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Suppose you run an insurance company that insures buildings against burglars. You recently sold insurance to a client with a building in a new city you have never operated in before. You need to know how likely it is for a burglar to break into your client's building.

The simplest way to know for sure if a burglar will break into your client's building is to hire a burglar yourself for \$2,000. Hiring a burglar yourself is worse than doing nothing at all because it's more important to protect your client from burglary than to get your predictions right.

A less direct way to establish the probability of whether a burglar will break into your client's building is to fund a prediction market. The prediction market's implied odds will converge to the probability a burglar will break into your client's building. Suppose the prior probability of a burglar breaking into your building is 5%. The price of "the building gets burgled" ought to rest at 0.05 and the price of "the building does not get burgled" ought to rest at 0.95.

Prediction markets require liquidity. Suppose you seeded your prediction market with liquidity such that an investor can invest \$10,000 into the market without noticeably moving the prices. A savvy investor would put \$10,000 into "the building gets burgled" which pays \$200,000 if the building gets burgled and then hire a burglar for \$2,000 to guarantee the building gets burgled. The investor pockets \$200,000 - \$10,000 - \$2,000 = \$188,000. By funding a prediction market, you have just paid \$190,000 to get your building burgled. The net result is \$188,000 worse than hiring a burglar yourself to break into your client's building.

Prediction markets have two sides. In the previous example, we incentivized burglary because we seeded both sides (including "the building does not get burgled") with liquidity. Buying shares of "the building does not get burgled" incentivizes others to burgle the building. What happens if you seed the market by buying shares only of "the building gets burgled"?

The prediction market starts out empty. We offer to buy shares in "the building gets burgled" for 0.05. Traders can therefore sell shares in "the building gets burgled" for 0.05 which equals buying shares of "the building does not get burgled" for 0.95. Traders are incentivized to influence the outcome by protecting our building, which is what we want.

We also generate liquidity at a cheaper price. In the first example we risked \$200,000 to generate only \$10,000 of liquidity because we bet on a rare (5%) outcome not occurring. If we bet on a rare (5%) outcome occurring then leverage works in the opposite direction. Traders must risk \$200,000 of their own money to exhaust the mere \$10,000 of liquidity we provided.

• Betting on rare events gets leverage to work in your favor when your goal is to seed liquidity into a new-created prediction market.
• Betting on undesirable outcomes happening prevents you (in theory) from accidentally incentivizing undesirable events from happening.

As a bonus, if a burglar breaks into our client's building then we could receive up to \$190,000 from the prediction market.

What happens if you got the odds wrong because the base probability of burglary is not actually 5%?

• If the base probability of burglary is 4% then traders buy all the shares of "the building does not get burgled" you are willing to sell. Mission accomplished. You have just spent \$8,000 to find out that the base probability of burglary is lower than 5%.
• If the base probability or burglary is 6% then nobody will buy shares of "the building does not get burgled". You have just spent \$0 to find out that the base probability of burglary is higher than 5%.

If your goal is to spend a small amount of money to discover the real probability of burglary then you should start your implied odds of burglary at a little bit higher then your actual estimated odds and then gradually lower your implied odds until a market equilibrium emerges.

New Comment

Doesn't the mere existence of the market incentivise burglars? Sure, you didn't provide extra liquidity at the beginning, but presumably the market exists because you expect some people to bet on no-burglary, which means that a prospective burglar can still bet on his side, maybe at odds worse than 5:95, but still good enough to make lots of profit after hiring a burglar. Not putting liquidity on the wrong side helps things for the insurance company, but they will still see themselves burglarised much more often than they should expect.

Beat me to it. Yes the lesson is perhaps to not create prediction markets that incentivise manipulation of that market towards bad outcomes. The post could be expanded to a better question of, given that prediction markets can incentivise bad behaviour, how can we create prediction markets that incentivise good behaviour?

This reminds me somewhat of the potentially self-fulfilling prophecy of defunding bad actors. E.g. if we expect that global society will react to climate change by ultimately preventing oil companies from extracting and selling their oil field assets. Then those assets are worth much less than their balance sheets claim, so we should divest from oil companies. That reduces the power of oil companies that then makes climate change legislation easier to implement and the prophecy is fulfilled. Here the share price is the prediction market.

Another solution for the insurance company is to have a market of "will more than 5% of the buildings in the city be burgled". The only way to influence the market is to burgle a large number of buildings, which is presumably intractable for the participants in the market. You do have to adjust it for the specifics of the building you want to insure, but an insurance company probably wants to insure a broad swatch of buildings anyway.

That just affects the scale.

If every building had insurance running said prediction market, you're right back to the same tipping point where it's advantageous for someone to hire burglars for 5% of the city.

(You can argue that it's easier to hire one burglar undetected than 20,000[1]. But is it 20,000 times harder?)

1. ^

http://documents.ottawa.ca/sites/documents.ottawa.ca/files/documents/adr_2014_en.pdf -> 398,119 occupied dwellings in Ottawa (as of 2014; likely has since increased.)

I would suspect that it is more than 20,000 times harder. Either you need to hire 20,000 people simultaneously (are there even that many people in Ottawa willing to be burglars? that's 2% of the population, and some are going to report you first) or you need an organization to run repeated burglaries without it being traced back to you. A sudden rash of burglaries is going to get a lot of attention. I suppose it might wind up being a way for existing burglary operations to get some extra profit on top though.

Of course, this whole situation is a bit absurd, and I think the original point of the post is roughly correct.

Much harder to put enough capital together to make it worthwhile,

Typo: "Prediction markets require liquidity. Suppose you seeded your prediction market with \$10,000 of liquidity such that an investor can invest \$10,000 into the market without noticeably moving the prices."

That number is wrong, and I'm not entirely sure which one was intended.

The number shouldn't be there at all. I have removed it. Thanks.