maximin

(mathematics) The maximum of a set of minima. In the theory of games, the largest of a set of minimum possible gains, each representing the least advantageous outcome of a particular strategy.

In game theory, the strategy of maximizing one's own pay-off on the minimum (i.e. worst) assumption about the other player(s)' strategy. Thus for example in two-person Chicken (see the pay-off matrix in that entry), my maximin strategy is ‘Swerve’. If I ‘Swerve’ I cannot get less than c, whereas if I ‘Keep going’ I may get d.

The idea has also been used in political philosophy. John Rawls (1921-2002), in A Theory of Justice (1971), argues that if people were placed behind a veil of ignorance, so that they were asked to make rules of justice for a world in which they did not know what their views, wealth, or status would be, they would agree on a maximin conception of justice. The Rawlsian maximin is expressed in the first part of his difference principle: ‘Social and economic inequalities are to be arranged so that they are . . . to the greatest benefit of the least advantaged.’