# Re: poly: Correlation vs. Causation in Decision Markets

From: Robin Hanson <rhanson@gmu.edu>
Date: Thu Oct 14 1999 - 06:52:01 PDT

> > In this situation, the speculators should reason that if the CEO is
> > kept that probably means that the decision makers were in fact
> > better informed than speculators, with private information favoring
> > keeping the CEO.
>
>Are the speculators figuring the board's knowledge into S and S'?
>Since that's part of the dump event, it seems like it should be. If
>we assume the board is rational and working for the benefit of
>the company, then we could rephrase the problem as
>
>S: price given the board thinks the company's better off keeping the CEO
>S': price given the board thinks the company's better off without the CEO
>
>Does that change anything?

It is important to distinguish the actual value of keeping or dumping
the CEO, from the stock value that results from any given board strategy
of deciding when to keep or dump the CEO. I've used S,S' to describe
the actual value, and P,P' to describe certain prices that result from
some particular assumed strategy. I assumed the board knew S,S' if informed,
and knew only the averages of S,S' if uninformed. The rational stock
price would be

Integral q(S,S')*S + (1-q(S,S'))*S' f(S,S') dS dS' ,

where f is the distribution over S,S', and q(S,S') is the probability
that the CEO is dumped, given actual values of S,S'. A good informed
board knows S,S', and so dumps if S>S'. A good uniformed board compares
averages

Integral S f(S,S') dS dS' vs. Integral S' f(S,S') dS dS' .

Bad boards may do differ things, and the goal is to induce bad boards
to act like good ones.

Robin Hanson rhanson@gmu.edu http://hanson.gmu.edu
Asst. Prof. Economics, George Mason University
MSN 1D3, Carow Hall, Fairfax VA 22030
703-993-2326 FAX: 703-993-2323
Received on Thu Oct 14 06:53:38 1999

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