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Social Choice and Welfare

Erschienen in:

01.06.2014 | Original Paper

On the informational basis of social choice with the evaluation of opportunity sets

verfasst von: Yukinori Iwata

Erschienen in: Social Choice and Welfare | Ausgabe 1/2014

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Abstract

This paper examines the informational basis of social choice in a broader conceptual framework. Formal welfarism is a social evaluation in which any information other than the well-being of individuals is excluded, where the notion of individual well-being can be conceived in various ways. We propose a notion of individual well-being defined over pairs of outcomes and opportunity sets from which they are chosen. The concept of consequentialism and non-consequentialism is naturally introduced by restricting individual evaluation functions over the pairs of outcomes and opportunity sets. The two formal welfarism theorems provide axiomatic characterizations of formal welfarism in the extended framework. We show that the presence of a consequentialist or a non-consequentialist affects the validity of the two formal welfarism theorems in the extended framework.

Vorheriger Artikel Fairness, freedom, and forgiveness in health care

Nächster Artikel Independence of downstream and upstream benefits in river water allocation problems

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See Blackorby et al. (2002), d’Aspremont and Gevers (2002) and Bossert and Weymark (2004) for surveys of the literature on the welfarist approach to social choice.

For example, utility is interpreted as “an index supposed to capture all relevant features of individual situations, and to synthesize all these features in a one-dimensional way” (Fleurbaey and Hammond 2004, p. 1189).

Blackorby et al. (2005), for example, suggest that “(i)t is possible to employ Sen’s theory in a welfarist context, nevertheless. What is needed is an individual goodness relation which ranks all the possible combinations of functionings and capabilities” (Blackorby et al. 2005, p. 257).

See Fleurbaey (2003) for discussions on formal welfarism and the informational basis of social choice in a broadened conceptual framework.

See Iwata (2007) for further discussions on the notion of individual well-being defined over the pairs of outcomes and opportunity sets.

A social ordering functional was originally introduced by Sen (1970) as a “social welfare functional,” which associates a social ordering over outcomes with each profile of admissible utility functions.

An individual evaluation function can be seen as a numerical representation of an “individual extended preference” over \(\Omega \), as proposed by Suzumura and Xu (2001, 2003). Since we assume that the number of alternatives is finite, such an extended preference is always numerically representable. See Suzumura and Xu (2003) for an analysis of a numerical representation of an extended preference for the case where the number of outcomes is infinite but the number of elements in an opportunity set is finite.

That is, \(\gg \) is the sign of a vector inequality such that for all \(\alpha =(\alpha _{1},\ldots ,\alpha _{n}),\beta =(\beta _{1},\ldots ,\beta _{n})\in \mathbb{R }^{n}\), \(\alpha \gg \beta \) if and only if \(\alpha _{i}>\beta _{i}\) for all \(i\in \{1,\ldots ,n\}\).

Since we assume that the number of alternatives is finite, \(R^{*}\) can always be numerically represented for all \(V\in \mathcal D \).

The function \(W:\mathbb R ^{n}\rightarrow \mathbb R \) is weakly monotonic if \(W(\alpha )>W(\beta )\) for all \(\alpha , \beta \in \mathbb R ^{n}\) with \(\alpha \gg \beta \).

See Dowding and Hees (2009) and Foster (2010) for surveys on ranking opportunity sets in terms of freedom of choice.

Other proofs for Theorems 3 and 4 can be found. It is possible to show that \(\mathcal D _{E}\) is a common and saturating domain, as defined below. Therefore, we can prove Theorems 3 and 4 by using arguments similar to those in Weymark (1998) and Bordes et al. (2005).

We need WP to obtain this result. In fact, as shown in Weymark (1998), the joint satisfaction of PI and BI without WP is not equivalent to welfarism for a “saturating utility profile domain” that is mathematically equivalent to a saturating domain defined below.

Blackorby C, Bossert W, Donaldson D (2002) Utilitarianism and the theory of justice. In: Arrow KJ, Sen AK, Suzumura K (eds) Handbook of social choice and welfare, vol 1. North-Holland, Amsterdam, pp 543–596

Blackorby C, Bossert W, Donaldson D (2005) Multi-profile welfarism: a generalization. Soc Choice Welf 24:253–267CrossRef

Bordes G, Hammond P, Le Breton M (2005) Social welfare functionals on restricted domains and in economic environments. J Public Econ Theory 7:1–25CrossRef

Bossert W, Weymark J (2004) Utility in social choice. In: Barberà S, Hammond P, Seidl C (eds) Handbook of utility theory: extensions, vol 2. Kluwer, Dordecht, pp 1099–1177

d’Aspremont C, Gevers L (1977) Equity and the informational basis of collective choice. Rev Econ Stud 44:199–209CrossRef

d’Aspremont C, Gevers L (2002) Social welfare functionals and interpersonal comparability. In: Arrow KJ, Sen AK, Suzumura K (eds) Handbook of social choice and welfare, vol 1. North-Holland, Amsterdam, pp 459–541CrossRef

Debreu G (1954) Representation of a preference ordering by a numerical function. In: Thrall R, Coombs C, Davis R (eds) Decision processes. Wiley, New York, pp 159–166

Dowding K, van Hees M (2009) Freedom of choice. In: Anand P, Pattanaik PK, Puppe C (eds) The handbook of rational and social choice. Oxford University Press, Oxford, pp 374–392CrossRef

Fleurbaey M (2003) On the informational basis of social choice. Soc Choice Welf 21:347–384CrossRef

Fleurbaey M, Hammond P (2004) Interpersonally comparable utility. In: Barberà S, Hammond P, Seidl C (eds) Handbook of utility theory: extensions, vol 2. Kluwer, Dordecht, pp 1179–1285

Fleurbaey M, Mongin P (2005) The news of the death of welfare economics is greatly exaggerated. Soc Choice Welf 25:381–418CrossRef

Foster JE (2010) Freedom, opportunity, and well-being. In: Arrow KJ, Sen AK, Suzumura K (eds) Handbook of social choice and welfare, vol 2. North-Holland, Amsterdam, pp 687–728CrossRef

Hammond P (1999) Roberts’ weak welfarism theorem: a minor correction. Working paper 99–021. Department of Economics, Stanford University

Iwata Y (2007) A variant of non-consequentialism and its characterization. Math Soc Sci 53:284–295CrossRef

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Suzumura K, Xu Y (2001) Characterizations of consequentialism and nonconsequentialism. J Econ Theory 101:423–436CrossRef

Suzumura K, Xu Y (2003) Consequences, opportunities, and generalized consequentialism and non-consequentialism. J Econ Theory 111:293–304CrossRef

Suzumura K, Xu Y (2004) Welfarist-consequentialism, similarity of attitudes, and Arrow’s general impossibility theorem. Soc Choice Welf 22:237–251CrossRef

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Titel: On the informational basis of social choice with the evaluation of opportunity sets
verfasst von: Yukinori Iwata
Publikationsdatum: 01.06.2014
Verlag: Springer Berlin Heidelberg
Erschienen in: Social Choice and Welfare / Ausgabe 1/2014
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-013-0764-9

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