Saturday, November 22, 2003

Greatest Good for the Greatest Number

Just out of curiosity, I did two Google searches just now. Here are the results:

1. "Greatest good for the greatest number." Number of hits: 12,400.

2. Morgenstern and "Greatest good for the greatest number". Number of hits: 111.1

This is bad. Clearly, thousands of webpages are discussing the main principle of utilitarianism, without mentioning the fact that John von Neumann and Oskar Morgenstern demonstrated that it is impossible. Here's what they say on page 11 of their Theories of Games and Economic Behavior (1943):
A particularly striking expression of the popular misunderstanding about this pseudo-maximum problem is the famous statement according to which the purpose of social effort is the "greatest possible good for the greatest possible number." A guiding principle cannot be formulated by the requirement of maximizing two (or more) functions at once.

Such a principle, taken literally, is self-contradictory. (In general one function will have no maximum where the other function has one.) It is no better than saying, e.g., that a firm should obtain maximum prices at maximum turnover, or a maximum revenue at minimum outlay. If some order of importance of these principles or some weighted average is meant, this should be stated. However, in the situation of the participants in a social economy nothing of that sort is intended, but all maxima are desired at once -- by various participants.
Imagine trying to play a basketball game where the aim was "score the most points in the least amount of time." You would never be able to determine a winner. The only way to determine a winner is to fix the amount of time (say, 40 minutes) and then see who scores the most points, or to fix the number of points (say, 11, as is common in pickup games) and see who gets there first.

1 Both of those numbers should increase by 1 as soon as Google picks up this post, which is one of the very reasons for posting.


Blogger Jonathan said...

Very insightful.

2:17 AM  

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