EA - Don't Interpret Prediction Market Prices as Probabilities by bob

Link to original articleWelcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Don't Interpret Prediction Market Prices as Probabilities, published by bob on May 5, 2023 on The Effective Altruism Forum.Epistemic status: most of it is right, probablyPrediction markets sell shares for future events. Here's an example for the 2024 US presidential election:This market allows any US person to bet on the gender of the 2024 president. Male shares and female shares are issued in equal amounts. If the demand for shares of one gender is higher than shares of the other, the price is adjusted.At the time of writing, female shares cost 17 cents, and male shares cost 83 cents. If a female president is elected in 2024, owners of female shares will be able to cash them out for $1 each. If not, male shares can be cashed out for $1. The prices of male and female shares sum up to $1, which makes sense given that only one of them will be worth $1 in the future.Because bettors think a female president is relatively unlikely, the price for male shares is higher. The bettors may be wrong here, but the beauty of prediction markets it that anyone can put their money where their mouth is. If you believe that a female president is more likely than a male president, you can buy female shares for 17 cents a piece. If you're right, each of these shares will likely appreciate to $1 by 2024, almost sextupling your investment. If enough people predict a female president to be more likely, the demand for female shares will grow until they are more expensive than male shares. As such, the price of the shares reflects the predictions of everyone involved in the market.Even if you believe a female president is, say, 25% likely, you'd still be inclined to buy a female share for 17 cents. (That is, if you'd take a 1 in 4 chance of a 500% return on investment.) The interesting thing is that whenever you buy shares, the price will move closer to the probability you perceive be true. Only when the price matches your perceived probability, the market is no longer interesting for you. Because of this, the price of a share reflects the crowd's perceived probability of the corresponding outcome. If the market believes the probability to be 17%, the price will be 17 cents.Or so the story goes.In reality, it's more complicated.You're betting in a currency and, as such, you're betting on a currency.Let's say you believe a male president is about 90% likely, so you're considering buying male shares at 83 cents. Every 83 cents you put in can only become $1, so your maximum return on investment (ROI) is about 20%. Your expected ROI is closer to about 8% because you believe there's only a 90% chance the president will be male. Still, that's a positive ROI, so why not make the bet?This bet is denominated in US dollars, and it will be only resolved in 20 months or so. The problem is that US dollars are subject to inflation.Instead of locking up our investing money in a long-term bet for nearly two years, we could instead put it in an index fund, like the S&P 500, or invest in a large number of random stocks. Both methods have historically had a 10% annualized return. That's much better than an 8% two-year return!Because everyone thinks this way, there will be an artificially low demand for boring long-term positions, like predicting that the next US president will be male. This will drive the price of these shares down, while driving the price of shares for low-probability events up. A share that pays out USD will never have a price that reflects the market's perceived probability, because most people believe there are better things to invest in than USD.There's a solution for this, although regulators might not like it: allow people to bet bonds or shares. The famous 1 million USD bet between Warren Buffett and Protege Partners was actually not denominated in USD, but in bonds and sh...