Formation of committees under constraints through random voting rules

Roy, Souvik and Sadhukhan, Soumyarup (2021): Formation of committees under constraints through random voting rules.

Abstract

We consider the problem of choosing a committee from a set of available candidates through a randomized social choice function when there are bounds on the size (the number of members) of the committee to be formed. We show that for any (non-vacuous) restriction on the size of the committee, a random social choice function (RSCF) is onto and strategy-proof if and only if it is a range-restricted random dictatorial rule. Next, we consider the situation where an “undesirable committee” can be chosen with positive probability only if everyone in the society wants it as his best committee. We call this property strong unanimity. We characterize all strongly unanimous and strategy-proof RSCFs when there is exactly one undesirable committee. A common situation where a single committee is undesirable is one where the null committee is not allowed to be formed. We further show that there is no RSCF satisfying strong unanimity and strategy-proofness when there are more than one undesirable committees. Finally, we extend all our results when strategy-proofness is strengthened with group strategy-proofness.

• Item Type: MPRA Paper
• Language: English
• Keywords: Committee Formation; Random Social Choice Function; Strategy-proofness; Ontoness; Strong unanimity; Group strategy-proofness
• Subjects: D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D82 - Asymmetric and Private Information ; Mechanism Design

References

BARBERA, S., J. MASSO, AND A. NEME (2005): “Voting by committees under constraints,” Journal of Economic Theory, 122, 185–205.

BARBERA, S., H. SONNENSCHEIN, AND L. ZHOU (1991): “Voting by committees,” Econometrica: Journal of the Econometric Society, 595–609.

BRETON, M. L. AND A. SEN (1999): “Separable preferences, strategyproofness, and decomposability,” Econometrica, 67, 605–628.

CHATTERJI, S., A. SEN, AND H. ZENG (2014): “Random dictatorship domains,” Games and Economic Behavior, 86, 212–236.

CHATTERJI, S. AND H. ZENG (2019): “Random mechanism design on multidimensional domains,” Journal of Economic Theory, 182, 25–105.

GIBBARD, A. (1977): “Manipulation of schemes that mix voting with chance,” Econometrica, 45, 665–681.

ROY, S., S. SADHUKHAN, AND A. SEN (2019): “Formation of Committees Through Random Voting Rules,” in Social Design, Springer, 219–231.

SERIZAWA, S. (1995): “Power of voters and domain of preferences where voting by committees is strategy-proof,” Journal of Economic Theory, 67, 599–608.