Steve Keen, the author of "Debunking Economics" (Pluto Press, 2001), has an argument to the effect that analyses like the one I have just demonstrated are misguided and misleading. This argument is presented online in a slide presentation "The 'curse of dimensionality' and the impossibility of utility maximisation" (Microsoft PowerPoint format).
Keen points out the empirical difficulty of identifying preferences, but has a more telling argument that can be summarised as follows. The number of different comparisons that need to be made in choosing n different commodities grows exponentially with n. In the real world, the number of commodities we could buy is very large, so the number of different comparisons is astronomically huge, even on conservative estimates. Thanks to this "curse of dimensionality", it is totally implausible that decisions actually are made by forming individual preferences between options.
Keen infers that the consumer makes a choice from a set that is miniscule compared to the set of all possible choices. Hence it is crucial to understand the factors that partition out this set of choices, such as advertising or the mere force of habit; factors that are ignored by the theory of rational choice. This could be argued to be giving more psychological realism to the theory of decision making. A stream of psychological research (associated with Amos Tversky and David Kahneman (see this glossary entry)) has shown that judgements of many kinds are distorted in the direction of "availability"; the ease with which something comes to mind. For instance, subjects wrongly judge that words beginning with "r" are more common than words with "r" as the third letter, because our memories can more easily retrieve words based on their first letter. Keen's argument seems to be a plea for an economic theory which gives an explicit role to availability.
In assessing whether we have to ditch the mathematics of utility maximisation, the question arises of what utility functions are supposed to mean. If utility maximisation across the whole space of possible choices is meant to be a description of some process that the consumer consciously goes through, then Keen's argument totally destroys it as a descriptive theory. However, that is simply not the purpose of economic analyses like the one we have considered.
The utility maximisation framework as we have used it is purely an approximate description of behaviour: it treats the decision-maker as a black box, not caring what utility actually is nor what options, if any, are consciously entertained. Keen is right that decisions are made partly by the cultural and physical environment (for example by the placement of goods in a supermarket) but this does not mean that utility maximisation is not a good description of what is going on. In fact we could re-read his account of these external influences as an answer to a question of how it is computationally possible to arrive at the huge numbers of preferences required by expected utility theory. This response disarms the curse of dimensionality, but the problem remains that people do not obey the predictions of simple utility-maximisation models. Some predictive failure is to be expected, because rational choice theory describes an equilibrium to which decision makers should be expected to gravitate in the long run. Hence whether Keen is right is not decided flat-out by his arguments, but is an empirical matter outside the scope of this essay.
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