A market demonstrated how some policy markets set prices based on correlation and not causation, inspired by this recent blog post.
I argue in my response that this flaw mostly can be eradicated entirely with some randomization and sometimes N/Aing the market; and that in reality, there is often some randomization present, so even in normal policy markets, the flaw is not really present.
So:
Suppose there’s a conditional prediction market for two coins. After a week of bidding, the markets will close. With 20% chance, I’ll pick a coin at random, that coin will be flipped and $1 paid to contract-holders for head. The other market is cancelled. With 80% chance, I’ll resolve both markets to N/A and flip whichever coin had contracts trading for more money.
Suppose you’re sure that coin A, has a bias of 60%. If you flip it lots of times, 60% of the flips will be heads. But you’re convinced coin B is a trick coin. You think there’s a 59% chance it always lands heads, and a 41% chance it always lands tails. You’re just not sure which.
... people might figure out if it’s an always-heads coin or an always-tails coin
There are two markets in this set, representing two different options I could choose with the help of our hypothetical futarchy. With 20% chance (using FairlyRandom), of the two, a random market will resolve YES or NO, the other one will resolve N/A. With 80% chanceI, both markets will be resolved to N/A.
The rules for resolving the markets involve randomness, and are as follows:
24 hours before the market closes, I will ask @FairlyRandom to (publicly) generate a number from 1 to 100. This represents the chance that coin B is an always-heads coin - if the number is 1-59 (59% chance), then B is an always-heads coin and if the number is 60-100 (41% chance) then B is an always-tails coin.
Then, once the market is closed, I will do the following:
I will ask FairlyRandom for another number 1-100. If the number is 1-10, I resolve market A. If the number is 11-20, I resolve market B. If the number is 21-100, I N/A both markets.
If the A market is to resolve I will ignore the previous number and ask FairlyRandom for another number 1-100. If the number is 1-60 I resolve Coin A to YES, otherwise I resolve it NO. I resolve coin B N/A.
If the B market is to resolve, I resolve it YES or NO according to whether it is an always-heads coin or not, respectively. I will resolve coin A N/A.
If both markets are N/A, I pick the coin with a higher price to throw. If it’s A, I ask FairlyRandom for another number 1-100, if the number is 1-60 I declare the coin Heads, if the number is 61-100, I declare it Tails in the comments. If it’s V, I declare Heads or Tails in the comments according to whether it is an always-heads coin or not. (This is me using the information the market provides about the causal consequences of picking a coin to throw the best coin. This procedure has no impact on the two N/Aed markets.)
Note that this market is not self-resolving: no matter the prices, the market’s resolution is not affected by its prices.
(Basically, this should trade at 60% for coin A and at 59% at coin B, until the first time FairlyRandom is called; then, B will trade at either ~0% or ~100% for a day.
In reality, you probably want to resolve the markets at random instead of N/Aing them a lot less often than in 20% of cases, subsidizing correspondingly more liquidity.)
The original market doesn't even seem to be about the observational/interventional distribution problem? It sure reads like the author thinks that because the coin market doesn't incentivize betting true beliefs that it's therefore "not causal", but these are just... different problems?
The other blog post proposing markets conditioned on random decisions does correctly get the interventional distribution, at least in theory.
@SG futarchy is using prediction markets to make decisions; it’s not necessarily using the default policy markets structure in unrealistic examples of binary choices and binary outcomes
(Basically, this should trade at 60% for coin A and at 59% at coin B, until the first time FairlyRandom is called; then, B will trade at either ~0% or ~100% for a day.
In reality, you probably want to resolve the markets at random instead of N/Aing them a lot less often than in 20% of cases, subsidizing correspondingly more liquidity.)