×

zbMATH — the first resource for mathematics

Hyper-stable social welfare functions. (English) Zbl 1341.91070
Summary: We define a new consistency condition for neutral social welfare functions, called hyper-stability. A social welfare function (SWF) selects a weak order from a profile of linear orders over any finite set of alternatives. Each profile induces a profile of hyper-preferences, defined as linear orders over linear orders, in accordance with the betweenness criterion: the hyper-preference of some order P ranks order Q above order Q’ if the set of alternative pairs P and Q agree on contains the one P and Q’ agree on. A special sub-class of hyper-preferences satisfying betweenness is defined by using the Kemeny distance criterion. A neutral SWF is hyper-stable (resp. Kemeny-stable) if given any profile leading to the weak order R, at least one linear extension of R is ranked first when the SWF is applied to any hyper-preference profile induced by means of the betweenness (resp. Kemeny) criterion. We show that no scoring rule is hyper-stable, unless we restrict attention to the case of three alternatives. Moreover, no unanimous scoring rule is Kemeny-stable, while the transitive closure of the majority relation is hyper-stable.

MSC:
91B14 Social choice
91B12 Voting theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Binmore, K, An example in group preference, J Econ Theory, 10, 377-385, (1975) · Zbl 0316.90004
[2] Bossert, W; Sprumont, Y, Strategy-proof preference aggregation, Games Econ Behav, 85, 109-126, (2014) · Zbl 1290.91055
[3] Bossert, W; Storcken, T, Strategy-proofness of social welfare functions: the use of the kemeny distance between preference orderings, Soc Choice Welf, 9, 345-360, (1992) · Zbl 0760.90004
[4] Coffman KB (2014) Representative democracy and the implementation of majority-preferred (Working paper)
[5] Igersheim, H, Du paradoxe libéral-parétien à un concept de m étaclassement des préférences, Recherches é conomiques de Louvain, 73, 173-192, (2007)
[6] Jeffrey, RC, Preferences among preferences, J Philos, 71, 377-391, (1974)
[7] Koray, S, Self-selective social choice functions verify arrow and Gibbard-Satterthwaite theorems, Econometrica, 68, 981-995, (2000) · Zbl 1026.91509
[8] Koray, S; Slinko, A, Self-selective social choice functions, Soc Choice Welf, 31, 129-149, (2008) · Zbl 1142.91438
[9] Koray, S; Unel, B, Characterization of self-selective social choice functions on the tops-only domain, Soc Choice Welf, 20, 495-507, (2003) · Zbl 1073.91561
[10] Laffond, G; Lainé, J, Majority voting on orders, Theory Decis, 49, 251-289, (2000) · Zbl 0994.91011
[11] Lainé J (2015) Hyper-stable collective rankings. In: Mathematical social sciences (in press) · Zbl 1331.91072
[12] Laslier JF (1997) Tournament solutions and majority voting. Springer, Berlin, Heidelberg, New York · Zbl 0948.91504
[13] McPherson, MS, Mill’s moral theory and the problem of preference change, Ethics, 92, 252-273, (1982)
[14] Sen, AK, The impossibility of a Paretian liberal, J Political Econ, 78, 152-157, (1970)
[15] Sen, AK; Korner, S (ed.), Choice, orderings and morality, 54-67, (1974), Oxford
[16] Sen, AK, Rational fools: a critique of behavioral foundations of economic theory, Philos Public Aff, 6, 317-344, (1977)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.