By Dr. Med. h. c. Tönjes Lange (auth.)
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There are four coins on the table and two players take turns in picking them up. On each turn, the player has to pick up either one or two coins. The player who gets the last coin wins and collects all the coins that were originally on the table. Suppose you are the player who has the first turn. Should you pick one or two coins? Obviously, you should pick one since regardless of what your opponent does, that guarantees that you still have either one or two coins left when it is time for your second turn.
For example, in evaluating institutions of higher education, several aspects of performance are usually invoked in the overall assessments: the quality and quantity of research conducted, the quality and quantity of teaching and training, the external impact of the institution on its environment, etc. Often the criteria are discussed, modified and elaborated by the representatives of the institutions under scrutiny. In these discussions, the introduction of criteria that favor their institutions can readily be seen as a weakly dominating option vis-à-vis settling for those already existing.
The computation of the best option is in all respects identical with the expected utility maximization under risk. 6 Axioms of rational behavior All the principles of choice under uncertainty have some justification which makes them plausible under some decision settings. The maximin rule amounts to guaranteeing a reasonable security level in making decisions. Consider a person trying to catch a bus which is about to leave the stop on the opposite side of a very busy road. Even if missing the bus would mean being some 10 minutes late in arriving at an important meeting, many people would choose to cross the street at traffic lights rather than hurrying to the other side of the road in the midst of the traffic.