__ A simple investment decision application __ Imagine that the outcomes are different levels of your wealth at the end of the year. For example A is $500k, B

__ A simple investment decision application __ Imagine that the outcomes are different levels of your wealth at the end of the year. For example A is $500k, B is $50k, C is $200k. What is the utility function that describes your preferences? (There should be one if you're rational in the sense of the EUT axioms.) Surely we agree that you prefer A to C and C to B. But would you prefer to have $500k or $50k with 50%/50% probability or to be certain of having $200k at the end of the year? EUT doesn't give you an answer. Of course it's easy to calculate the expected value of the first alternative ($275k) but nobody says that you should prefer the "risky" $275k to the certain $200k. That's the point of introducing utility functions in the analysis, that preferences may be non-linear. What EUT says is that if you're rational (etc) there are three numbers U($500k), U($50k) and U($275k). The expected utility of the first option is 0.5 U($500k) + 0.5 U($50k) and the expected utility of the second option is U($200k). These expected utilities can be compared to see if you which option do you prefer. If you prefer one, you could also be indifferent. EUT says that the rational decision is to chose the option with higher expected utility. __ Remarks __ EUT doesn't fix the form of the utility function. Usually it's assumed that instead of linear it's concave. This means that a certain dollar is better than a dollar in expectation and you would never take fair bets. (The fact that people plays in the casino where bets are not even fair could be explained with convex utility. One could explain it as well saying that there is utility obtained from the entertainment that offsets the monetary loss.) The utility function describing someone's preferences could be very complex. Simple models are used for many reasons including tractability or theoretical properties. For example power functions (logarithmic utility is a special case). There are some reasons to like logarithmic utility (including growth-optimality arguments) but it doesn't work too well empirically. This is why, at least in some settings, it may be better to use the more general power utilities that have a parameter that can be adjusted. Using logarithmic utility, the $200k option is preferable to the $500k/$50k bet. The certainty equivalent is $158k. Logarithmic utility (like the rest of the power utilities) is scale invariant. The amounts could by 100 times larger or 100 times smaller and the answer would be the same. Does Ole Peters claim that the use of EUT here is wrong? I guess so. Parallel universes again, probably. Would you say that there is a problem with EUT up to this point? What are the problematic assumptions made by EUT? In my opinion it's EE who cannot really solve this problem without making "unphysical" assumptions. The solution corresponds to using the logarithmic utility above, EE declares any other preference the agent may have wrong. (To be continued, maybe.)