Eliciting socially optimal rankings from unfair jurors

Abstract

El objetivo esencial de esta institución es fomentar cuantitativa y cualitativamente una línea de estudios e investigaciones científicas que contribuyan a un más preciso y detallado conocimiento de Andalucía, y difundir sus resultados a través de varias líneas estratégicas.El Centro de Estudios Andaluces desea generar un marco estable de relaciones con la comunidad científica e intelectual y con movimientos culturales en Andalucía desde el que crear verdaderos canales de comunicación para dar cobertura a las inquietudes intelectuales y culturales.Las opiniones publicadas por los autores en esta colección son de su exclusiva responsabilidad

A natural mechanism for eliciting rankings when jurors have favorites

“…Although our impartiality is defined by Definition 1, our result may hold even under weaker impartiality settings. As explained in page 5, the degree of impartiality in Amorós (2009) is lower than in our setting. However, our a-juror-for-a-pair condition is not sufficient for our mechanism to work in his setting, since it allows contestants not included in the impartial set to be "enemies" of the juror-who can, in order to rank them in unjustly low positions, choose a at some stage (π , a).…”

“…This proof is structured in the same way as is that of Proposition 2 in Amorós (2009). Note that this result does not depend on what equilibrium concept we choose.…”

“…These types of preferences are contained in R j (I j , π), where [N \ I j ] is a singleton. On the other hand, Amorós (2009) considers environments where jury j does not necessarily prefer the modified ranking to the ranking where b ∈ I j is ranked unjustly higher than a ∈ N as long as (i) a is not in I j or (ii) a does not lie next to b in the ranking. The case of (i) means that j prefers ranking a contestant in whom j has a stake unjustly lower than a contestant in whom j has no stake; that is, the stake is an adversarial relationship.…”

“…Although Amorós (2009) shows that is also a sufficient condition for Nash implementation as well, he needs to use a Maskin-type mechanism to do so. (In Appendix A, I will show that the same results hold under my setting, where z is not fixed to n, unlike in his.)…”

“…They consider this problem in a framework where each juror is assumed to be biased in favor of a unique and distinct contestant and show that the socially optimal ranking is Nash implementable. Amorós (2009) considers a framework with a wider class of preferences-for example, a juror with one or more "friends" (contestants the juror would want to benefit) and "enemies" (contestants the juror would want to prejudice). Given this wide range, he provides the necessary and sufficient condition for the jury to determine the socially optimal ranking with respect to several equilibrium concepts, using decision-making methods similar to the canonical mechanism in Maskin (1999).…”