Interpersonal Comparisons of Utility
or
I was the least miserable person at Jean Francois Mertens' seminar

Over at Brad's blog, point 4 below has lead to a discussion of interpersonal comparisons of utility.



What is it with this obsession with pareto efficiency in welfare economics? Almost no relevant policy initiatives will ever be pareto effecient, but will, arguably, be very a great net welfare improvement.

Why this fear of interpersonal utility comparisance? Is it cause needs (as opposed to wants) might sneak in an muddy the waters or is it an atavistic leftover from a time when the liberalistic market was sacrosankt in economics?

Posted by: Tomas | June 12, 2007 at 01:05 PM


Tomas, the reason people hate interpersonal utility comparisons is because they don't work. For example, if you multiply anyone's utility function by a constant, and their observable behavior won't change at all. This means that people don't have uniquely determined utility functions, which means you can't compare them.

That is, if you try to compare two people's utilities directly, then you get to make up any result you want, because you can multiply one guy's utility by whatever constant makes the right person's utility bigger.

Posted by: Neel Krishnaswami | June 12, 2007 at 05:01 PM


Excellent point Tomas. 'Nother excellent point Neel Krishnaswami. I think the (valid) argument that interpersonal comparisons of utility are impossible has had immense influence on economists.

There are two ways to make interpersonal comparisons. One is explained by Jean Francois Mertens (this is a joke as "explained by Jean Francois Mertens" is an oxymoron). As far as I can tell after listening to him for 90 minutes, his proposal is as follows. First consider people whose happiness is definitely bounded above and below so there is an epsilon so small no outcome so wonderful that they would trade 90% of their lifetime wealth for epsilon chance of that outcome and vice versa there is none so horrible so that they would trade 90% of their lifetime wealth to avoid an epsilon risk of that outcome. This is reasonable, otherwise one can get to a St Petersburb paradox (warning pdf)


if so, for each agent say the upper bound of his utility is 1 and the lower bound is zero. The rest can be filled in observing his choices over lotteries. Now we have interpersonally comparable utility.

This can also work even if happiness is, in principle, unbounded, so long as, for each person there is an upper and lower bound of technologically feasible happiness (misery).

Finally, it can work even if there are no psychological or technological limits, there can be limits based on some non utilitarian principle of fairness (say starving to death is infinitely horrible but we believe as a moral principle that before we begin adding up utils we have to save everyone from starvation if we can(or maybe torture is infinitely awful but also before we think about utils we must respect peoples right to not be tortured as a prior and absolute moral principle)). The 0 is the lower bound of misery which we can morally allow someone to suffer (even if technology makes a much more horrible outcome possible).

This is really a simple method to arrive at comparable numbers which are linear in happiness such that your argument does not apply.

I wonder why this idea is not more influential (again a joke, Mertens may be the worlds worst lecturer).



The other is an "assume we have a can opener" approach based on absolutely absurd assumptions about mega rationality. Imagine being someone else (a super mega rational being can do this). Now imagine your soul being removed from you and planted in a random person (a super duper mega ratoinal being can do this). Now, if you can make rational choices under risk, you can decide how to maximize the sum of human happiness e voilà (this approach is advocated by a friend of mine, Peter Hammond, so I am being polite).

Of to be really picky now that no one is reading, Tomas
technically you are arguing that Pareto improvements are impossible in the real world Pareto efficiency just occurs when no Pareto improvement is possible so there are many many Pareto efficient outcomes (slavery was Pareto efficient or else slaveowners would have freed their slaves). Pareto improvements are always impossible in the real world which is complicated (in simple models there can be simple Pareto improvements). Thus Pareto efficiency is just about nothing. It gets attention because of the result that, under very strong assumptions, the market outcome is Pareto efficient. Arrow proved this and has been trying to explain (to no avail) that the proof amounts to just about nothing ever since.