I loved this, and the paper perfectly illustrates why I love algebra – you can find any answer with it. They based their cake cutting algorithms on the assumption that every person is “risk-adverse<\/i>: He or she will never choose a strategy that may yield a more valuable piece of cake if it entails the possibility of getting less than a maximum piece.” This is especially true in the case of kids cutting their own pieces. I would know; I have three.<\/p>\n

Their research led them to search the answer to satisfy these three key features.<\/p>\n

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1. The first is envy-freeness<\/i> – where every person thinks they are getting the best piece so they don’t envy the next person’s slice.<\/li>\n
2. The second is efficiency <\/i>– where there is no other cut that is better.<\/li>\n
3. And the last is equability <\/i>– where every person thinks that each cut is the same as, or just as good as, the next person’s.<\/li>\n<\/ol>\n

   It will always remain a challenge to cut a cake so that everyone has that perceived ‘perfect slice of cake,’ especially when multiple people are vying for it. But even the authors admit “there may be no envy-free division that is also equitable.” I guess even in cake cutting, tough choices have to be made. The paper discusses proportional equability, and in some parts base their assumptions that the people involved are being truthful in the equitable procedure, and is a pleasing pastry\/mathematical read all around. <\/p>\n

   Below: Galton’s Example via Numberphile.<\/p>\n