The shape of the tolerance zone

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There are ten of you, and you want to go to dinner. The other nine people include two vegetarians, a curry-addict and someone who likes anything ethnic. Some of the rest have very mild preferences; others aren’t really bothered where they eat. You have boiled down the choice to six restaurants.

How on earth do you decide where to go?

Currently, the way in which we try to resolve such problems can be highly unsatisfactory.  People may game the system by exaggerating the intensity of their feelings – noisily campaigning for their favourite option to the exclusion of anyone else. After all, you have nothing to lose by pretending to care a huge amount about going to a restaurant you only slightly prefer to all the others.

Or perhaps the opposite happens. In a kind of triumph of lazy compromise, you end up going to the restaurant the fewest people object to. This generally means that everyone ...