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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  • JW Ogden

    I think you have the word “stick” a couple of places where you mean “stink”.

  • If the market price is public information, the person with the highest price would expect that they’re likely to have interactions with such plants, while those with low prices and rest easy knowing they’re less likely to have wrongdoing exposed.

    • That’s how police patrolling is supposed to work. Better to deter foul play than to have to catch and prosecute it.

      • If the reporter is working for a for-profit media outlet, they may theoretically have the goal of deterring bad behavior, but “catching” it is actually optimal for the organization.

  • rossry

    If the selected investigation is chosen (even in part) based on market prices, it can reward market manipulation in the villain market itself, damaging its predictive power (and indeed, the usefulness of picking investigations this way at all).

    Consider a market participant A who wishes that C1 not be investigated (whether because they are already short “C1 is investigated and found stinky”, or because C1 being investigated would be harmful to them personally, or for some other ulterior reason).

    A decides to decrease the chance that C1 is investigated at all by selling “C1 is found stinky, conditional on being investigated” to drive down the price. So they get short various contracts of “Pays $100 if C1 is investigated and found stinky”, getting longer contracts of “Pays $X if C1 is investigated” for lower and lower values of $X. If they are successful at driving down the price of “C1 is found stinky, conditional on being investigated”, then C1 won’t be investigated, both their long and short contracts will settle to $0, and their trading will come at no realized cost.

    Now, perhaps there is some baseline chance that even the lowest-priced case is investigated, in which case A has some chance of losing a fair amount of money, but if [the cost of their trading activity if C1 is investigated] times [the chance C1 is investigated] is smaller than the gains they get by lowering the chances C1 is investigated at all, then this manipulation will be profitable in expectation.

    An example: Say Senator X would pay $100k/month to avoid an investigation; if the investigation mechanism chooses the highest-priced Senator half the time and a Senator uniformly at random half the time, then Senator X should be willing to do manipulative trade bad-to-fair by up to $1mln/month if they have a 10% chance to take her from the highest-priced Senator to outside that group.

    How should a small-scale villain market avoid falling prey to such manipulations?

    • renato

      “Pays $X if C1 is investigated” contracts also have a market value. In the post example, they are issued by paying their face value in advance and probably expect that it won’t change if there is no market manipulation. However, if there is a perception that C1 won’t be investigated, i.e. those $X won’t be paid in the (near) future, the value of “Pays $X if C1 is investigated” will fall. In that case, someone might profit by buying them at a lower value and then doing (or commissioning) the investigation to receive the $X from the contract.
      If someone try to manipulate the market be issuing too many “Pays $X if C1 is investigated” contracts, they just increase the market volume, eventually leading to the investigation of C1.

    • Theory, lab data, and field data all consistently find that the existence of folks who want to manipulation *increases* market accuracy. When others suspect it, they are eager to jump in on the other side.

  • The problem of villains manipulating the market was mentioned above but the effect of warning a potential
    villain of investigation is troublesome as well. For many kind of
    villainy the moment any kind of non-trivial money shows up betting on their villainy they will destroy any evidence and stop villainous behavior.

    Indeed, in many respects this is a better mechanism to use to warn potential villains of likely investigation than it is to allocate scarce investigative resources. Of course, if this leads bad actors to stop bad behavior early that doesn’t necessarily need to be a harmful outcome but I expect that depends on the circumstances.

    • To be clear I’m arguing the fact that almost any attention would be a warning to a villain to close up shop that would stop even a clever algorithm for assigning investigative resources based on prices in the market from working. If villains were willing to continue engaging in potentially incriminating behavior as long as their villain stock was relatively low one would have to solve for the equilibrium to see whether it would be worthwhile.

    • But that’s the whole point of police patrolling, to deter by showing that you will notice those inclined to violate.

      • I was trying to indicate that by saying it doesn’t necessarily need to be a harmful outcome. However, there is the risk that we lower the expected cost to being a villain by substituting prison for simply being warned off.

        But yes, I agree it might be a net positive this is just a potential negative. I don’t mean to just be a downer on new odd ideas but I think it does offer some information on where this kind of market should be used.

      • David Simmons

        Yes, but it also distorts the market by decreasing the incentive to bet on the discovery of villainy for which the evidence can be easily destroyed (even if a surprise investigation would have been able to uncover the evidence). In the end if no one is willing to bet on such villanies, then they are not deterred.

    • Silent Cal

      Is it possible to have a secret-price market, where traders just submit limit orders without knowing what will execute? Or does this make it too hard to detect and exploit manipulation?

