Comments on: King Solomon’s Dilemma At The Olympic Trials

By: Daniel

Daniel — Tue, 26 Jun 2012 12:01:27 +0000

I believe runners know whether their time was better or worse than their expected performance. If AF thinks she is worth 11 flat and Jeneba thinks she is worth 11.1, then Jeneba would go for Coin-toss while AF would go for run-off. Since the USATF has commitment, that is incentive compatible, but the USATF is not using that information (they should send AF to the Olympics in that case). What is not the case is that it is common knowledge among them who is better (which is the case in the Solomon’s Dilemma). I guess that they only know whether their time was above or below their expected performance and their expectation over their rival’s performance is exactly their time.

By: Anonymous

Anonymous — Tue, 26 Jun 2012 10:08:08 +0000

I do not see how it relates to King Solomon’s dilemma. Do the runners know something that the judge(s) do not know?

By: Mild Speculation

Mild Speculation — Tue, 26 Jun 2012 03:14:27 +0000

A related question: is there a threshold for competitiveness after which the U.S.A. or any given country is disadvantaged? That is, can 4 athletes competing for 3 spots be worse than 3? Athletes who are clear favorites can plan their training so that they peak at the Olympics, but in events where there are no clear favorites, athletes must peak for the Olympic Trials, which is suboptimal for Olympic performance (the degree to which is it is suboptimal depends on the sport).

How could an athlete’s skill be modeled by a few parameters, and how might one express preferences over menus of athletes? Can these preferences be represented by a utility function?