PROSPECT THEORY 267 8 to 2. The following pair of choice problems illustrates the certainty effect with PROBLEM A: 50% chance to win a three- B: a one-week tour of C: 5% chance to win a three- D 10% chance to win a one k tour of england france, and Italy N=72[67] [33] The certainty effect is not the only type of violation of the substitution axiom Another situation in which this axiom fails is illustrated by the following problems PRO A:(6,000,45),B:(3,000,,90) [86] P C:(6,000,,001),D:(3,000,.002) 66[73] [27] Note that in Problem 7 the probabilities of winning are substantial (.90 and. 45), and most people choose the prospect where winning is more probable. In Problem 8, there is a possibility of winning, although the probabilities of winning are minuscule(002 and. 001 )in both prospects. In this situation where winning is possible but not probable, most people choose the prospect that offers the larger gain. Similar results have been reported by MacCrimmon and Larsson [28] The above problems illustrate common attitudes toward risk or chance that cannot be captured by the expected utility model. The results suggest the following empirical generalization concerning the manner in which the substit tion axiom is violated If (y, pa) is equivalent to(x, p), then(y, pqr)is preferred to (x, pr),0<p, q, r<1. This property is incorporated into an alternative theory, developed in the second part of the paper