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Social Choice and Welfare
Erschienen in: Social Choice and Welfare 1-2/2023

18.11.2022 | Original Paper

Where should your daughter go to college? An axiomatic analysis

verfasst von: William Thomson

Erschienen in: Social Choice and Welfare | Ausgabe 1-2/2023

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Abstract

We consider the problem of choosing a location in an interval so as to best take into account the preferences of two agents who will use this location. One has single-peaked preferences and the other single-dipped preferences. The most preferred location for the agent with single-peaked preferences is known and it is the least preferred location for the agent with single-dipped preferences. We show that the only efficient and strategy-proof rules are dictatorial.
Vorheriger Artikel The possibility of generalized social choice functions and Nash’s independence of irrelevant alternatives

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Fußnoten
1
Immaterial multiplicities occur when both participants are indifferent between the two endpoints of the interval of possible locations.
 
2
This is the game in which the strategy space of each agent is the space of their possible preferences, the outcome function is the function that associates with each strategy profile the location that the rule would select for that profile, and each agent evaluates outcomes in terms of their true preferences. For surveys of the literature on strategy-proofness see Barberà (2011) and Thomson (2022).
 
3
It is called a “contamination” step by Thomson (2022) to suggest that an unpleasant conclusion reached on a subdomain of preference profiles ends up permeating the entire domain.
 
4
On the entire domain \({\mathcal {R}}_1 \times {\mathcal {R}}_2\) the Pareto set could consist of a finite or countably infinite number of intervals.
 
5
We realize of course that Theorem 1 and Theorem2 3–4 are proved under conflicting assumptions about what our two characters’ preferences truly are.
 
6
A step in the proof of Zhou (1991) dictatorship result for such economies is that if one of the origins of the box is in the range of an efficient and strategy-proof rule, then the range is that origin. This means one agent always gets everything: they are the dictator. Schummer (1997) is another example. The argument does not apply to the n-agent case unless a property such as “non-bossiness” is required of rules.
 
7
If preferences are not so restricted, the Pareto set may be the disjoint union of more than two intervals. In fact, it may be the disjoint union of countably many intervals.
 
Literatur
Alcalde-Unzu J, Vorsatz M (2018) Strategy-proof location of public facilities. Games Econom Behav 112:21–48CrossRef
Barberà S (2011) Strategy-proof social choice. In: Arrow KA, Sen A, Suzumura K (eds) Handbook of social choice II. North-Holland, Amsterdam, pp 731–831
Barberà S, Berga D, Moreno B (2010) Individual versus group strategy-proofness: When do they coincide? J Econ Theory 145:1648–1674CrossRef
Barberà S, Berga D, Moreno B (2012) Domains, ranges and strategy-proofness: the case of single-dipped preferences. Soc Choice Welfare 39:335–352CrossRef
Carroll G (2012) When are local incentive constraints sufficient. Econometrica 80:661–686CrossRef
Ching S (1997) Strategy-proofness and median voters. Int J Game Theory 26:473–490CrossRef
Cho WJ (2016) Incentive properties for ordinal mechanisms. Games Econ Behav 95:165–177CrossRef
Gibbard A (1973) Manipulation of voting schemes. Econometrica 41:587–601CrossRef
Haeringer G, Halaburda H (2016) Monotone strategyproofness. Games Econ Behav 98:68–77CrossRef
Manjunath V (2008) Anonymous, Pareto-efficient, and strategy-proof allocation rules for pure public good economies with single-dipped preferences. mimeo
Moulin H (1980) On strategy-proofness and single peakedness. Public Choice 35:437–455CrossRef
Peremans W, Storcken T (1999) Strategy-proofness on single-dipped preference domains. In: de Swart H (ed) Logic, game theory and social choice. Tilburg University Press, Tilburg, pp 296–313
Sato S (2013) A sufficient condition for the equivalence of strategy-proofness and nonmanipulability by preferences adjacent to the sincere one. J Econ Theory 148:259–278CrossRef
Satterthwaite M (1975) Strategy-proofness and Arrow’s conditions: existence and correspondence theorem for voting procedures and social choice functions. J Econ Theory 10:187–217CrossRef
Schummer J (1997) Strategy-proofness versus efficiency on restricted domains of exchange economies. Soc Choice Welfare 14:47–56CrossRef
Thomson W (2022) Strategy-proof allocation rules. Lecture notes
Zhou L (1991) Inefficiency of strategy-proof allocation mechanisms in pure exchange economies. Soc Choice Welfare 8:247–254CrossRef
Metadaten
Titel
Where should your daughter go to college? An axiomatic analysis
verfasst von
William Thomson
Publikationsdatum
18.11.2022
Verlag
Springer Berlin Heidelberg
Erschienen in
Social Choice and Welfare / Ausgabe 1-2/2023
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI
https://doi.org/10.1007/s00355-022-01438-y

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