Selecting one of us: How to exploit prior information

What is it about?

Consider the case where a number of peers need to select one of them to receive a prestigious prize based on merit. To find the most distinguished member, they cast approval votes on each other. The peers however are not to be trusted: whenever they get a chance, they are going to misreport their nominations to receive the prize for themselves. An impartial mechanism nullifies this behaviour, by ensuring that no peer can change from a loser to a winner, only by changing its casted votes. This work focuses on the Approval Voting with Default mechanism, a rather straightforward rule to select the winner. In high level, this mechanism awards the prize to the peer with most votes, given that this peer is unique; otherwise, the prize is given to a pre-selected peer, whose votes are ignored. While this mechanism cannot always find the optimal winner, it is impartial, and under sufficient prior information is guaranteed to return a winner whose support is vary close to the support of the most distinguished peer.

Featured Image

Photo by Giorgio Trovato on Unsplash

Photo by Giorgio Trovato on Unsplash

Why is it important?

Impartial selection is a problem that got severe attention by economists and and computer scientists in the last decade. While impartiality is a highly desirable property, it is now known that the design of impartial mechanisms is severely limited. For example, in the worst-case, any impartial mechanism inevitably selects a winner voted by 0 other participants, while there is someone voted by all! This work is the first to explore how prior information on the voters' preferences can be used to tackle these inefficiencies and presents mechanisms which perform significantly better than the worst-case.