#### Discover more from Overcoming Bias

Imagine that you have a large pool of cases, where in each case you weakly suspect some sort of villainous stink. But you have a limited investigative resource, which you can only apply to one case, to sniff for stick there.

For example, you might have one reporter, who you could assign for one month to investigate the finances of any one member of Congress. Or you might have one undercover actor, whom you could assign to offer a bribe to one member of the police force of a particular city. Or you might assign a pretty actress to meet with a Hollywood producer, to check for harassment.

Imagine further that you are willing to invite the world to weigh in, to advise you on where to apply your investigative resource. You are willing to say, “Hey world, which of these cases looks stinky to you?” If this is you, then I offer you *villain markets*.

In a villain market, some investigative resource will be applied at random to one case out of a set of cases. It will report back a verdict, which in the simplest case will be “stinky” or “not stinky”. And before that case is selected for investigation, we will invite everyone to bet anonymously on the chances of stickiness in each case. That is, anyone can bet on the probability that the verdict of case C will be found stinky, *given* that case C is selected for investigation. So if you have reason to suspect a particular member of Congress, a particular police officer, or a particular Hollywood producer, you might expect to gain by anonymously betting against them.

Imagine that we were sure to investigate case C87, and that the market chance of C87 being found stinky was 2%, but that you believed C87’s stinkiness chances were more like 5%. In this situation, you might expect to profit from paying $3 for the asset “Pays $100 if C87 found stinky”. After your bet, the new market chance might be 4%, reflecting the information you had provided the market via your bet.

Now since we are not sure to investigate case C87, what you’d really do is give up “Pays $3 if C87 investigated” for “Pays $100 if C87 investigated and found stinky.” And you could obtain the asset “Pays $3 if C87 investigated” by paying $3 cash and getting a version of this “Pays $3 if C investigated” investigation asset for *every* possible case C.

So you could reuse the same $3 to weigh in on the chances of stinkiness in every possible case from the set of possible cases. And not only could you bet for and against particular cases, but you could bet on whole categories of cases. For example, you might bet on the average stinkiness of men, or people older than 60, or people born in Virginia.

To get people to bet on all possible cases C, there needs to be at least some chance of picking every case C in the set of possible cases. But these choice chances do not need to be equal, and they can even depend on the market prices. The random process that picks a case to investigate could set the choice chance to be a strongly increasing function of the market stinkiness chance of each case. As a result, the overall chance of the investigation finding stink could be far above the average market chance across the cases C, and it might even be close to the maximum stinkiness chance.

So far I’ve describe a simple version of villain markets, but many variations are possible. For example, the investigation verdict might choose from several possible levels of stink or villainy. If the investigation could look at several possible areas A, but would have to choose one area from the start, then we might have markets trading assets like “Pays $100 if stink found, and area A of case C is investigated.” The markets would now estimate a chance of stink for each area and case combination, and the random process for choosing cases and areas could depend on the market stinkiness chance of each such combination.

Imagine that a continuing investigative resource were available. For example, a reporter could be assigned each month to a new case and area. A new set of markets could be started again each month over the same set of cases. If an automated market maker were set up to encourage trading in these markets, it could be started each month at the chances in the previous month’s markets just before the randomization was announced.

Once some villain markets had been demonstrated to give well-calibrated market chances, other official bodies who investigate villainy might rightly feel some pressure to take the market stinkiness chances into account when choosing what cases to investigate. Eventually villain markets might become our standard method for allocating investigation resources for uncovering stinking villainy. Which might just make for a much less stinky world.

## Villain Markets

>In any financial market, those who have too little info per trade should stay out, relative to those with more info.

"should stay out relative to those with more info", indeed. This does not always mean "stay out completely".

I mean, in many financial markets it is in my interest to participate even though I expect some losses from information asymmetry. Say stock market: The alternative of not using the market at all does not look nice, but I should reduce exposure, e.g. by trying for "mostly neutral" index-funds or something. Or insurance: The non-linearity of utility as a function of money is large enough that people are willing to participate (buy insurance) even though they lose money in expectation. This holds in both of natural disaster insurance (where the insurance company has better info) and in personal insurance like health or driver's (where the customer has better info). Likewise real estate: Even though I lose in expectation (worse info/judgement than real-estate professionals), it may make sense to buy for personal use, for the increased efficiency (I know that I will treat the property well, and want to internalize this), and try to keep the number of transactions / moves to a minimum.

That is, having little info is a big disincentive for market participation ("little info" compared to "expected info of counterparty").

Armed with this viewpoint, I kinda understand why many real-world markets manage to avoid the lemon market equilibrium: The extra pressure for market participation is enough to pay for making info common knowledge/priced in, which reduces costs for participants.

Alas, how do you get market participation in prediction markets?

How can noise traders survive if they must expect their counterparty to be either noise-trader/marketmaker or have secret info (because the counter-party self-selected for market participation)?

With external pressure this problem goes away, because the noise trader can amortize the losses from secret-knowers over profits from the large number of captive participants.

In any financial market, those who have too little info per trade should stay out, relative to those with more info. But as long as there are noise traders or formal subsidies, most all info gets out anyway.