Abstract
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.
A. Bjelde and M. Klimm—The research was carried out in the framework of Matheon supported by the Einstein Foundation Berlin.
F. Fischer—Part of the research was carried out while the author was a member of the Statistical Laboratory at the University of Cambridge.
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Acknowledgements
We thank the anonymous referees for their suggestions to improve the presentation of the results.
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Bjelde, A., Fischer, F., Klimm, M. (2015). Impartial Selection and the Power of up to Two Choices. In: Markakis, E., Schäfer, G. (eds) Web and Internet Economics. WINE 2015. Lecture Notes in Computer Science(), vol 9470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48995-6_11
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DOI: https://doi.org/10.1007/978-3-662-48995-6_11
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