Abstract
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.
Similar content being viewed by others
Notes
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.
References
Barberà, S., Maschler, M., & Shalev, J. (2001). Voting for voters: a model of electoral evolution. Games and Economic Behavior, 37, 40–78.
Barberà, S., & Perea, A. (2002). Supporting others and the evolution of influence. Journal of Economic Dynamics and Control, 26, 2051–2092.
Berga, D., Bergantiños, G., Massó, J., & Neme, A. (2004). Stability and voting by committees with exit. Social Choice and Welfare, 23, 229–247.
Berga, D., Bergantiños, G., Massó, J., & Neme, A. (2006). On exiting after voting. International Journal of Game Theory, 34, 33–54.
Berga, D., Bergantiños, G., Massó, J., & Neme, A. (2007). An undominated Nash equilibrium for voting by committees with exit. Mathematical Social Sciences, 54, 152–175.
Bergantiños, G., Massó, J., & Neme, A. (2015). The division problem under constraints. Games and Economic Behavior, 89, 56–77.
Bergantiños, G., Massó, J., & Neme, A. (2017). On societies choosing social outcomes, and their memberships: strategy-proofness. Social Choice and Welfare, 48, 857–875.
Jackson, M., & Nicolò, A. (2004). The strategy-proof provision of public goods under congestion and crowding preferences. Journal of Economic Theory, 115, 278–308.
Nizamogullari, D., & Özkal-Sanver, İ. (2014). Characterization of the core in full domain marriage problems. Mathematical Social Sciences, 69, 34–42.
Nizamogullari, D., & Özkal-Sanver, İ. (2015). Consistent enlargements of the core in roommate problems. Theory and Decision, 79, 217–225.
Özkal-Sanver, İ. (2013). Minimal conversely consistent extension of the men-optimal solution. Social Choice and Welfare, 40, 89–99.
Sasaki, H., & Toda, M. (1992). Consistency and characterization of the core of two-sided matching problems. Journal of Economic Theory, 56, 218–237.
Roberts, K. (1999). “Dynamic voting in clubs,” mimeo, London School of Economics.
Sobel, J. (2000). A model of declining standard. International Economic Review, 41, 295–303.
Thomson, W. (1994). Consistent solutions to the problem of fair division when preferences are single-peaked. Journal of Economic Theory, 63, 219–245.
Thomson, W. (2007). On the existence of consistent rules to resolve conflicting claims: a geometric approach. Review of Economic Design, 11, 225–251.
Author information
Authors and Affiliations
Corresponding author
Additional information
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.
Rights and permissions
About this article
Cite this article
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
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11238-017-9644-6