Prelec's (1998) compound-invariant family provides an appealing way to model probability weighting and is widely used in empirical studies. Prelec (1998) gave a behavioral foundation for this function, but, as pointed out by Luce (2001), Prelec's condition is hard to test empirically. Luce proposed a simpler condition, reduction invariance, to characterize Prelec's weighting function that is easier to test empirically. Luce pointed out that testing this condition is an important open empirical problem. This paper follows up on Luce's suggestion and performs an experimental test of reduction invariance. Our data support reduction invariance both at the aggregate level and at the individual level where reduction invariance was the dominant pattern. A special case of reduction invariance is reduction of compound gambles, which is often considered rational and which characterizes the power weighting function. Reduction of compound gambles was rejected at the aggregate level even though 60% of our subjects behaved in line with it.

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Aydogan, I., Bleichrodt, H., & Gao, Y. (2016). An experimental test of reduction invariance. Journal of Mathematical Psychology, 75, 170–182. doi:10.1016/