Pricing schemes for the Variance market
Sent to the Variance project mailing list and the Overcoming Bias NYC group. Variance was a play-money prediction-market experiment run out of the OBNYC community (Zvi Mowshowitz and Sarah Constantin among the participants named below), in which players bet tokens on probability estimates rather than yes/no shares. The post lays out the existing “market clearing price” rule, identifies a bias-toward-50% problem, and asks the group for concrete alternative pricing schemes.
There seems to be a lot of disagreement about what the best way to determine a market price for the Variance system is. Here’s how the system works, in general (regardless of pricing scheme): The market price is X. Those who guessed more than X get paid out 1 / X : 1 if the event happens. Those who guessed less than X get paid out 1 / (1 − X) : 1 if it doesn’t happen. E.g., if I put five tokens on 30%, and the market price is 20%, I get paid out 5 × 1 / 0.2 = 25 tokens if the event happens.
For every combination of probabilities and amounts, there is a natural “market clearing” price, which is the point where everyone gets to bet the full amount that they wanted to bet. E.g., if I put in a token at 40%, and you put in a token at 60%, the natural “market clearing” price is 50%. If the market price is 50%, I will get two tokens back (1:1 payout) if it doesn’t happen, and you will get two tokens back (1:1 payout) if it does happen. The betting pool is two tokens (mine + yours), so it all adds up.
Right now, we just set the price equal to the market clearing price, unless the clearing price is too close to the most extreme bet (e.g. if people bet 10%, 12%, 14%, 16%, 18% and 20%, the market price has to be between 11% and 19%). However, the disadvantage this has is that the market price will be “biased” towards 50% (even odds). Here’s why.
If there are one-token bets at 18%, 16%, 14%, 12%, 10% and 8%, the “market clearing” price will be 16.6% (1/6), even though the median of the bets is lower than that. This is because the market has to “clear”, so if the odds are long, a lot more people have to bet on the safe side than on the risky side. For instance, suppose we set the market price to 13%, the median. Three people are betting above the median, so they should get paid 1 / 0.13 × 3 = 7.7 tokens each if the event happens. But there’s a problem: if the event happens, we have to pay out 7.7 × 3 = 23.1 tokens. The whole betting pool, the chips that people put in, is only six tokens. So we don’t have enough money in the pot to pay for everyone’s winnings.
Hence, if the price is not the market clearing price, for whatever reason, we have to reduce the size of people’s bets if they’re betting on a longshot, so that there’ll be enough money in the pot to pay for their winnings. In this case, if the market price were 13%, we’d reduce the bets of everyone on the long side to 0.15 tokens (from 1 token). That way, we’d have to pay out 3.45 tokens if it happened, and the total betting pool would be 1 × 3 + 0.15 × 3 = 3.45 tokens, so everything matches again. (The other 0.85 tokens would be automatically refunded, whether or not they won.)
A lot of people don’t seem to like the “price = market clearing price” scheme, which is basically what we have now. However, it seems like everyone has a different idea of what they want to do instead. So, if there’s a new pricing scheme — a new way of determining the market price — that anyone would like to see, please post it. Schemes should be well-specified, meaning that there’s a single, definite, easy-to-calculate price for any combination of probabilities and quantities. (Unfortunately, saying “XYZ sucks” doesn’t count as a proposal; you have to specify a clear alternative.) If there’s a scheme posted that you like or don’t like, please do speak up and say why. Forward to victory!