Aggregating extended preferences (original) (raw)

Extended preferences and freedom of choice

Social Choice and Welfare, 2000

The common choice theory in economics is based on the assumption that an individual is de®ned in terms of a binary preference relation. This preference relation is de®ned over alternatives without taking into account menu dependence and, in particular, freedom of choice or, more generally, the set that contains the alternatives. In this study we clarify the nature and the signi®cance of freedom of choice which may positively or negatively a¨ect the individual's welfare. Our proposed extended preference relation of the individual takes into account both the particular alternative and the opportunity set that he faces. This extended relation does not induce ranking of opportunity sets. Its restriction to a particular opportunity set is the paradigmatic preference relation and it can capture the dependence of preferences on freedom of choice. Our main result establishes the inconsistency between dependence of extended preferences on freedom of choice and the existence of a utility that represents the paradigmatic preference relation and any of its restrictions. Sen (1988, pp. 289±290) interprets the set of alternatives faced by an individual as a set of feasible actions from which the individual can choose. If the only role freedom of choice plays is the distinction between feasible and nonfeasible alternatives, then the following options are equivalent: This paper is based on chapter 4 of Eyal Baharad's Doctoral Dissertation prepared at

A Theorem on Preference Aggregation

2003

I present a general theorem on preference aggregation. This theorem implies, as corollaries, Arrow's Impossibility Theorem, Wilson's extension of Arrow's to non-Paretian aggregation rules, the Gibbard-Satterthwaite Theorem and Sen's result on the Impossibility of a Paretian Liberal.

On a Theorem due to Alan D. Taylor about Aggregation of Preferences

Arthaniti: Journal Of Economic Theory And Practice, 2018

In this paper, we show that there does not exist any triple acyclic preference aggregation rule that satisfies Majority property, weak Pareto criterion and a version of a property due to Alan Taylor. We also show that there are non-dictatorial preference aggregation rules and in particular non-dictatorial social welfare functions which satisfy the weak Pareto criterion and Taylor's Independence of Irrelevant Alternatives. Further, we are able to obtain analogous results for preference aggregation functionals by suitably adjusting the desired properties to fit into a framework which uses individual utility functions rather than individual preference orderings. Our final result is a modest generalisation of Sen's version of Arrow's impossibility theorem which is shown to hold under our mild domain restriction.

Extended Preferences and Interpersonal Comparisons of Well-being

An important objection to preference-satisfaction theories of well-being is that these theories cannot make sense of interpersonal comparisons of well-being. A tradition dating back to Harsanyi (1953) attempts to respond to this objection by appeal to so-called extended preferences: very roughly, preferences over situations whose description includes agents' preferences. This paper examines the prospects for defending the preference-satisfaction theory via this extended preferences program. We argue that making conceptual sense of extended preferences is less problematic than others have supposed, but that even so extended preferences do not provide a promising way for the preference satisfaction theo-rist to make interpersonal well-being comparisons. Our main objection takes the form of a trilemma: depending on how the theory based on extended preferences is developed, either (a) the result will be inconsistent with ordinary preference-satisfaction theory, or (b) it will fail to recover sufficiently rich interpersonal well-being comparisons, or (c) it will take on a number of other arguably odd and undesirable commitments.

Concepts of extended preference

Journal of Economic Behavior & Organization, 1985

This paper remedies ambiguity in the discussion of interdependent preferences by developing a consistent set of distinctions, which span the full range of sympathetic and antipathetic interaction, for the two-person case without reactive behavior. It defines concepts such as benevolence, generosity, altruism, destructiveness, and willingness to begrudge transfers to others and indicates how their use can clarify the discussion of economic behavior. The definitions take account of preferences (indicated by rates of substitution) and prices (indicated by rates of exchange) at critical income allocations. 'If charity cost no money and benevolence caused no heartache, the world would be full of philanthropists.'

Arrovian impossibilities in aggregating preferences over non-resolute outcomes

Social Choice and Welfare, 2008

Given a society confronting a set of alternatives A, we consider the aggregation of individual preferences over the power set A of A into a social preference over A. In case we allow individuals to have any complete and transitive preference over A, Arrow's impossibility theorem naturally applies. However, the Arrovian impossibility prevails, even when the set of admissible preferences over A is severely restricted by strong axioms that relate preferences over A to preferences over A. In fact, we identify a very narrow domain of lexicographic orderings over A which exhibits the Arrovian impossibility in all of its superdomains. As the lexicographic extension we use is compatible with almost all standard extension axioms, we interpret our results as the strong prevalence of Arrow's impossibility theorem in aggregating preferences over sets.

A reconsideration of the empirical implications of additive preferences

1974

IN the last twenty years, the theory of utility maximisation has had extensive application as a basis for deriving empirically estimable demand equations. This method of analysing and measuring demand has tended not to use general utility functions, but rather to depend upon specifications which assume that preferences are either directly or indirectly additive.

Preference aggregation theory without acyclicity: The core without majority dissatisfaction

2010

Acyclicity of individual preferences is a minimal assumption in social choice theory. We replace that assumption by the direct assumption that preferences have maximal elements on a fixed agenda. We show that the core of a simple game is nonempty for all profiles of such preferences if and only if the number of alternatives in the agenda is less than the Nakamura number of the game. The same is true if we replace the core by the core without majority dissatisfaction, obtained by deleting from the agenda all the alternatives that are non-maximal for all players in a winning coalition. Unlike the core, the core without majority dissatisfaction depends only on the players' sets of maximal elements and is included in the union of such sets. A result for an extended framework gives another sense in which the core without majority dissatisfaction behaves better than the core.

Non-dictatorial extensive social choice

Economic Theory, 2005

Different social planners may have different opinions on the wellbeing of individuals under different social options . If utilities are translation-or ratio-scale measurable, or if the social ranking might be incomplete, or if interplanner comparability is allowed; then there exists non-dictatorial aggregation rules. We propose extensions, intersections, and mixtures of the Pareto, utilitarian, leximin, Kolm-Pollak, and iso-elastic rules. * We are extremely grateful to the referee who was willing to review this paper four times. Her/his 'extensive' and in-depth comments had a strong impact. Further thanks are due to Bart Capéau, Marc Fleurbaey, Maurice Salles, Erik Schokkaert, and Alain Trannoy. The first author gratefully acknowledges the financial support by the TMR network Living Standards, Inequality and Taxation (ERBFMRXCT 980248) of the European Communities.

An extension of a theorem on the aggregation of separable preferences

Social Choice and Welfare, 1999

An Excess-Voting Function relative to a pro®le p assigns to each pair of alternatives xY y, the number of voters who prefer x to y minus the number of voters who prefer y to x. It is shown that any non-binary separable Excess-Voting Function can be achieved from a preferences pro®le when individuals are endowed with separable preferences. This result is an extension of Hollard and Le Breton (1996). Soc Choice Welfare (1999) 16: 159±167 Many thanks are due to Jean-FrancË ois Laslier and to two referees for their valuable remarks to improve this paper. I would like to thank Basudeb Chaudhuri for his careful reading.