods for decision-making and rules of group choice in the social choice area. Initially the aggregation of individual opinions is formulated as a pattern recognition problem; firstly it is shown that individual preferences lead to a natural representation in terms of binary patterns. Then we proceed to show how the search for a group preference pattern can be conducted by classifying the input preference patterns into various pattern classes and using the resulting classification boundaries to define the area of mutual agreement over some of the available alternatives. This leads to a decision-theoretic problem which consists in defining a decision rule (for classification) that is least likely to lead to misrecognition of arbitrary preference patterns. A maximum likelihood solution is obtained and compared with some well-known rules of group decision-making. Other solutions are also possible, on the basis of different optimality criteria, and their social choice interpretation is suggested. Finally, a method using Coleman's linear model for attributes is applied to yield group decision rules by feature weighting of election issues.     

A theorem for Bayesian group decisions

This paper presents a natural extension of Bayesian decision theory from the domain of individual decisions to the domain of group decisions. We assume that each group member accepts the assumptions of subjective expected utility theory with respect to the alternatives from which they must choose, but we do not assume, a priori, that the group as a whole accepts those assumptions. Instead, we impose a multiattribute utility independence condition on the preferences of the group with respect to the expected utilities of its actions as appraised by its members. The result is that the expected utility of an alternative for the group is a weighted average of the expected utilities of that alternative for its members. The weights must be determined collectively by the group. Pareto optimality is not assumed, though the result is consistent with Pareto optimality.     

On some suggestions for having non-binary social choice functions

The various paradoxes of social choice uncovered by Arrow [1], Sen [10] and others have led some writers to question the basic assumption of a binary social choice function underlying most of these paradoxes. Schwartz [8], for example, proves an important theorem which may be considered to be a generalization of the famous paradox of Arrow, and then lays the blame for this paradox on the assumption of a binary social choice function. He then proceeds to define a type of choice functions which, like binary choice functions, define the best elements in sets of more than two alternatives on the basis of binary comparisons, but which, as he claims, have an advantage over binary choice functions, in so far as they always ensure the existence of best elements for sets of more than two alternatives irrespective of the results of binary comparisons. The purpose of this paper is to show that even a considerable weakening of the assumption of a binary social choice function does not go very far towards solving some of the paradoxes under consideration, and that if replacing the requirement of a binary social choice function by a Schwartz type social choice function solves these paradoxes, it does so only by violating the universally acceptable value judgment that in choosing from a set of alternatives, society should never choose an alternative which is Pareto inoptimal in that set (i.e., the socially best alternatives in a set should always be Pareto optimal). This argument is substantiated with the help of an extended version of Sen's [10] paradox of a Paretian liberal, and thus a by-product of our analysis is a generalization of the theorem of Sen [10]. The argument itself, however, is more general and applies also to the impossibility result proved by Schwartz [8].We are extremely grateful to Amartya Sen for his helpful comments.

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Conditions for the optimality of simple majority decisions in pairwise choice situations

Recently it has been proved in a number of studies, that, under a proper set of assumptions, the optimal group decision rule in pairwise choice situations is a weighted majority rule, with weights that are proportional to the logarithms of the decision makers' odds of choosing the correct alternative.The purpose of the present note is to specify the necessary and sufficient conditions for this rule to coincide with the simple majority rule, and with restricted simple majority rules (which are defined as rules of simple majority, based on some subset of the most competent group members). These conditions are formulated in terms of inequalities between the group members' weights, thereby permitting easy verification of the optimality of the above mentioned rules.     

Pareto principles,positive responsiveness,and majority decisions

This article investigates the relationship among the weak Pareto principle, the strong Pareto principle, and positive responsiveness in the context of voting. First, it is shown that under a mild domain condition, if an anonymous and neutral collective choice rule (CCR) is complete and transitive, then the weak Pareto principle and the strong Pareto principle are equivalent. Next, it is shown that under another mild domain condition, if a neutral CCR is transitive, then the strong Pareto principle and positive responsiveness are equivalent. By applying these results, we obtain a new characterization of the method of majority decision.     

