Does the Preference Reversal Phenomenon Necessarily Contradict the Independence Axiom
探讨偏好反转现象是否必然违背传递性公理，指出该现象可能违背独立性公理而非传递性，并提出一种满足传递性和独立性但不满足简化复合彩票公理的决策机制。
One of the most puzzling paradoxes in decision theory is the preference reversal phenomenon. This phenomenon seems to contradict the transitivity axiom, for a long time, one of the cornerstones of utility theory. This paradox is established whenever a decision maker prefers lottery X to lottery Y, but is willing to put a lower selling price on X than on Y. Such experiments, first reported by Harold Lindman, 1971; and Sarah Lichtenstein and Paul Slovic, 1971, were repeated by David Grether and Charles Plott, 1979; Werner Pommerehne et al., 1982; and Robert Reilly, 1982. Although the later researchers improved the mechanism through which the selling price emerges, they all found systematic reversals. A new approach to this problem was developed by Charles Holt, 1986, and Edi Karni and Zvi Safra, 1987. From two different starting points, these authors showed that the preference reversal phenomenon does not necessarily prove a violation of the transitivity axiom, as it may contradict the independence axiom. This implies that people do not maximize expected utility, but in that case the preference reversal phenomenon becomes just another evidence against expected utility theory, but not against the transitivity axiom. These results have their own disadvantages. Although the independence axiom is not as fundamental as transitivity, it is nevertheless very appealing on normative grounds. Of course, the preference reversal phenomenon necessarily contradicts at least one of the assumptions of expected utility theory, but empirical evidence shows that despite its normative appeal, violations of the reduction of compound lotteries axiom may happen (see, for example, Joshua Ronen, 1971, and Doug Snowball and Clif Brown, 1979). In this paper I therefore suggest a decision mechanism for the preference reversals lotteries which is transitive and satisfies the independence axiom, but not the reduction axiom.