      • Yes, that is possible, and manipulation wouldn’t obviously be more problematic there. But it would substantially hinder information aggregation.

  • renato

    The problem of alerting the villains was mentioned, but the most interesting would be the opposite, someone who has some privileged information that someone is a villain, and probably will keep behaving as one.

    It might also work as an incentive for victims to denounce them while protecting themselves from eventual retaliation and loss of future income. They can do that by betting against that villain, or even being part of the investigation (providing documents or even working on a sting operation).

  • How do the “investors” get paid? If it’s “Pay $100 if X is found stinky”, but no investigation ever finds stinky, this looks like the mob version of the lottery, where someone is announced to win, but no one knows that person, and no one actually wins. Or perhaps winning is artificially rare, just to keep hopes up.

    • I specified that exactly one case would be investigated. It would be easy for users to check that this constraint is satisfied.

  • Ronfar

    Possible perverse incentive: bet heavily on yourself to be found stinky, and then make sure that you are. Make more money than the cost of being found stinky.

    • By default any one market won’t have that much money in it.

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  • That would give a very strong incentive to frame good people. If Officer A is squeaky-clean, the payout would be big if he was found to be stinky. That would give a very strong incentive to bet on all the cleanest officers then be ready to put drugs in their pockets when they’re investigated. Presumably payout would come before conviction? (Otherwise betting would have more to do with legal particulars than with actual perception of wrongdoing)

    • The legal system already gives many parties incentives to frame people, and so we have always needed a system pretty resistant to such framing. Also, typically there is only a small amount to be gained betting on each case.

  • Joseph Smith

    Robin, Villain markets strike me as tremendously valuable. But how does one pay for the random inspections and/or maintaining the market?

    Investigative reporting and/or forensic auditing is (extremely) expensive and electronic markets require sysadmins.

    • Electronic markets can be very cheap to maintain. And the whole point is to make more effective use of a limited investigative resource. Sometimes such resources are spent; this is a way to spend them better.

  • Trimegistus

    Where official corruption or scandals about celebrities are involved, people’s judgement would be affected by what they WANT to be true, rather than what they think is actually likely. In the current environment, for instance, you’d have every Democrat betting on investigating Trump, and nobody looking into Menendez.

    • Prediction markets have already been shown to be well calibrated and informative in politically charged situations such as elections.

      • Trimegistus

        But election prediction markets don’t affect the actual outcome of the election. This “villain market” you propose would be used to allocate investigative resources. That’s a powerful incentive to bet on people you want removed, even if you know there are better targets.

      • There is a large literature showing prediction markets to be especially resistant to such attempts at manipulation.

  • anon

    Does this not run the risk of becoming a lemon market?

    That is: Once market volume is large enough, it pays to commission a secret investigation to figure out more about the villainy of person X, make profitable trades, and then commission an official investigation (or leak the incriminating details).

    On the one hand, this is good: People are incentivized to become insiders, and offer this knowledge to the market.

    On the other hand, this disincentivizes people without massive inside information from participating in the market at all, reducing market volume.

    I would guess that the resulting limit is something like “tiny market volumes with huge spreads”, where everyone is paranoid about potential insiders taking them to the bank, and every possible market-maker trying to profit from spreads risks being taken.

    • anon

      Sorry for double post, I failed at disqus UI.

      Why this critique does not apply to standard stock markets is the following: Stock markets are positive-sum (you get better expected returns on index-fund compared to treasury bills), which stabilizes an equilibrium of a high-cap/liquidity market, where info that is available to a cheap investigation is expected to be priced in already (and hence to become common knowledge, because it provides fame to the publisher and there are no incentives any longer to keep it secret).

      This critique also does not apply to prediction markets where external forces pay for a high lower-bound on publicly available/priced-in knowledge. And it also does not apply to markets that are about feeling smug / fun, like prediction markets for elections (you have many market participants who expect and accept to make a loss, for the sake of fun / theory), or with forced market participants, like subjects in an experimental study.

      It does, however, apply to general prediction markets where market participation and capitilization is self-selected, running with monetary profit-motive. I am unsure how to experimentally test such a thing; by definition, it does not help to give a student $100 with the stipulation that he must invest it in your prediction market.

      But the general literature must say something about this, I’d guess? This objection cannot be new; do you know a reference?

      Sorry for asking such a naive question, I am not an economist, but would surely enjoy reading a paper discussing this failure mode.

      • 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.

      • anon

        >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.