Why are interpersonal utility comparisons not possible 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?
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
$$u(\text{Paris}) = 2 &gt; u(\text{London}) = 1;$$or instead that
$$u(\text{Paris}) = 7 &gt; u(\text{London}) = 3;$$or more generally assign
any utility values such that $$u(\text{Paris}) &gt; u(\text{London}).$$ 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'?