Why is it not possible to compare utility across individuals?
Is this only impossible when we consider ordinal utility where we have no numerical unit?
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Whether `interpersonal comparisons of utility' are possible depends on what you mean by 'utility':
- If you mean something like welfare, i.e. the extent to which a person's life goes well, then interpersonal comparisons are obviously possible. Example: if Anna is tortured on a daily basis, whereas Bob lives a life of luxury, then we would (given standard background assumptions) be justified in believing that Bob has a higher level of welfare than Anna. (If you don't like the example, feel free to change the details. The general point is that, in some cases at least, it is reasonable to believe that one person is better off than another person.)
- In 'standard' microeconomics, however, the word 'utility' has come to mean something rather different to welfare. Instead, utility is defined as whatever people maximise. To be more precise, a utility function is simply a way of representing individual rankings over outcomes; and the outputs of that function are termed utilities. Now, if all utilities are supposed to do is represent rankings, it is clear that there are many possible ways of assigning utility values. For example, if I go prefer Paris to London, we could say that $$u(\text{Paris}) = 2 > u(\text{London}) = 1;$$or instead that $$u(\text{Paris}) = 7 > u(\text{London}) = 3;$$or more generally assign any utility values such that $$u(\text{Paris}) > u(\text{London}).$$ And as a result, it is clearly meaningless to say that your utility level is higher than mine. For utility levels are purely arbitrary: we can always make your utility higher than mine, but also rescale the utility functions so that my utility is higher than yours.
- So if you are wondering whether utility levels can be compared across individuals, you need to ask yourself a simple question: what do you mean by 'utility'?
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Why are interpersonal utility comparisons not possible
They are not impossible. Instead, whether or not interpersonal utility comparisons are possible is merely an opinion. (In the language of the positive-normative dichotomy, any claims as to whether or not such comparison are possible is a normative one.)
The standard/orthodox approach taken in pure microeconomic theory is that the assumption of interpersonal utility comparisons is not necessary (to get many results in microeconomic theory). We thus make no such assumption (without necessarily making the dogmatic claim that such comparisons are impossible).
However, the actual approach taken by economists who want to say anything about the real world or do any welfare economics—in other words, most economists—is that we can and do make interpersonal utility comparisons.
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Correct this is impossible only with ordinal utility with cardinal utility you can make interpersonal comparisons.
The reason why you can’t do it with ordinal utility intuitively is that with ordinal utility that there is no measurable utility that individual derived from some good. Under ordinal utility you can only say that Lisa prefers ice cream to cereal, but you can’t say that she derives let’s say twice as big utility $u$(cerial)=10 and $u$(ice cream)=20. The same holds between people if there is Margaret who also prefers ice cream to cereal it does not mean they have the same utility. Their utility of ice cream and cereal could be same, greater or lower and all this would still be consistent with saying they both prefer ice cream to cereal.
However, with cardinal utility you can say that some person, let’s say Margaret, derived 30 utils from ice cream and Lisa derived just 20 utils so Margaret prefers ice cream more.
