Tuesday, July 24, 2007

Ordinal vs. Cardinal Utility

If we wish to understand how people make decisions, we must understand the concept of utility. How does the brain make comparisons among many different objects? Does ever object have a utility value associated with it such that we can simply find the utility of a group of objects by adding these values? It would seem to be the case that purely linear utility does not exist intrinsically in the brain because we can observe decreasing marginal utility. Furthermore, it seems logical that simply getting more of something is not necessarily worth the same to someone when they already have a lot of the item. 

Therefore, often in economic theory I have found the use of an ordinal concept of utility. It seems as if cardinal concepts are always mentioned but then pushed aside as not that important because as long as we can order objects we can use monotone transformations and preserve all of the meaning. However, we cannot really do the math one might desire with such a utility framework. We might like to know how certain choices rank in a cardinal sense because for example this would make complex decisions less complicated as they could be broken down into smaller decisions.

The obvious question then becomes how does one assign an objective number of utility units to a certain choice. This would be unique for each individual as everyone has their own utility structure. Furthermore, we must preserve transitivity in order to preserve some semblance of rationality. I think that neuroscience will allow us to understand how the brain creates a utility map and then uses this to make decisions. It might seem that we would have to monitor people's choice behavior and create the utility structure from observation. However, I believe that if we actually understand how the brain processes new information and updates its internal utility structure, we should be able to create a robust concept of cardinal utility albeit somewhat localized to individual behavior. That is, aggregate utility is most likely beyond the reach of this method, however aggregate utility in itself is flawed and thus this is not a major issue.

The goal must therefore be to study the action potential sequences generated in the parts of the brain most likely linked to cognitive decision making; use the sequences obtained when a subject is asked to make choices to create a model for the generation of such sequences given a choice to be made. We should then be able to predict actual choice behavior if we know the choices to be made and the action potential sequence observed when a subject is presented with separate alternatives. From this framework, we should be able to infer a utility structure that is cardinal for the individual being studied.