fair division

Is the proposed ABBA rule for penalty shootouts really fairer than the existing rule? Maths shows that it is, and also suggests another, more subtle rule.

Computer scientists have made a breakthrough in the theory of cake cutting.

Disputes over property are all too common. It's quite easy to share a cake, but how do you share out indivisible goods, such as houses or cars, without causing resentment? Here are two easy methods.

In soccer a coin toss is used to decide who goes first in a penalty shootout and similarly in American football a coin decides who plays offence in overtime. But is this really fair? This article explores an alternative.

When you try to put democracy into action you quickly run into tricky maths problems. This is what happened to Andrew Duff, rapporteur for the European Constitutional Affairs Committee, who was charged with finding a fair way of allocating seats of the European Parliament to Member States. Wisely, he went to ask the experts: last year he approached mathematicians at the University of Cambridge to help come up with a solution. A committee of mathematicians from all over Europe was promptly formed and today it has published its recommendation.

Bonuses are a fact of business life. Last year the Guardian newspaper calculated that the cash rewards paid to London's financial chiefs comfortably outstripped the UK's entire transport budget. With such large sums at stake, envy is bound to raise its ugly head, nver a good thing for company morale. So how should you decide who gets how much? Steven J. Brams suggests a method that's not only fair, but also encourages honesty.
The maths of fair division