the characteristics of decision weights contribute to theattractiveness of both lottery tickets and insurance policies.The nonlinearity of decision weights inevitably leads to violations ofinvariance
as illustrated in the following pair of problems:Problem 5 (N = 85): Consider the following two-stage game. Inthe first stage
there is a 75% chance to end the game withoutwinning anything and a 25% chance to move into the secondstage. If you reach the second stage you have a choice between:A. a sure win of $30 (74%)B. 80% chance to win $45 (26%)Your choice must be made before the game starts
i.e.
beforethe outcome of the first stage is known. Please indicate theoption you prefer.Problem 6 (N = 81): Which of the following options do you prefer?C. 25% chance to win $30 (42%)D. 20% chance to win $45 (58%)Because there is one chan ce i toce in four to move into the secondstage in Problem 5
prospect A offers a .25 probability of winning $30
andprospect B offers .25 Ã .80 = .20 probability of winning $45. Problems 5and 6 are therefore identical in terms of probabilities and outcomes.However
the preferences are not the same in the two versions: A clearmajority favors the higher chance to win the smaller amount in Problem 5
whereas the majority goes the other way in Problem 6. This violation ofinvariance has been confirmed with both real and hypothetical monetarypayoffs (the present results are with real money)
with human lives asoutcomes
and with a nonsequential representation of the chance process.We attribute the failure of invariance to the interaction of two factors: theframing of probabilities and the nonlinearity of decision weights. More
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