Maximin Principle

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Maximin Principle


The maximin principle is a principle for making choices when one is not sure of the outcome that will result from ones choice. The principle says to evaluate each option in terms of the worst possible outcome that could result from choosing that option, and to pick the option that offers the best worst outcome (the maximum minimum or maximin). Rational choice theory generally divides situations in which agents do not know for sure the outcome of their choices into three types: risk, uncertainty, and games. In situations of risk, the probabilities of various outcomes resulting from particular choices are known. In situations of uncertainty, those probabilities are not known, and in some cases the possible outcomes are also unknown. Games are strategic interactions, where the outcome that results from each players choice is determined not merely by externalpossibly randomfactors, but by the play of other rational agents.

Maximin is both risk and uncertainty averse, because it minimizes the degree of risk or uncertainty faced by the agent. Many rational choice theorists argue that risk aversity is irrational, as it involves a kind of double counting, valuing the mere avoidance of risk over and above its effect on the expected value of the possible outcomes. Subjects in psychological tests display a fair range of attitudes toward risk, from positively valuing it to extreme risk adversity. Some rational choice theorists argue that aversion to uncertainty is more rational, and experimental results confirm that aversion to uncertainty is more widespread. Finally, in the case of games where the gains of ones opponents are ones own losses (so-called zero-sum games), maximin strategies are more clearly rational. If player ones opponent, player two, is rational, and player twos maximizing behavior will have the effect of giving player one the minimal result that can arrive from the options that player one faces, then it is rational for player one to try to maximize over those minimums. Furthermore, if such games have what is called a pure-strategy equilibrium, it will result from all players adopting a maximin strategy.

The importance and notoriety of the maximin principle outside of rational choice theory is due in large part to its connection with John Rawlss A Theory of Justice (1971). Something resembling a maximin principle appears at two crucial moments in Rawlss argument for the conception of justice he calls justice as fairness. First, at the heart of justice as fairness are two principles of justice, part of the second of which is the so-called difference principle. The difference principle states that social and economic inequalities are to be arranged to give the greatest benefit to the least advantaged members of society. Because the difference principle requires maximizing the share of goods that go to those with the smallest share, it is often described as a maximin principle of justice. Rawls rejected that name, however, because of its tendency to be confused with the maximin principle of choice.

Second, Rawlss argument for the two principles, from what he calls the original position, is often thought to involve an invocation of the maximin principle. In the original position, artificial rational agents must make a unanimous choice about principles of justice for a society, and do so without any particular knowledge about the people they represent or their society. Rawls argues that in such a situation, purely rational agents would choose his principles of justice over utilitarian principles. Many have read that argument as resting on the claim that it would be rational to use the maximin principle for choice in the original position. Such critics as John Harsanyi then argue that because the maximin principle is not a rational principle for choice under risk, Rawlss argument fails. Defenders of Rawlss theory (including Rawls himself) have offered three sorts of replies: (1) Risk aversion in the original position is rational because of the stakes and finality of the choice; (2) the choice in the original position is really one under uncertainty, not risk, and aversion to uncertainty is a much weaker and thus more defensible assumption to make than aversion to risk; (3) the original position is best thought of as a game, whose players are looking for an equilibrium, and this justifies their adoption of the maximin principle. In his Justice as Fairness: A Restatement (2001), Rawls further clarifies the role of the maximin principle in his argument, arguing in addition that its role is limited to supporting the adoption of his first principle, which guarantees adequate liberties to all, rather than the second principle, which includes the difference principle.

SEE ALSO Gambling; Game Theory; Justice; Justice, Distributive; Justice, Social; Maximization; Minimization; Rawls, John; Risk; Social Contract; Uncertainty


Harsanyi, John. 1975. Can the Maximin Principle Serve as a Basis for Morality? A Critique of John Rawlss Theory. American Political Science Review 69(2): 594606.

Luce, R. Duncan, and Howard Raiffa. 1957. Games and Decisions. New York: Wiley.

Rawls, John. 2001. Justice as Fairness: A Restatement. Ed. Erin Kelly. Cambridge, MA: Harvard University Press.

Anthony Laden