Story: The election is 1 year away, you check on Predictit to see what Elizabeth Warren's chances are you see it's 23c for a yes contract.
What is the minimum probability they have of winning and what is the maximum?
There are 3 main sources of inefficiency in prediction markets
Rake: Rake is the amount the casino charges winners after they win the bet. This covers costs for the house. Predictit has a rake of 10%
Taxes, gambling winnings are taxed :( the smart Predictit users (who are good at forecasting) are in the federal 24-32% income tax bracket + state taxes, Taxes vary by state but for now, we can say the total tax is 30% between state and federal. If you're me it's more like 42% (YUCK)
Expected gains from the stock market. If predictit is offering you a 6c contract on an event with a 0% chance of happening, the stock market would be a better bet since it pays 7%.
Due to the associative property of multiplication, we can combine factors 1 and 2 to a single factor I (standing for inefficiency) sadly factor 3 is much more frustrating to model, as it's a raw EV minimum rather than some factor. When doing final substitution substitue the EV of putting money in the stock market into the EV part of the equation.
Ok proving this is short but Reddit formatting for math sucks. Here we go
I=Inefficency of market (1-rake) *(1-taxes)
EP= expected profit
EL= expected loss
P= Probability given by market (price)
T= True probability
EV = Expected profit-expected loss
EP = I(T)(1-P)
EL = (1-T)(P)
EV = I(T)(1-P)-(1-T)(P)
simplified EV= IT-ITP+PT-P
For buying a no-contract (our minimum)
EP= I(1-T)(P)
EL = (T)(1-P)
EV = I(1-T)(P) - (T)(1-P)
Simplified EV=IP-ITP-T+TP
Now to solve the problem stated above we put I=0.63 and P=0.23 and EV=0.07
We have Elizabeth Warren having a probability of winning between 8.2% and 42% If the election were tommorow it would be between 15.8% and 32%
So while prediction markets are a reasonable baseline, groups like 538 and The Good Judgement Project will probably outperform them in the long run. The groups like 538 will not be able to profit from their superior knowledge compared to prediction markets, because the rake is so high.