The impossibility of a paretian loyalist

Amartya Sen has argued the impossibility of the Paretian liberal. While his abstract argument is compelling, the concrete significance of the conclusion is in some doubt. This is because it is not clear how important liberalism in his sense is; in particular it is not clear that the sort of liberalism required for the impossibility result is a compelling variety. We show that even if the argument cannot be used to establish the inconsistency of Paretianism and common-or-garden liberalism, it can be adapted to prove a parallel impossibility. This is the impossibility of combining the Pareto criterion with a loyalty constraint involving certain claim-rights rather than liberty-rights. The impossibility of the Paretian loyalist is of interest in itself but it is also interesting for the light it throws on the source of Sen-style impossibilities.     

Rawlsian Nash solutions

We investigate the conditions which guarantee the choice of Rawlsian solutions by players of unequal maximin positions bargaining under Nash rules. The conditions, viz., subsymmetry and the location of the Pareto set, relate to the structure of the utility set,S.     

Abstract Aggregations and Proximity Preservation: An Impossibility Result

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 result in this paper has been presented in the Staff Seminar at the University of Graz and at the 2001 Meeting of the Public Choice Society in San Antonio. We are grateful to all participants, especially Hannu Nurmi and Don Saari, and to an anonymous referee for helpful comments.     

Social Structure,Economic Performance and Pareto Optimality

This paper shows that, if the performance of the economy is independent of the identities of individuals, then many welfare criteria yield sets of optimal social states that are equal to the Pareto optimal set. This result is proved for income distributions and extended to more general social choice problems. If the independence condition holds, then the set of optimal states is invariant to the adoption of an anonymity axiom, and to the utility information available.     

主权基金国际规则的主导权斗争

自2007年夏季起,主权财富基金问题便成为国际舆论和国际政治经济理论界关注的一个热门问题。这一现象所反映的是西方大国同新兴工业国以及资源出口国之间在全球主权投资规则主导权上的博弈和争夺,其中的核心问题包括:政治性或战略性投资是否合理合法,透明度要求如何实施,以及国际规则制定的适格主体和程序。本文认为,中国应当积极参与规则制定的辩论和角力,明确提出保持全球资本市场开放性的国际伦理和政治价值的主张。最后,本文就中国在这场围绕主权投资规则制定权的博弈中应采取的立场和策略做了探讨。     

Welfare judgments and future generations

The author argues that long-range welfare policies - policies designed to provide significant, widespread, continuing benefits to future generations, remote as well as near, at some cost to ourselves - cannot be justified by appeal to the welfare of remote future generations. He questions whether they can be justified at all. The problem is that the failure to adopt such a policy would not make any of our distant descendants worse off that he would otherwise be, since had the policy been adopted, he would not even have existed. These considerations also bring out a conflict between utilitarian and Paretian principles.     

The independence condition in the theory of social choice

Arrow's theorem is really a theorem about the independence condition. In order to show the very crucial role that this condition plays, the theorem is proved in a refined version, where the use of the Pareto condition is almost avoided.A distinction is made between group preference functions and group decision functions, yielding respectively preference relations and optimal subsets as values. Arrow's theorem is about the first kind, but some ambiguities and mistakes in his book are explained if we assume that he was really thinking of decision functions. The trouble then is that it is not clear how to formulate the independence condition for decision functions. Therefore the next step is to analyse Arrow's argument for accepting the independence condition.The most frequent ambiguity depends on an interpretation of A as the set of all conceivable alternatives, while the variable subset B is the set of all feasible or available alternatives. He then argues that preferences between alternatives that are not feasible shall not influence the choice from the set of available alternatives. But even if this principle is accepted, it only forces us to require independence with respect to some specific set B and not to every B simultaneously. Therefore the independence condition cannot be accepted on these grounds.Another argument is about an election where one of the candidates dies. On one interpretation this argument can be taken to support an independence requirement which leads to a contradiction. On another interpretation it is a condition about connexions between choices from different sets.The so-called problem of binary choice is found to be different from the independence problem and it plays no essential role in Arrow's impossibility result. Other impossibility results by Sen, Batra and Pattanaik and by Schwartz are of a different character.In the last section, several weaker independence conditions are presented. Their relations to Arrow's condition are stated and the arguments supporting them are discussed.     

