From Robert Eastaway
“Fair shares for all” (17 June) used cakes to explore the mathematics of envy. There is another cake-related problem which opens up a completely new investigation, this time into the mathematics of guilt.
The problem is this: the vicar’s wife has invited five friends round for afternoon tea. She brings in a plate with biscuits on it, including four which are chocolate. All the guests love chocolate biscuits. The plate is offered to the first guest, who takes a chocolate biscuit. The same with the second and third. The fourth guest of course sees only a single chocolate biscuit on the plate and knows that if she takes it she is depriving the fifth guest of a chocolate biscuit. She feels guilty and so doesn’t take it.
The question is: should the other guests also have felt guilty and if so, how do you allocate the amount of guilt each guest should feel? Is the third guest more guilty than the first?
I would be fascinated to know if anyone has resolved this problem, since as a guilt-ridden biscuit-eater I encounter it regularly.
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