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[Michael Abramowicz, guest-blogging, January 31, 2008 at 4:41pm] Trackbacks
Predicting Decisions and Their Effects:

So far, my posts have implicitly assumed independence between forecasts and decisions. Now, let's consider some ways in which we might structure prediction markets to forecast the decisions themselves and their consequences, so that the forecasts might influence the decisions.

(1) Markets predicting decisions. A market that predicts a decision might end up affecting the decision. Suppose that Eugene is elected dictator, but because of his blogging responsibilities, His Tremendousness must make many decisions. So, he establishes prediction markets forecasting what decisions he will make.

Now, Eugene is presented with a decision to make, and he quickly analyzes the problem and leans toward Decision A. But then he checks the market and sees that it forecasts that he will make Decision B. He wonders, why is that? He looks more carefully and realizes that he has missed some aspects of the problem.

Some of the dynamics of the deliberative market are present here. A trader predicting a decision can profit by developing arguments that will persuade the decision maker. For example, the trader can write an argument for Decision A and bet on Decision A just before releasing the argument. Eugene might thus create a market predicting his decisions as a way of generating research and arguments relevant to those decisions.

(2) Conditional markets. A conditional market predicts some variable contingent on a condition. A simple way to run such a market is to stipulate that all money spent on the prediction market will be refunded if the condition does not occur. For example, one market could predict a corporation's stock price if a corporation decides to build a factory, and a separate market could predict the stock price if it doesn't build the factory. The corporation can compare the forecasts to assess the market's perception of the effect of building the factory on stock price.

These are a useful tool, but there are important caveats. First, small deviations between two markets can't be taken too seriously. If Market A predicts a stock price of $30.00 and Market B predicts a stock price of $30.01, the difference could just be noise. Relatedly, if the condition will have little effect on the stock price, even subsidized prediction markets will give people little incentive to study the effect of the condition. Instead, the subsidy will just give general incentives to study all factors that might affect future stock price.

Second, traders will recognize that information unknown to them may affect the decision. For example, last May, Hillary Clinton's chance of winning the Presidency conditional on being nominated was estimated based on prediction markets at over 70%. That could indicate that Clinton was a strong candidate. It also could mean that the Democrats would stick with a weak candidate like Clinton only if other factors, like the economy, were pointing so strongly in the Democrats' direction that Democratic primary voters did not care about electability.

In our next installment, I'll show that "normative markets" combine the two market approaches considered above.

Chris Smith (mail):
For 1), see http://en.wikipedia.org/wiki/Observer_effect
1.31.2008 5:02pm
Duffy Pratt (mail):
Suppose the decisionmaker were a petulant contrarian?
1.31.2008 5:25pm
conrad (mail):
Your point 1 is commonly called feedback, which occurs often in natural and technical systems.
1.31.2008 6:35pm
Michael Abramowicz (mail):
Chris and Conrad -- Yes, these terms are useful here. There can be an observer effect or feedback from the prediction to the decision.

Duffy Pratt -- The prediction market in this example will follow the idiosyncracies of the decision maker. If we have a group of generally good decision makers, we could have the market predict a decision to be made by a randomly selected group member. Over time, this might help expose idiosyncratic decision makers.
1.31.2008 6:47pm
Guest 1L:
For 1), with the feedback, there'd be a endogenously stable price where
p = P(p). p being the price (or predicted probability) on the mkt for decision A, and P(p) being the probability (subjective from the mkt's pov) given a mkt price p. A simple example shows that there could be multiple eq'a. That doesn't seem so good.

Imagine the decision is made as follows:

First the decision maker flips a coin.
If heads, she flips the coin again to determine her decision.
If tails, she decides based on the mkt: if p > 0.5, she decides A.

P(p) = 0.25 for p <= 0.5, and P(p) = 0.75 for 0.5 < p. So, there are two mkt eq'a, p = 0.25, and p = 0.75.

This is obviously a very stylized example, but the cheesier aspects of it aren't what drives the multiple eq'a. The decision maker's coin flip is just a stand in for uncertainty from the pov of the mkt. The decision itself wouldn't necessarily be random. Also, of course, the 0.5 probability of the coin makes it seem even more random and arbitrary, but I just used 0.5 for simplicity. Even the discontinuity in P(p) (here at 0.5) isn't necessary to get multiple eq'a. (Although, without a graph, it's hard to show why that's true.)

OK, so what if there are multiple eq'a? Manipulation of prediction markets is generally difficult to sustain in a thick enough mkt. If there are multiple eq'a, though, it might be possible for a participant to influence the mkt toward his preferred eq'm. Even without external incentives to manipulate, market participants might struggle to influence the eq'm choice. If the market's at the 0.25 eq'm, owners of decision A shares would like to see a shift to the 0.75 eq'm.

I don't know that I have a larger point, but it does seem somewhat chaotic. Interesting, but chaotic.
2.1.2008 12:20pm
Michael Abramowicz (mail):
Guest 1L -- This is a very interesting point. One artificial aspect of the example is that the decision maker will either blindly follow the market or completely ignore it. In a more complicated setting, especially with the deliberative market, the decision maker would presumably look to see what arguments have been raised. But I wouldn't rule out the possibility that there could still be multiple equilibria. Overall, I find normative markets more attractive than markets predicting actual decisions, but it would be interesting to explore further the problem that you identify.
2.2.2008 10:11am