### 69 - Incoherent Preferences

G. Charles-Cadogan

Under Bruno De Finetti’s coherence theory of additive probability, the expected value of a sequence of mutually exclusive bets should not expose the bettor to certain loss for any of the bets in the sequence (i.e. no formation of Dutch books). However, decision makers (DMs) are known to have non-additive probability preferences represented in the frequency domain. This conundrum of choice implies that DMs are incoherent. If so, then preference reversal (PR) is more likely to occur. That is, DMs response to choice and valuation procedures (with similar expected value) are more likely to be dissimilar or their preferences may appear to be intransitive. We prove that even when the true states of choice experiments are procedure invariance and transitive preferences, PR will still be observed because of: (1) phase incoherence between paired gambles with the same expected value–when probability cycles are incomplete, and (2) experimenter interference in probability measurement. We introduce a utility coherence ratio for paired gambles, and estimates from simulated phase transition from incoherent states to coherent states in binary choice to illustrate the theory. We find that coherence measures are very sensitive to measurement error, coherent states have higher frequency phase transition, and incoherent states represent momentary lapse in judgment that eventually disappear. So, Dutch books and PR are prevented.