Minimax, and the economics of “Survivor”

The hit television show Survivor finished last night as improbably as it was through its recent “Pearl Island” run. Lill, a Boy Scout troop leader, seemingly gave away a million dollars.

Here is what happened: Lill could select who her fellow contestant would be for the final pair, and either her or that person would win a million dollars depending on the jury’s vote. Her choices were an appealingly direct mother, Sandra, or a young fellow, Jon, who lied extravagantly throughout the game (including about having had his grandmother die in mid-show). The rational decision seemed to be Jon, who had few friends in the jury.

But Lill chose Sandra, and Sandra went on to win $1 million by a 6-1 vote. Some immediately called Lill dumb, pointing out that she should have known Jon, the liar, would have few votes — she should have known she would have beat him at the end (and a subsequent straw vote by the jury seemingly showed that). Yet Lill chose Sandra instead, and got hammered.

Lill’s explanation was an unorthodox application of (conservative) game theory — she wanted to minimize her maximum regret (Minimax). She was so unhappy with the idea of Jon possibly winning that she willingly lowered her own chances of winning by bringing Sandra with her to the final two instead of Jon. Apparently her hypothesized regret from a Jon win was so high, despite that win being a relatively low likelihood , that she was willing to accept the high probability of losing to Sandra.

(As a side note, it is worth wondering whether Jon had a higher likelihood of winning than some thought. The straw vote showed four votes for Lill if she were paired off against Jon. That is a bare one-vote win, not exactly daunting, and certainly something that could have easily shifted in a real vote.)