In a recent episode of Top Chef, the remaining contestants were split into two groups, say A and B. Group A had to vote for the best and worst dishes in Group B and vice-versa. One the two contestants with the worst dishes gets eliminated by the usual judges, i.e.not the contestants.
All the contestants cooked in the same kitchen so they could match each dish to each chef (and, in any case, each chef introduced his own dish). So, each voter knows which chef’s chances of surviving she is affecting by voting for or against his dish. In the next episode, each voter – if they survive till the next round – competes with the remaining chefs. So, other things being equal, the optimal strategy is simple: each voter should vote for the weakest candidate in the other group and against the strongest candidate. There have been enough episodes for everyone to pretty much agree on who the best and worst cooks are in each group. The “rational choice” calculation: you want to maximize the chances of winning so you want to be matched up against the worst chefs in future rounds and get rid of the best chefs if possible.
One caveat is that in future rounds, contestants will be judged by the usual crew of Tom, Padma etc so you might care about your reputation with them. But the evidence from past series strongly suggests that they do not vote against “strategic” contestants. Food is important and, for the producers, drama. Strategic behavior might actually help you survive longer if you create drama.
This “rational choice” prediction had at most a 50% success rate. One group did choose one of the strongest contestants, Kenny, from the other group for the worst dish. And he did claim that he’d been put on the chopping block to eliminate a future threat. But the strongest guy in the other group, Angelo, did not get close to elimination. And maybe Kenny did have the worst dish.
It’s interesting to speculate on why the obvious rational choice prediction is not borne out. Perhaps people are honest or it is very hard to lie about a dish when its obviously good – the verifiable information makes it difficult to dissemble. It’s also hard to be disliked. The contestants all live in the same house. In some episodes they cook together and have to coöperate. Everyone cam remember the hated Marcel from an earlier season! Voting is sequential which exasperates the problem – the first person to vote does not want to come out as an evil strategic player and the later people to vote know they can’t impact the outcome anyway. So, perhaps reputation among the contestants themselves is important.
If they use the same Cold War conceit next season, I would love to have anonymous voting. Behind the veil of ambiguity, people might be more strategic. It would add to the drama – the following week’s episode will be full of intrigue if a good chef gets knifed (figuratively!) in the back.