# Measuring and assigning utility numbers

I was recently introduced to the concept of cardinal utility. In real life, how do we assign these utility levels? For example if i wanted to assign numbers to my own utility indifference curve for two things, how would i go about it? What happens if one of the things is not exactly measurable in terms of quantities on an individual level? For example lets say the two things i am considering are convenience of traveling by car to air pollution, then how would i go about it?

I have tried to look on the internet and i have come across some techniques like time-trade off, but these are mostly used in measuring health related aspects which can still be imagined/estimated in mind. This is related to a project, so i am looking for simple feasible methods that i can use to estimate my own preferences, and not something complex like neuro imaging etc

• Typically, utilities are estimated from survey data, such as quality of life. Namely, the survey method obtains a score for the person - and this score can be transformed into a utility value. As far as I am aware, this practice is not particularly wide-spread outside health economics. In fact, to the contrary, a large body of theoretical work has gone into making the case that we can assume change in a latent variable (utility) from the individual's material welfare (i.e change in income). For example, this is the assumption which goes into saying 'people are worse off' because CPI increased – EB3112 Nov 7 '20 at 22:11

There are no simple methods for estimating cardinal utility (ordinal utility would be a different matter - you could just observe few of your choices).

This is not because cardinal utility would necessary be unmeasurable. Although this is not completely settled question (see Moscati (2018) Measuring Utility: From the Marginal Revolution to Behavioral Economics), if you are willing to buy into the von Neumann-Morgenstern (1944) derivation of cardinal utility, then the cardinal utility is measurable.

According von Neumann-Morgenstern (1944) cardinal utilities could be measured in principle since by the axioms of von Neumann-Morgenstern (vNM) cardinal expected utility you should, in principle, be able to measure it.

According to vNM assuming that axioms of completeness, transitivity, continuity and independence are satisfied (see von Neumann-Morgenstern (1944) Theory of Games and Economic Behavior), there is some function $$u$$ that assigns to each potential outcome of a gamble $$X$$ a real number $$u(X)$$ such that for any two gambles ($$X_1, X_2$$):

$$X_1\prec X_2 \qquad \text{iff} \qquad E(u(X_1))

Consequently, $$u$$ can be uniquely determined, and be fully measurable, by measuring preferences between some simple gambles (e.g. gambles such as $$pX_1 + (1 − p)X_2$$). However, to measure the cardinal utility in full you would have to run infinite number of such gambles (even with just two outcomes $$X_1$$ and $$X_2$$ you can construct infinite number of different simple gambles). In addition those have to be real gables with stakes not just 'made up' gambles as otherwise you can never be sure if in real situation you would choose completely differently.

A potential proxy for measuring cardinal utility could be willingness to pay. This could be considered a proxy for some cardinal money-metric utility function but even that approach has some issues (Fleurbaey, M. 2011). However, this is probably the most practical approach. This is also reason why willingness to pay is so widespread in the cost-benefit analysis in public economics. However, even with this approach you will have to do some serious data collection on various purchases you make and other control variables such as your income for example.