Villain Markets

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.

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