Mathematician Refuses To Split Restaurant Bill Evenly, Cites Fairness Axioms

A dinner among six colleagues ended forty-five minutes after dessert when a mathematician insisted on dividing the bill using Shapley values rather than splitting it evenly, producing an allocation that differed from equal shares by an average of $2.37 per person. Dr. Priya Coalitional of MIT's Department of Mathematics performed the calculation on the back of the receipt, assigning each diner a payment proportional to their marginal contribution to the collective dining experience. "Splitting evenly is a heuristic, not a solution," Coalitional explained as her colleagues watched their parking meters expire. "Marcus ordered only a salad. To charge him the same as Rebecca, who ordered the lobster and two cocktails, violates every axiom of fair division. Symmetry, efficiency, the null player property — all violated." The Shapley value calculation required Coalitional to consider every possible ordering in which the six diners could have hypothetically arrived at the table and compute each person's marginal contribution to the total bill in each scenario. For six diners, this involves 720 permutations. "She was writing permutations on a napkin for twenty minutes," reported colleague James, who had ordered pasta. "I offered to just pay for my own meal. She said that would ignore the positive externalities of the shared appetizer platter, which I did eat three pieces of." The final allocations ranged from $28.14 for Marcus (the salad) to $67.92 for Rebecca (the lobster). An even split would have been $48.50 per person. "Was the forty-five minutes of computation worth saving Marcus twenty dollars?" asked Rebecca, who was the last to arrive at her now-ticketed car. "In a utilitarian framework, absolutely not. But Priya doesn't use utilitarian frameworks. She uses axiomatic ones." Coalitional has since created a mobile application called FairSplit that computes Shapley values for restaurant bills. It has been downloaded fourteen times, twelve of which are by other mathematicians.