Choice and individual welfare

We propose an abstract method of systematically assigning a "rational" ranking of outcomes to choice data which may not be rationalizable in any sense. An individual welfare functional maps stochastic choice functions into weak orders. A stochastic choice function gives the empirical frequency of choices for any possible opportunity set (framing factors may also be incorporated into the model); we call such general choice functions "choice distributions." We require that for any two alternatives x and y, if our individual welfare functional recommends x over y given two distinct choice distributions, then it also recommends x over y for any mixture of the two choice distributions. Together with some mild technical requirements, such an individual welfare functional must weight every opportunity set and assign a utility to each alternative x which is the sum across all opportunity sets of the weighted probability of x being chosen from the set. It therefore requires us to have a "prior view" about how important a choice of x from a given opportunity set is.