Duplex decomposition and general segregation of lotteries of a gain and a loss: An empirical evaluation

We investigate the empirical validity of two hypotheses, duplex decomposition (DD) and general segregation (GS), regarding decomposition of a binary gamble of a gain and a loss into two unitary gambles in which one consequence of each gamble is no change from the status quo. Four binary lotteries (money gambles with specified probabilities) and four decomposed lotteries designed to test GS and four decomposed lotteries to test DD were constructed, and certainty equivalents (CEs) were estimated for each lottery. Respondents’ indifference between a binary lottery and a decomposed lottery was determined by evaluating the equality between the CE of a mixed binary lottery and the CE of the corresponding decomposed lottery. Given the variability of estimates of CEs and the lack of a clear statistical definition for the equality between two CEs, we applied several criteria: we counted responses where the difference between two CEs was either ±2% (the strictest criterion), ±4%, ±6%, or ±8% (the most lenient criterion) of the range of lottery outcomes. The results showed that under the strictest criterion, GS held for 25% of the responses and DD for 22%. Under the most lenient criterion, GS held for 56% of the responses and DD for 52%. Depending upon the criterion used, between 39 and 75% of the responses were consistent with at least one of the hypotheses. Several methodological problems in determining the indifference between two lotteries are discussed.