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In MWG, the authors introduce the consequentialist view of risk by assuming for any risky alternative, only the reduced lottery over final outcome matters to decision maker.

From philosophical view, how reasonable and unreasonable is this assumption? Can you provide examples where this assumption is in fact reasonable while it isn't?

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This assumption is usually considered as reasonable from a normative perspective. For instance, consider the following situations:

  • in situation A, you face an urn with 5 blue balls and 5 red balls. A ball is selected randomly and you can bet on its color. You receive a monetary prize if your bet is correct.

  • in situation B, you face an urn which contains 10 balls that are either blue or red. The number of blue balls has been selected randomly between 0 and 10 according to a uniform distribution. Once the urn is formed (you don't know its content), a ball is selected randomly and you can bet on its color. You receive a monetary prize if your bet is correct.

In the expected utility theory we usually consider these two situations as equivalent since the probability distribution over the final outcomes (the color of the ball) is the same: there is a 50% chance that a blue ball is selected, and a 50% chance that a red ball is selected. Therefore from a theoretical perspective it is hard to think of any reason why people would strictly prefer one situation to another.

However, empirically a substantial fraction of people exhibits a strict preference for the situation A rather than the situation B, for instance in this paper. According to my experience, most researchers are inclined to see this behavior as a mistake that reflects some difficulties with the computations of probabilities. Interestingly, this behavior is associated with ambiguity aversion, which is also sometimes considered as an anomaly. However, this is largely a matter of interpretation and other researchers prefer not to make any normative judgment on this behavior, as a matter of principle, and prefer instead to try to find rational explanations for it. It is for instance sometimes argued that the additional layer of uncertainty which is added in situation B would be a legitimate reason for risk-averse individuals to strictly prefer situation A.

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