 Before concluding this discussion of measuring utility, two related limitations regarding the information such measures convey should be mentioned. First, since the utilities of options, whether ordinal or interval-valued, can only be determined relative to the utilities of other options, there is no such thing as the absolute utility of an option, at least not without further  assumptions.[2]  Second, by the same reasoning, neither interval-valued nor ordinal utility measures, as discussed here, are interpersonally commensurable with respect to levels and units of utility. By way of a quick illustration, suppose that both you and I have the preference ordering described above over the holiday options: \(A\prec B \prec C\). Suppose too that, as per the above, we are both indifferent between \(B\) and the lottery \(L'\) that has a \(3/4\) chance of yielding \(C\) and a \(1/4\) chance of yielding \(A\). Can we then say that granting me Cardiff and you Bangkok would amount to the same amount of “total desirability” as granting you Cardiff and me Bangkok? We are not entitled to say this. Our shared preference ordering is, for instance, consistent with me finding a vacation in Cardiff a dream come true while you just find it the best of a bad lot. Moreover, we are not even entitled to say that the difference in desirability between Bangkok and Amsterdam is the same for you as it is for me. According to me, the desirability of the three options might range from living hell to a dream come true, while according to you, from bad to quite bad; both evaluations are consistent with the above preference ordering. In fact, the same might hold for our preferences over all possible options, including lotteries: even if we shared the same total preference ordering, it might be the case that you are just of a negative disposition—finding no option that great—while I am very extreme—finding some options excellent but others a sheer torture. Hence, utility functions, whether interval-valued or ordinal, do not allow for meaningful interpersonal comparisons. (Elster and Roemer 1993 contains a number of papers discussing these issues; see also the entry on  social choice theory.)