A Comment on 'A Psychologically Plausible Goal-Based Utility Function'

Introduction An individual's neoclassical utility function is typically defined over their current situation (e.g., how much of various commodities they own) and is not explicitly a function of the individual's needs and aspirations. Thus it does not typically describe the executive whose utility depends on how much his income exceeds the income of his peers. For these and other reasons, Gill (2008) proposed replacing this neoclassical utility with a utility that explicitly depends on the individual's goals. Gill's seminal paper showed that this goal-based utility function addresses many violations of utility theory observed in psychological experiments. He also discussed how this utility function, unlike the stable neoclassical utility function, could change as the individual learned. This paper shows how Gill's goal-based utility function can be explicitly written in terms of the neoclassical utility function. We show that this goal-based utility also appears (under other names) in different fields. We then show that small changes in this goal-based utility leads to models that can explain some of the cases in which the neoclassical utility function is often inconsistent with observed human behavior. The paper closes by discussing how goal-based utility includes those cases in which an individual uses multiple criteria in defining his or her utility. The Goal-Based Utility The neoclassical utility function is defined as a function of known quantities (e.g., known levels of consumption of various goods.) But in many cases, individuals often make purchasing decisions about items which do not yet have known consequences. For example, an individual may own a lottery ticket which has some chance of giving the individual $1000 and some chance of giving the individual nothing. But even an individual who owns a car is typically uncertain about how many repairs the vehicle may require in the future. Thus many items should be viewed as gambles. Since some items are gambles, the neoclassical utility function must be written in terms of gambles (as opposed to known quantities.). To rewrite the utility function appropriately, suppose gamble i leads to a known outcome x with probability p(x|i). (The outcome x could be a vector specifying the individual's consumption of many different products.) Based on plausible assumptions about individual rationality, Von Neumann and Morgenstern (1944) showed that the utility of this gamble, U(i), can be written as U(i) = [[SIGMA].sub.x] U(x)p(x\i) where U(x) is a strictly monotonic function of the neoclassical utility function and represents the utility of a gamble which always yields the same outcome. In an extension of Borch (1968), Castagnoli and LiCalzi (1996) and Bordley and LiCalzi (2000) showed that for any utility function, U, there always exists a benchmark gamble 0 such that U(i) is just the probability of the individual considering the outcome of gamble i to be no worse than the outcome of gamble 0. For example, an individual may want a vehicle that will meet his future needs. But the individual---who intends to keep the vehicle for five years--may not know the maximum number of people he or she will need to carry comfortably in the car or the maximum amount of luggage he or she will need to carry in the car's trunk. (In other words, the individual is uncertain about what is exactly required to meet his or her needs.) In this case, the uncertainty in gamble 0 reflects the individual's uncertainty about the future demands which will be placed on the vehicle. Suppose the individual's goal is to have a vehicle which achieves an outcome (i.e., offers a capability) that is no worse than the outcome of gamble 0 (i.e., which is enough to meet all his or her future needs.) Then U(i) is just the probability of the individual successfully achieving that goal with vehicle i. As another example, suppose our investment goal in 2012 is to earn at least as much money as we would have earned if we had invested our money in an index fund (whose return matches the 2012 return of the S&P 500). …