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Published in:

18-11-2022 | Original Paper

Where should your daughter go to college? An axiomatic analysis

Author: William Thomson

Published in: Social Choice and Welfare | Issue 1-2/2023

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.

previous article The possibility of generalized social choice functions and Nash’s independence of irrelevant alternatives

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Immaterial multiplicities occur when both participants are indifferent between the two endpoints of the interval of possible locations.

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).

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.

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.

We realize of course that Theorem 1 and Theorem2 3–4 are proved under conflicting assumptions about what our two characters’ preferences truly are.

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.

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.

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Title: Where should your daughter go to college? An axiomatic analysis
Author: William Thomson
Publication date: 18-11-2022
Publisher: Springer Berlin Heidelberg
Published in: Social Choice and Welfare / Issue 1-2/2023
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-022-01438-y

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