Beschreibung: I'm now sure Keen has the right interpretation and that you missrdenutand what vN&M where trying to do. In that particular example, their goal is to determine how much utility an individual will get from consuming a second unit of a good. Let's use this technique to determine the marginal utility of consuming a second unit of beer. To start, let's set an arbitrary value for the first beer consumed of 1 util. The subject will then have choose between getting 1 beer for sure or get two beers with the probability a or nothing with the probability 1-a. The goal is to find the probabilty a where the subject is indifferent about taking the gamble or not, which means a is equal to q (the ratio of the utility of possessing 1 unit of a certain good to the utility of possessing 2 units of the same good). If we're facing diminishing marginal utility, a will be greater than 0,5. Let's say that we find out that the suject is indifferent to taking the gamble when a is equal to 0,6. We now have a = q = 0,6 which means that the utility of consuming 1 beer divided by the utility of consuming 2 beers is equal to 0,6 (u1/u2 = 0,6). You can then work out the marginal utility of consuming a second beer, which is equal to 0,67. Starting from that, the procedure can be repeated for different quantities and different goods. For this to work, it is essential that the subject always choose the higher expected value, because what you want to find out is the point where the expected value of taking the gamble is equal to the expected value of not taking it. For example, the expected value of not taking the gamble is the quantity of util gained by consuming 1 beer (1) multiplied by the probability of getting 1 beer (1), so the expected value of not taking the gamble is 1. The point we’re looking for is therefore : 1 = 1,67 * a ... a = 0,6. If you do the experiment as a one time gamble, the subject won’t choose the higher expected value and you’re not gonna find out the marginal utility of consuming 1 extra unit of a good, you’re gonna get a chimera of utility and tolerance to uncertainty and won’t be able to isolate either of them.Once you have worked out a numerical value of utility, it’s possible to use this known value to determine an individual’s tolerance to uncertainty using one time gambles, maybe vN&M talked about that as well in their book, I don’t know, but it’s clear to me that Keen has the right interpretation.