Abstract
We consider a society whose members have to choose not only an outcome from a given set of outcomes but also the subset of agents that will remain members of the society. We assume that each agent is indifferent between any two alternatives (pairs of final societies and outcomes) provided that the agent does not belong to any of the two final societies, regardless of the chosen outcome. Under this preference domain restriction we characterize the class of all strategy-proof, unanimous and outsider independent rules as the family of all serial dictator rules.
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Notes
All these examples will be included as particular instances of our model. However, the strong incentive requirement of strategy-proofness will be incompatible with any stability notion related to voluntary membership.
See the last section of the paper for a discussion about the consequences of requiring stronger domain restrictions.
For instance, complex and sequential algorithms defined for matching problems induce rules mapping preference profiles into alternatives.
Note that we are admitting the possibility that the society selects all outcomes with no agent in the final society; i.e., for all \(x\in X\) , \((\varnothing ,x)\in A\).
See the final section of the paper for an indication of the class of strategy-proof and unanimous rules that are not outsider independent.
Observe again that the preferences we are considering satisfy (P.1) and hence, rules do not operate on the universal domain of preferences over A. Thus, the Gibbard–Satterthwaite theorem can not be applied.
The preference \(R_{N^{*},\succ _{i}}\) may not depend on \(\succ _{i},\) but for simplicity we maintain the notation \(R_{N^{*},\succ _{i}}\) .
We thank a referee of this journal for suggesting us these two domain restrictions. However, to obtain full characterizations of interesting classes of non-trivial and strategy-proof rules, on the two corresponding domains, seems to require a complete analysis, which is outside the scope of the present paper.
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We are grateful to two referees and an Associate Editor of this journal for very useful comments and suggestions that helped us to write a better version of the paper. The work of G. Bergantiños is partially supported by research Grants ECO2014-52616-R from the Spanish Ministry of Science and Competitiveness, GRC 2015/014 from “Xunta de Galicia”, and 19320/PI/14 from “ Fundaci ón Séneca de la Región de Murcia”. J. Massó acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2015-0563) and Grant ECO2014-53051, and from the Generalitat de Catalunya, through Grant SGR2014-515. The paper was partly written while J. Massó was visiting the Department of Economics at Stanford University; he wishes to acknowledge its hospitality as well as financial support from the Ministerio de Educación, Cultura y Deporte through project PR2015-00408. The work of A. Neme is partially supported by the Universidad Nacional de San Luis, through Grant 319502, and by the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), through Grant PIP 112-200801-00655.
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Bergantiños, G., Massó, J. & Neme, A. On societies choosing social outcomes, and their memberships: strategy-proofness. Soc Choice Welf 48, 857–875 (2017). https://doi.org/10.1007/s00355-017-1041-0
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DOI: https://doi.org/10.1007/s00355-017-1041-0