Bayesian decision theory,rule utilitarianism,and Arrow's impossibility theorem

The first part of this paper reexamines the logical foundations of Bayesian decision theory and argues that the Bayesian criterion of expected-utility maximization is the only decision criterion consistent with rationality. On the other hand, the Bayesian criterion, together with the Pareto optimality requirement, inescapably entails a utilitarian theory of morality. The next sections discuss the role both of cardinal utility and of cardinal interpersonal comparisons of utility in ethics. It is shown that the utilitarian welfare function satisfies all of Arrow's social choice postulates avoiding the celebrated impossibility theorem by making use of information which is unavailable in Arrow's original framework. Finally, rule utilitarianism is contrasted with act utilitarianism and judged to be preferable for the purposes of ethical theory.     

Characteristic properties of FPTP systems

In this article, we model FPTP systems as social preference rules and give two characterizations. We show that a social preference rule is an FPTP system if, and only if, it satisfies the axioms of subset consistency, district consistency, subset cancellation, and district cancellation. The second characterization consists of the axioms of subset consistency, subset anonymity, neutrality, topsonlyness, Pareto optimality, district consistency and district cancellation. The characterizations give us an opportunity to compare the characteristic properties of FPTP systems to the characteristic properties that we found for list systems of proportional representation (list PR systems) in Hout et al. (Social Choice and Welfare, 27:459–475, 2006), where we modelled those systems also as social preference rules. We find that consistency and anonymity distinguish list PR systems from FPTP systems. On the other hand, it is district cancellation that distinguishes FPTP systems from list PR systems.     

Regret theory with general choice sets

The regret theory of choice under uncertainty proposed by Loomes and Sugden has performed well in explaining and predicting violations of Expected Utility theory. The original version of the model was confined to pairwise choices, which limited its usefulness as an economic theory of choice. Axioms for a more general form of regret theory have been proposed by Loomes and Sugden. In this article, it is shown that a simple nonmanipulability requirement is sufficient to characterize the functional form for regret theory with general choice sets. The stochastic dominance and comparative static properties of the model are outlined. A number of special cases are derived in which regret theory is equivalent to other well-known theories of choice under uncertainty.I would like to thank Graham Loomes, Robert Sugden, Peter Wakker, and Nancy Wallace for helpful comments and criticism.     

Even-chance lotteries in social choice theory

This paper discusses aspects of the theory of social choice when a nonempty choice set is to be determined for each situation, which consists of a feasible set of alternatives and a preference order for each voter on the set of nonempty subsets of alternatives. The individual preference assumptions include ordering properties and averaging conditions, the latter of which are motivated by the interpretation that subset A is preferred to subset B if and only if the individual prefers an even-chance lottery over the basic alternatives in A to an even-chance lottery over the basic alternatives in B. Corresponding to this interpretation, a choice set with two or more alternatives is resolved by an even-chance lottery over these alternatives. Thus, from the traditional no-lottery social choice theory viewpoint, ties are resolved by even-chance lotteries on the tied alternatives. Compared to the approach which allows all lotteries to compete along with the basic alternatives, the present approach is a contraction which allows only even-chance lotteries.After discussing individual preference axioms, the paper examines Pareto optimality for nonempty subsets of a feasible set in a social choice context with n voters. Aspects of simple-majority comparisons in the even-chance context follow, including an analysis of single-peaked preferences. The paper concludes with an Arrowian type impossibility theorem that is designed for the even-chance setting.     

Partial information on decisional competences and the desirability of the expert rule in uncertain dichotomous choice situations

The paper analyzes the expert resolution problem by employing extended versions of the uncertain dichotomous choice model. The main purpose of this study is to illustrate how the analysis of optimal decision rules can be carried out while dispensing with the common restrictive assumption of full information regarding individual decisional competences. In contrast to most previous studies in this field we here evaluate the expert rule under alternative assumptions regarding the available partial information on judgmental competences rather than compare it in an ad hoc manner to some common alternative rules, such as simple majority rule. A fuller optimality analysis allowing the evaluation of all relevant decision rules, and not merely the expert rule, is attempted for a five-member panel of experts assuming a uniform distribution of individual competences. For three-member groups the optimality issue is resolved by assuming no information on individual competences and interpreting the expert rule as an even-chance lottery on skills.