Characterizing Minimal Impartial Rules for Awarding Prizes

The 17th ISER-Moriguchi Prize (2014) Awarded Pape

メカニズムデザインにおける小論集

Tohoku University大瀬戸真次課

Nash implementation of supermajority rules

A committee of n experts from a university department must choose whom to hire from a set of m candidates. Their honest judgments about the best candidate must be aggregated to determine the socially optimal candidates. However, experts’ judgments are not verifiable. Furthermore, the judgment of each expert does not necessarily determine his preferences over candidates. To solve this problem, a mechanism that implements the socially optimal aggregation rule must be designed. We show that the smallest quota q compatible with the existence of a q-supermajoritarian and Nash implementable aggregation rule is A committee of n experts from a university department must choose whom to hire from a set of m candidates. Their honest judgments about the best candidate must be aggregated to determine the socially optimal candidates. However, experts’ judgments are not verifiable. Furthermore, the judgment of each expert does not necessarily determine his preferences over candidates. To solve this problem, a mechanism that implements the socially optimal aggregation rule must be designed. We show that the smallest quota q compatible with the existence of a q-supermajoritarian and Nash implementable aggregation rule is q = n −⌊n−1m⌋. Moreover, for such a rule to exist, there must be at least m ⌊n−1 m⌋+ 1 impartial experts with respect to each pair of candidates.Funding for open access charge: Universidad de Málaga/CBUA. Financial assistance from Ministerio de Ciencia e Innovación under project PID2020-114309GB-I00 and Junta de Andalucía under project P18-FR-2933 is gratefully acknowledged

Prizes versus contracts as incentives for innovation

Procuring an innovation involves motivating a research effort to generate a new idea and then implementing that idea efficiently. If research efforts are unveriable and implementation costs are private information, a trade-off arises between the two objectives. The optimal mechanism resolves the trade-off via two instruments: a cash prize and a follow-on contract. It primarily uses the latter, by favoring the innovator at the implementation stage when the value of the innovation is above a certain threshold and handicapping the innovator when the value of the innovation is below that threshold. A cash prize is employed as a supplementary incentive only when the value of innovation is sufficiently high. These features are consistent with current practices in the procurement of innovation and the management of unsolicited proposals

A Game of the Throne of Saint Peter

In the Roman Catholic Church, the pope is elected by the (cardinal) electors through “scrutiny,” where each elector casts an anonymous nomination. Using historical documents, we argue that a guiding principle for the church has been the protection of electors from the temptation to defy God through dishonest nomination. Based on axiomatic analysis involving this principle, we recommend that the church overturn the changes of Pope Pius XII (1945) to reinstate the scrutiny of Pope Gregory XV (1621), and argue that randomization in the case of deadlock merits consideration

Impartial Rank Aggregation

We study functions that produce a ranking of $n$ individuals from $n$ such rankings and are impartial in the sense that the position of an individual in the output ranking does not depend on the input ranking submitted by that individual. When $n \geq 4$, two properties concerning the quality of the output in relation to the input can be achieved in addition to impartiality: individual full rank, which requires that each individual can appear in any position of the output ranking; and monotonicity, which requires that an individual cannot move down in the output ranking if it moves up in an input ranking. When $n \geq 5$, monotonicity can be dropped to strengthen individual full rank to weak unanimity, requiring that a ranking submitted by every individual must be chosen as the output ranking. Mechanisms achieving these results can be implemented in polynomial time. Both results are best possible in terms of their dependence on $n$. The second result cannot be strengthened further to a notion of unanimity that requires agreement on pairwise comparisons to be preserved

Impartial Selection and the Power of Up to Two Choices

ta no_volume: no_number: no_pages: A:X–A:Y no_year: pdf: publications/bfk_impartial.pdf no_tr: no_http: slides: publications/slides_wine15.pdf keywords: web,recent,journal cvnote: \contrib33%ta no_volume: no_number: no_pages: A:X–A:Y no_year: pdf: publications/bfk_impartial.pdf no_tr: no_http: slides: publications/slides_wine15.pdf keywords: web,recent,journal cvnote: \contrib33%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 k of agents are severely limited and cannot extract a constant fraction of the nominations of the k most highly nominated agents. We prove here that this impossibility result can be circumvented by allowing the mechanism to sometimes but not always select fewer than k agents. This added flexibility also improves the performance of randomized mechanisms, for which we show a separation between mechanisms that make exactly two or up to two choices and give upper and lower bounds for mechanisms allowed more than two choices