Impartial Selection and the Power of up to Two Choices
We study mechanisms that select members of a set of agents based on nominations by other members and that are impartial in the sense that agents cannot influence their own chance of selection. Prior work has shown that deterministic mechanisms for selecting any fixed number of agents are severely limited, whereas randomization allows for the selection of a single agent that in expectation receives at least 1 / 2 of the maximum number of nominations. The bound of 1 / 2 is in fact best possible subject to impartiality. We prove here that the same bound can also be achieved deterministically by sometimes but not always selecting a second agent. We then show a separation between randomized mechanisms that make exactly two or up to two choices, and give upper and lower bounds on the performance of mechanisms allowed more than two choices.
We thank the anonymous referees for their suggestions to improve the presentation of the results.
- 1.Alon, N., Fischer, F., Procaccia, A.D., Tennenholtz, M.: Sum of us: Strategyproof selection from the selectors. In: Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge, pp. 101–110 (2011)Google Scholar
- 3.Bousquet, N., Norin, S., Vetta, A.: A near-optimal mechanism for impartial selection. In: Liu, T.-Y., Qi, Q., Ye, Y. (eds.) WINE 2014. LNCS, vol. 8877, pp. 133–146. Springer, Heidelberg (2014) Google Scholar
- 5.Fischer, F., Klimm, M.: Optimal impartial selection. In: Proceedings of the 15th ACM Conference on Economics and Computation, pp. 803–820 (2014)Google Scholar
- 8.Mitzenmacher, M., Richa, A.W., Sitaraman, R.: The power of two random choices: a survey of techniques and results. In: Rajasekaran, S., Pardalos, P.M., Reif, J.H., Rolim, J. (eds.) Handbook of Randomized Computing, vol. 1, pp. 255–312. Springer (2001)Google Scholar