A note on identification in discrete choice models with partial observability

This note establishes a new identification result for additive random utility discrete choice models. A decision-maker associates a random utility \(U_{j}+m_{j}\) to each alternative in a finite set \(j\in \left\{ 1,\ldots ,J\right\} \), where \(\mathbf {U}=\left\{ U_{1},\ldots ,U_{J}\right\} \) is unobserved by the researcher and random with an unknown joint distribution, while the perturbation \(\mathbf {m}=\left( m_{1},\ldots ,m_{J}\right) \) is observed. The decision-maker chooses the alternative that yields the maximum random utility, which leads to a choice probability system \(\mathbf { m\rightarrow }\left( \Pr \left( 1|\mathbf {m}\right) ,\ldots ,\Pr \left( J| \mathbf {m}\right) \right) \). Previous research has shown that the choice probability system is identified from the observation of the relationship \( \mathbf {m}\rightarrow \Pr \left( 1|\mathbf {m}\right) \). We show that the complete choice probability system is identified from observation of a relationship \(\mathbf {m}\rightarrow \sum _{j=1}^{s}\Pr \left( j|\mathbf {m} \right) \), for any \(s<J\). That is, it is sufficient to observe the aggregate probability of a group of alternatives as it depends on \(\mathbf {m}\). This is relevant for applications where choices are observed aggregated into groups while prices and attributes vary at the level of individual alternatives.     

Independent social choice correspondences

A fixed agenda social choice correspondence on outcome set X maps each profile of individual preferences into a nonempty subset of X. If satisfies an analogue of Arrow's independence of irrelevant alternatives condition, then either the range of contains exactly two alternatives, or else there is at most one individual whose preferences have any bearing on . This is the case even if is not defined for any proper subset of X.     

Inequality and social choice

This paper is concerned with the welfare and inequality rankings of income distributions whose Lorenz curves cross. A simple inequality measure is proposed which gives unambiguous results in many cases.     

Weakly implementable social choice rules

Previous investigations have shown that a social choice function which is partially implementable must be characterized by pervasive veto power. This paper investigates how much additional latitude in the design of social choice functions, and how much relief from this vetoers result, can be achieved by examining multi-valued social choice rules and relaxing the requirement of partial implementability to a requirement that we call weak partial implementability. We find that the power structures which characterize partially implementable social choice functions, including the veto properties, also characterize weakly partially implementable social choice rules. The conclusion is that invoking multi-valuedness and implementation of appealing social choice rules in strong Nash equilibria. Our results apparently exhaust the possibilities for implementation in strong Nash equilibrium. If any implementation possibility results are to be achieved, they can apparently come only by weakening the equilibrium requirement.     

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.     

A note on decisions under uncertainty: the impact of the choice of the welfare measure

The paper addresses the question, how policy decisions under uncertainty depend on the underlying welfare concept. We study three different welfare measures: The first is directly based on the ex ante (expected) utility of a representative consumer whereas the second relies on an ex ante and the third on an ex post valuation of policy changes compared to the status quo. We show that decisions based on these measures coincide if and only if risk-neutral expected utility maximization is applied. Differences between the decisions are analyzed for both, risk-averse expected utility maximization and the MaxiMin criterion. For risk-averse decision makers, differences between the first and the second concept arise if the absolute risk-aversion of the decision maker is not constant in income. For risk-aversion and the MaxiMin criterion, the effort levels to provide a public good based on an optimization of ex post utility changes exceed those based on the first or second concept. Implications for environmental policy decisions based on the concepts of abatement costs and benefits from abatement are discussed.     

Disparate goods and Rawls' difference principle: A social choice theoretic treatment

Rawls' Difference Principle asserts that a basic economic structure is just if it makes the worst off people as well off as is feasible. How well off someone is is to be measured by an index of primary social goods. It is this index that gives content to the principle, and Rawls gives no adequate directions for constructing it. In this essay a version of the difference principle is proposed that fits much of what Rawls says, but that makes use of no index. Instead of invoking an index of primary social goods, the principle formulated here invokes a partial ordering of prospects for opportunities.     

Decision-making under ignorance with implications for social choice

A new investigation is launched into the problem of decision-making in the face of complete ignorance, and linked to the problem of social choice. In the first section the author introduces a set of properties which might characterize a criterion for decision-making under complete ignorance. Two of these properties are novel: independence of non-discriminating states, and weak pessimism. The second section provides a new characterization of the so-called principle of insufficient reason. In the third part, lexicographic maximin and maximax criteria are characterized. Finally, the author's results are linked to the problem of social choice.     

The reasonable man — a social choice approach

Most legal systems rely heavily on the notion of the reasonable man. Here an attempt is made to analyze the reasonable man in a social choice model. The main argument is that if the reasonable man satisfies a certain set of axioms, he essentially coincides with one of the individuals, both in terms of his preferences and in terms of his expectations.     

Modernizing social security: Changing responsibilities and individual choice

Social security needs to be reformed to make it sustainable. We argue that it is necessary to consider not only system characteristics (such as the level and duration of benefits, insured population), but also the division of responsibilities. Social security is not solely a state matter; firms, trade unions, industrial sectors and the individual play a role as well. As social risks are to some extent endogenous, insurance ought to be taken care of at the level at which the risk can be most directly influenced in order to improve efficiency. This may partly take place within the public system, for example through risk rating. Alternatives would include shifting from collective to more individual arrangements, prominent examples being multipillar systems and savings accounts. Multipillar systems mainly imply a new division of responsibilities, taking the endogeneity of social risks and the implications of modern life cycles into account. At the same time they offer more individual choice. Savings accounts reduce moral hazard without affecting individual choice. Either way, in reforming social security a balance needs to be found between competing goals or principles: between equity and efficiency, between solidarity and freedom of choice, between the risks of moral hazard and adverse selection. This choice is difficult because social security is not only about "security". It is an important part of the way we organize our society and embodies many of society's values.     

On admissible strategies and manipulation of social choice procedures

A collective choice mechanism can be viewed as a game in normal form; in this article it is shown, for very attractive rules and for sets with any number of alternatives, how individuals involved in a collective decision problem can construct the preferences they choose to express. An example is given with a version of plurality rule. Manipulability results are deduced from such a characterization.     

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.     

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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Race as social science hegemony: a note on Southeast Asian populations

Emergence of Southeast Asian populations in Western societies corresponds to hegemony. As per hegemony, race is assumed the universal, governing category of human populations. It is on the basis of this hegemonic conceptual view that the construct of race is challenged by the emergence of alternative human population phenomena. For social scientists who will engage in research specific to Southeast Asian populations, race must be reduced in proportion to its significance in their lives. The utilization of non-racial constructs includes the need to acknowledge culture. The outcome will contribute to the evolution of social science despite the prevalence of race constructs as hegemony vis-à-vis Southeast Asian populations.     

Notes on Ostrogorski's paradox

Conclusion This note has investigated the necessary conditions for the existence of Ostrogorski's Paradox, and it showed that the paradox depends on the sizes of the groups taking each possible set of stands on the salient issues. By revising its positions on relevant issues, the majority party can avert the paradox. With increased emphasis on single-issue voting observed in the United States and other Western democracies, the analysis of the paradox should guide the understanding of parties' responses to coalition formation processes among special interest groups. Indeed, the Apex conditions characterizing the paradox provide clues as to the strategy to be followed by the majority party in selecting its platform: the party should generally follow positions advocated by the largest group while presenting a coalition of all other groups.The helpful comments of Howard Tamashiro on an earliar draft of this paper are greatfully acknowledge.