Testing the indifference between a binary lottery and its edited components using observed estimates of variability

Past studies have shown inconsistent conclusions on the empirical validity of the duplex decomposition assumption that Luce proposed (1997). The duplex decomposition assumption states that a person would feel indifferent between playing a mixed (gain and loss outcomes) lottery and playing two lotteries simultaneously or successively where one lottery is the gain part and the other lottery is the loss part of the original mixed lottery. The current study tested this assumption by investigating the equality between the certainty equivalent of a binary lottery, CE (BL), and the certainty equivalent of the duplex decomposed lottery, CE (DDL), while controlling for the response variability in the estimated CEs. The results from two experiments showed that for 69% of responses, the difference between the CE (BL) and CE (DDL) was smaller than or equal to the response variability in estimating CEs, implying that duplex decomposition cannot be rejected for a majority of responses. The size of response variability in estimated CEs was discussed.