A Simple Solution for a Group Choosing a Restaurant

Perhaps the common social choice problem that any of us face in practice is when we find ourselves in a group that must choose one restaurant at which all of us will eat. We propose a method where, similar to the I-choose-you-cut rule for dividing a cake, individuals in the group take turns restricting the set of choices for the group. Specifically, under our method the first person restricts the set of restaurants to a certain number the second person restricts the set to a smaller number and so on until the last person in the group selects one restaurant. We derive a formula for choosing these numbers such that — under a natural assumption about individual preferences - the probability that the group will choose any individual’s favorite restaurant is equal for each individual. For the case where there are only two people in the group and there are n restaurants, under our method the first person selects the square root of n restaurants. The second person then chooses one restaurant from this set. When there are k individuals, our method requires the first person to select n(k-1)/k restaurants. From this set the second person selects n(k-2)/k restaurants, and so on, until the final person selects one restaurant.