The following is related to my dissertation, but should be easily understood without any statistical background. I wrote it for a job interview, no success yet…
Many decisions we make involve uncertainty, such as whether to buy flood insurance, whether to hold an event outside, or which candidate to offer the job to. A common way of modelling such decisions is utility theory. According to this theory, for any person facing a decision, each possible outcome has a number called its utility. Together with the probabilities involved in the decision, these utilities determine which choice they make.
So how do we determine these utilities? Well, suppose a person indicates that she is equally happy to receive 4,000 pounds for certain or to take a gamble where there is a 50 percent chance she receives 10,000 pounds and a 50 percent chance she receives nothing. Then utility theory gives us the equation that the utility of 4000 pounds is equal to half the utility of 10,000 pounds. With more information about her preferences, involving different sums of money and probabilities, we will get more equations which we should be able to solve to find her utilities.
Unfortunately there is a problem. Often we can’t solve the equations because the preferences are inconsistent. This is often dealt with by fiddling the figures to arrive at estimates for the utilities. This is a very unsatisfactory approach because there is no proper justification for the results.
However, I have developed a more justifiable method for dealing with this problem. It is based on a model of how a person’s preferences depend randomly on his/her utilities. This model depends on the unknown utilities and another number which represents how well the person discriminates between choices.
My approach involves 4 components:
- The person’s view of his/her utilities, i.e. how cautious he/she is.
- The person’s view of how well he/she discriminates, i.e. how strongly he/she responds to changes in the choices,
- The person’s specific preferences, i.e. the pairs of choices that he/she finds equally desirable and
- The model itself.
By combining these 4 components the estimates of the unknown utilities can be calculated. This can easily be done on a computer.
We don’t have to calculate estimates for every utility. In my report I have used these 4 components to find an equation for the utilities. I’ve used a mathematical computer program to calculate the exact form of my chosen utility function.
This method provides a simple, but justifiable way of calculating the utilities required for making decisions, based on utility theory, and which takes into account the inconsistent nature of preferences.