Committee Expert Advice and the Weighted Majorit

Authors: Yann Braouezec

Publish Date: 2009/12/19

Volume: 35, Issue: 3, Pages: 245-267

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Abstract

We consider a repeated pricing decision problem of a monopolist the decisionmaker who does not know the demand function of some new product and hence the profit function To decide she is helped by a committee of N experts Each expert has an estimation of the unknown demand function and use it to advise the decisionmaker on how she should modify the current price Decisions are taken with a weighted majority rule where the weight of each expert which may be interpreted as her decision power evolves as a function of its accuracy When a perfect exists ie who always gives the correct advice we show that she ends up with all the decision power in the longrun so that the decisionmaker finds the optimal price When such a perfect does not exist the decisionmaker is actually unable to consistently select an expert over time so that the sequences of prices and weights describe a limit cycle Interestingly enough if the decisionmaker takes a large sample of the stationary behavior of prices the empirical mean turns out to be arbitrarily close to the optimal price independently of the “quality” of the experts as long as there experts are “diverse” enough This result gives thus support to the thesis developed in the books of Surowiecki The wisdom of the crowd Why the many are smarter than the few and how collective wisdom shapes business economies societies and nations 2005 and Page The difference How the power of diversity creates better groups firms schools and societies 2007

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