Splitting the Cake

Question

Two people must split a non-uniform cake (one loves the frosting corner, the other the fruit) with no referee and no trust. Design a procedure where each is guaranteed, by their own valuation, at least half.

Accepted Answer

Cut and choose: one person cuts the cake into two pieces they value as exactly equal; the other picks whichever piece they prefer. - The chooser gets the better of two pieces by their own measure → at least half of their total valuation (the max of two pieces is at least the average). - The cutter is indifferent by construction → exactly half by their measure, whichever piece remains. Neither guarantee depends on the other party's honesty or preferences, each player's floor is secured by their own action. That's the design principle: align the discretion with the exposure. The cutter holds the risk of a bad cut, so the cutter controls the cut; the chooser holds the risk of a bad assignment, so the chooser controls the assignment. For two players this is even envy-free (nobody prefers the other's piece). Interviewers extend toward mechanism design: it's a 2-line example of making a protocol incentive-compatible instead of assuming good behavior, the same reason exchanges use auctions rather than asking participants to self-report fair value. A deviation check seals it: if the cutter cuts unevenly, the chooser takes the bigger piece (by the cutter's own measure the cutter now gets le

Splitting the Cake

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