September 1, 2014 11 Comments
Mainstream economics has been based on the idea of people producing and trading in order to maximize their utility, which depends on their assigning values and conditional probabilities to outcomes. Thus, in particular, mainstream economics implies that people do best by assigning probabilities to possible outcomes, even when there seems no sensible way to do this (such as when considering a possible crash). Ken Arrow has asked, if one rejects utility maximization, what should one replace it with?
The assumption here seems to be that it is better to have a wrong theory than to have no theory. The fear seems to be that economies would grind to a holt unless they were sanctioned by some theory – even a wrong one. But this fear seems at odds with another common view, that economies are driven by businesses, which are driven by ‘pragmatic’ men. It might be that without the endorsement of some (wrong) theory some practices, such as the development of novel technical instruments and the use of large leverages, would be curtailed. But would this be a bad thing?
Nonetheless, Arrow’s challenge deserves a response.
There are many variations in detail of utility maximization theories. Suppose we identity ‘utility maximization’ as a possible heuristic, then utility maximization theory claims that people use some specific heuristics, so an obvious alternative is to consider a wider range. The implicit idea behind utility maximization theory seems to be under a competitive regime resembling evolution, the evolutionary stable strategies (‘the good ones’) do maximize some utility function, so that in time utility maximizers ought to get to dominate economies. (Maybe poor people do not maximize any utility, but they – supposedly – have relatively little influence on economies.) But this idea is hardly credible. If – as seems to be the case – economies have significant ‘Black Swans’ (low probability high impact events) then utility maximizers who ignore the possibility of a Black Swan (such as a crash) will do better in the short-term, and so the economy will become dominated by people with the wrong utilities. People with the right utilities would do better in the long run, but have two problems: they need to survive the short-term and they need to estimate the probability of the Black Swan. No method has been suggested for doing this. An alternative is to take account of some notional utility but also take account of any other factors that seem relevant.
For example, when driving a hire-car along a windy road with a sheer drop I ‘should’ adjust my speed to trade time of arrival against risk of death or injury. But usually I simply reduce my speed to the point where the risk is slight, and accept the consequential delay. These are qualitative judgements, not arithmetic trade-offs. Similarly an individual might limit their at-risk investments (e.g. stocks) so that a reasonable fall (e.g. 25%) could be tolerated, rather than try to keep track of all the possible things that could go wrong (such as terrorists stealing a US Minuteman) and their likely impact.
More generally, we could suppose that people act according to their own heuristics, and that there are competitive pressures on heuristics, but not that utility maximization is necessarily ‘best’ or even that a healthy economy relies on most people having similar heuristics, or that there is some stable set of ‘good’ heuristics. All these questions (and possibly more) could be left open for study and debate. As a mathematician it seems to me that decision-making involves ideas, and that ideas are never unique or final, so that novel heuristics could arise and be successful from time to time. Or at least, the contrary would require an explanation. In terms of game theory, the conventional theory seems to presuppose a fixed single-level game, whereas – like much else – economies seem to have scope for changing the game and even for creating higher-level games, without limit. In this case, the strategies must surely change and are created rather than drawn from a fixed set?
Some evidence against utility maximization. (Arrow’s response prompted this post).