Selection Under Veto with Limited Foresight

I consider a class of two-party, zero sum sequential selection games where players compete over the composition of a panel comprising one or more seats. The players have a limited number of vetoes which can be used to reject panelists, with replacements being selected at random from a pool. One player wishes to maximize, and the opposing player wishes to minimize a utility function over panelist ratings. This selection game is notable in that 1) it is common, with application in fields such as trial jury selection, selection of job applicants by committee, selection of panelists and moderators for a debate, arbitrator selection, and group decision making, and 2) it leads to complex games, obscuring optimal strategies and thereby increasing the costs of optimal play. In this paper, I consider various simplified, limited foresight panel selection strategies and compare these with optimal play. I find that a commonly used limited foresight strategy – vetoing panelists less favorable than some fixed value, such as the replacement pool average - is not generally effective for selection games, such as jury selection, which comprise more than a few slots.