Decision Selection Bias in Conditional Markets
Special thanks to @0xdist, Advaith Sekharan, @frankeislost, and Robin Hanson for reviewing drafts of this post. Cross posted from X: https://x.com/metaproph3t/status/1858607154858783222
Conditional Markets
Conditional markets allow traders to bet on the impact of events.
For example, we could have a conditional market where traders bet on what the price of UNI would be if Uniswap turned on the fee switch.
Conditional markets are also called decision markets because we can use them to make decisions. For example, Uniswap could use the above market to decide whether to turn on the fee switch - turning it on if traders bet that it would make UNI more valuable.
Trades in conditional markets are like normal trades except they can be either finalized or reverted. If I placed a buy order in the above market with $100, I would receive 8.47 conditional UNI. Then, if the fee switch is turned on, the trade is finalized and I get my 8.47 UNI. If the fee switch isn’t turned on, the trade is reverted and I get my $100 back.
Adverse Selection
Recently, I met up with another anon. At one point he asked me to guess how old he was. I told him that I would bet him $100 that he was between 23 and 27.
It was stupid to offer him this bet. If he was between 23 and 27, he wouldn’t take my bet and I wouldn’t make any money. If he was younger or older, he would take my bet and take money from me.
This is the basic idea of adverse selection, which can be encapsulated in the phrase “conditional on getting to trade, your trade wasn’t all that great.”
Decision Selection Bias
Imagine there’s a country, let’s call it Powergrabistan, that’s deciding whether to invade its resource-rich neighbor, Minelandia.
Powergrabistan only wants to invade Minelandia if there’s at least a 50% chance of the invasion succeeding.
To make this decision, Powergrabistan creates a conditional prediction market on “would Powergrabistan conquer Minelandia if it invaded?” This market works like a normal prediction market, with the buying and selling of YES and NO shares, except all trades will be reverted if Powergrabistan doesn’t invade Minelandia.
Suppose the current probability is 5%. Suppose also that you have some information that the true probability is even lower than 5% - maybe you’re a member of the military who knows that Powergrabistan’s generals are all incompetent. You should be able to profit by buying NO, right?
Here’s the problem: Powergrabistan only wants to invade if the probability is above 50%. So if the market incorporates your information and the market remains below 5%, Powergrabistan won’t invade and your trade will be reverted. You’ll get your original money back, but not any profit.
But if you’re wrong - if, for example, news breaks out that Minelandia is completely unfortified and the probability shoots up to 70% - Powergrabistan will invade and your crappy trade will be locked in.
Seem familiar?
Because of this asymmetry, we’d expect conditional markets to be biased in the direction of the finalization criteria. If finalization is correlated with a high number, we’d expect the market to be biased upwards. If it’s correlated with a low number, we’d expect the market to be biased downwards. Robin Hanson calls this "decision selection bias."
The Bias Seems Manageable
One could assume from the above that a risk-free strategy would be buying UP at $0.49 and selling it at $0.50, but this doesn't work. If enough people are doing this, the market is at risk of being finalized. This would leave you and the other “arbitrageurs” with an asset worth $0.05 that you bought for $0.49.
So it's not like there's a clear cutoff point. Instead, the bias gets less important as the conditional market price gets closer to and moves past threshold:
In practice, MetaDAO has created 78 conditional markets, including 2 that were structured nearly identically to the Powergrabistan market. This adverse selection problem should affect all of these markets in theory, but it doesn’t seem to affect trader behavior that much in practice.
Remedies
Decision-maker oversight
One way to help with this issue is to give decision-makers ultimate authority on how markets resolve. If there’s a credible threat that a market will be finalized even if it’s below its threshold, there’s even less of a “risk-free arb” from buying below the threshold and selling above. Drift’s decision market on how many views their marketing campaign would get didn’t set a clear threshold but instead stated that the final decision would be made by Drift. Our proposal to Jito DAO states that the grant committee would have ultimate authority to overturn the market.
Private or random thresholds
Another more longer-term solution would be to somehow incorporate private or random thresholds. For example, Powergrabistan could use a VRF to randomly set the threshold to be somewhere between 45 - 55%, where the random threshold is calculated at finalization time.
Occasional random decisions
Both of the above mitigate the bias, but @0xdist found a way to completely remove it for at least a subset of DAOs.
The mechanism is as follows:
For example, imagine there’s a DAO where you can only make one type of proposal: a request for a $10k grant. The DAO has $1m in the bank, so there will be a total of 100 successful proposals.
When someone creates a proposal, this creates conditional markets on “what would be the value of the DAO token if the grant is given?” and “what would be the value of the DAO token if the grant is not given?” People trade their DAO tokens in these two markets.
90% of the time, you take the action that has the higher price (e.g., pass the grant if the price in the pass market is higher) and revert all trades in both markets.
10% of the time, you take the decision at random and finalize the trade in the relevant market. For example, if you randomly pass the proposal, you finalize all the trades in the pass market. Because people don’t know when the decision will be made randomly versus following prices, everyone has an incentive to accurately price both markets.
This completely solves adverse selection since market finalization is uncorrelated to market price.
The problem is obvious: randomly deciding things is dangerous, especially in the context of DAOs! What happens if an attacker raises a proposal to move all of the DAO’s funds to themself, and then the DAO randomly passes it? For this reason, I think this only works in a limited subset of DAOs.
Conclusion
Adverse selection is a real problem in conditional markets and is caused by market finalization being correlated with conditional market prices. We’ve discussed why this problem is less severe than it seems at first glance and how one can mitigate or potentially solve it.
If you have any other ideas on how one could mitigate or solve it, please reach out to me! I am happy to pay $500 - $2k bounties for mechanisms that could improve the capabilities of MetaDAO and futarchy more broadly.