# poly: Correlation vs. Causation in Decision Markets

From: Robin Hanson <rhanson@gmu.edu>
Date: Wed Oct 13 1999 - 10:54:19 PDT

I've suggested that markets which offer conditional estimates of outcomes
given choices may inform those choices. But there has remained a nagging
doubt about the relation between such correlations and causation.
In the last week, I've done some formal analysis of this. There is a real
problem, though there do seem sufficient remedies for most cases.

Consider the example of the future stock price of a company contingent on
whether the CEO gets dumped. We can make markets where the price P in one
market should estimate the future stock value S conditional on dumping the
CEO, and the price P' in another market can estimate the future stock value
S' conditional on not dumping the CEO.

The idea is that the board of directors should feel compelled to follow the
market's advice, and dump the CEO if P > P', and not if P < P'. The problem
with this is that even when everyone expects the company to do better on
average if the CEO is dumped, the market price can rationally indicate
P < P'. The existence of this phenomena could give the board cover to

This problem happens when
1) from the view of uncertain speculators, the variation in S' is large
relative to the variation in S and the difference between the averages
of S and S',
2) speculators fears that the decision makers, in this case the board,
might be better informed than they are now when the decision is made,
and in such a case will decide based on their expectations about S,S'.
3) An not-better-informed board is pretty sure to dump the CEO.

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. Given this, a high variation in S' implies a high
price P'. The price P, in contrast, should be pretty near the average
of S. [I'm not boring you with my math that backs all this up.]

One reason a speculator might fear a better informed decision maker
is if the decision might be made later, when both speculators and
decision makers will know more than they know now. Thus one remedy
for this problem is to be careful to give tight time constraints on
decision times. The bets should be on "will dump the CEO at the
next board meeting on date X", rather than "will dump in the next year."
Then it is the price the day or hour before the meeting that the board
should defer to.

A speculator might also fear that the board is better informed at the
same moment, due to inside information the board has which the
speculator does not. A remedy for this is to enable board members to
anonymously speculate, and to expect them to do so if they have inside
information. Claims that the market price was deceptive could be met
with the reply "If so, then why didn't you bet and fix it?".

These remedies are probably sufficient for most cases. If not,
a more robust remedy is to somehow ensure that there always remains
some substantial chance that a not-better-informed board might go
either way. The board might throw two ten-sided dice, and if they
both came up ones they might then randomly decide whether to dump the
CEO.

Another possibility to be concerned about is where an uninformed
board somehow uses a threat of being informed or something to
distorts the dump price P down relative to the keep price P',
to use as a cover to keep a bad CEO. I haven't been able to generate
any examples where this happens though.

So the bottom line is: there's a real problem, which seems to be
remedied by using narrow time definitions of decisions, and by
expecting decision makers to speculate.

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 Wed Oct 13 10:56:47 1999

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