Ein Spiel Gegen Die Natur

Decision theory is applied to a situation of conflict which a mother of two actually faced in an isolated home in the American Rocky Mountains. While the father was away on a trip which he thought to last seven days, the mother was bitten by a poisonous snake. She thought the bite to be fatal. To spare her two children, aged two months and two years, the agony of death by starvation, she decided to kill them. The mother faced a decision problem under uncertainty. A theoretical analysis of the situation shows which rational decision would have been optimal. However, a rational decision derived in an objective fashion is not free of subjective elements. Assigning utility measures to the possible types of death of the children, suppositions as to nature's strategies, and the choice of one of four established decision criteria are subjective. The criteria of Wald and Savage picture nature as a hostile opponent wanting to inflict greatest possible injury. The difference between them consists merely in the valuation of the disutility of death. Rational behaviour of the mother calls for selecting that strategy which promises the best of the worst possible outcomes. The Hurwicz criterion can accommodate all variations of nature's attitude, from malignant to benignant. According to the mother's optimism a distribution is supposed over nature's most favourable and unfavourable strategies. The probabilities of all other possible strategies are assumed to be zero. The criterion of Laplace assumes an indifferent nature. All possible strategies of nature are equally likely to eventuate. Three strategies are open to the mother, leave both children alive, kill one child, kill both children. Depending on the utility valuations the mother attaches to the different possible types of death, one of these strategies is optimal. If a decision is arrived by the Wald or Savage criterion a mixed strategy is superior to a pure one. The possibility of the childrens survival through the arrival of a stranger only affects the choice of the mother's strategy if she uses the Laplace criterion.