We consider a society whose members have to choose not only an outcome from a given set of outcomes but also a subset of agents that will remain members of the society. We study the extensions of approval voting, scoring methods and the Condorcet winner to our setting from the point of view of their internal stability and consistency properties.
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A rule is outsider independent if it is invariant with respect to the change of the preferences of an agent who is not a member of the two final societies.
Example 1 shows that without those adaptations, the voting methods are not internally stable.
A rule is unanimous if it always selects an alternative belonging to the set of common best alternatives, whenever this set is non-empty. A rule is outsider independent if it is invariant with respect to the change of preferences of an agent who is not a member of the two final societies.
The Borda rule is the scoring method when the points are the integers \(k-1,\ldots ,1,0\) where k is the number of alternatives. The Plurality rule is the scoring method when one point is assigned to the top-ranked alternative and zero points are assigned to the other alternatives.
To obtain the vote of an agent we have to use information contained in the full profile, but since we are not considering the strategic aspect of preference revelation, this is not an issue.
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We are grateful to two referees for many useful comments and suggestions. 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 “Fundación 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: internal stability and consistency. Theory Decis 84, 83–97 (2018). https://doi.org/10.1007/s11238-017-9644-6
- Internal stability