Abstract
We characterize unanimous and strategy-proof random social choice functions in the classical committee formation model in terms of the properties of marginal decomposability and monotonicity. We show that if committees of a fixed size have to be selected, then an onto and strategy-proof random social choice function must be an appropriately defined random dictatorship.
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Notes
- 1.
There are several ways in which this can be done. Here we follow the standard stochastic dominance approach developed in Gibbard (1977).
- 2.
A random social choice function satisfies unanimity if it picks a committee that is first-ranked by all agents, with probability one.
- 3.
We will consider one such problem in the next section.
- 4.
To see that it is possible to construct such a preference ordering, consider a lexicographic (and hence separable) preference over A where k is the lexicographic worst component (details may be found in Chatterji et al., 2012).
References
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Roy, S., Sadhukhan, S., Sen, A. (2019). Formation of Committees Through Random Voting Rules. In: Trockel, W. (eds) Social Design. Studies in Economic Design. Springer, Cham. https://doi.org/10.1007/978-3-319-93809-7_13
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DOI: https://doi.org/10.1007/978-3-319-93809-7_13
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