A quick glance at the comment section suggests that people are not unanimous about which consideration is most important. This is a sign that the disconnect between prediction market prices and probabilities hasn't been given enough thought, i.e. that this post is prompting a useful discussion. Thank you for the contribution.

I started writing a comment, but it got too long, so I wrote it up here.

This is a good post. I think that in practice the inflation/opportunity cost consideration is by far the biggest effect here. Some reasons:

• It applies a definite bias in the same direction to all long term markets (pushes them away from the extremes). Hedging might result in a one sided distortion in some cases, if really cold temperatures are bad for crops but not the other way around. But not every hedge-able market has the exact same distortion
• It affects the decisions of all bettors on all markets. Whereas other distortions only apply to a niche subset such as Spanish farmers or the overly risk averse
• Importantly, it impacts the decisions of more skilled predictors more strongly. This is because they can expect a higher return on average, so they have a higher opportunity cost.
  
  E.g. for an unskilled predictor looking at a market that resolves in 1 year, they might only bet if they expect to make over a 10% return; so if their probability estimate falls outside a narrow band close to the market price it still makes sense for them to bet. But a skilled predictor might be making 50% a year on average, so a much wider range of probabilities are wiped out. 
  
  This is a big effect on Manifold because the top predictors tend to double their money every few months, so there is not much incentive for them to bet on markets longer than a year^[1] unless they have a very large edge. I'm not sure how much this effect applies to real money markets

1. ^{^}

   There is a loan system which helps with this somewhat, but also increases your risk exposure so it's not clear what the overall effect is

One more point to consider, you can sell your shares before the market closes which introduces another distortion in the probability: a lot of times I am thinking not so much in what the result of a market will be, but more on what probability people are going to assign to it. So if I see a market at 50% but I know that and event that just occurred will make people update the probability to 75%, I will buy YES at 50% all the way to say 70%, wait for the market to set to 75% and then sell to make a profit, perhaps having an effect on the market by my sell. If everybody does the same, the price is more of an estimate of people's intuition than a probability for the event. This effect is stronger in things like politics or sports, where people overprice their teams.

Yet another one: just as with stocks, big players can influence the price and sometimes make the market move the way that they want (big name is betting NO, I should probably sell my YES) which won't reflect on the real probability.

And to your last paragraph: you can actually compare "reliability" by estimating metrics such as the log score or (I think better) the Brier score. For example, Jack, one of the most successful users at manifold.markets, compared results for the election forecasts among multiple platforms: https://firstsigma.substack.com/p/midterm-elections-forecast-comparison-analysis the results were 1. Metaculus (which is non-monetary but also has their own system of aggregating forecasts), 2. 538 (poll aggregation and statistical modeling), 3. Manifold (non-monetary* pure prediction), and then other platforms including Polymarket. So at least for the last elections, that analysis supports your argument.
 

*: they give you some starting "money", you can buy with real money more, and you can cash out their "money" to real money only to send it via donations
 

By far the biggest problem with interpreting (certain) prediction markets as probabilities, especially in the tails, is the fee structures. PredictIt charges 10% of all winnings plus a 5% withdrawal fee. The latter fee in particular strongly disincentivizes adding new money to arbitrage small deviations in the tails. E.g. if a "yes" contract is trading at 98 cents and you are 100% sure it will happen (and you're correct), investing 98 cents now and withdrawing the resulting $1 after the market turns over (even if it ends tomorrow, so we abstract from inflation), will yield a loss of 0.98-((1-.98)*0.9+0.98)*0.95 = 3.19 cents. This problem is much smaller when betting on long shot outcomes, so it will tend to push prediction markets away from "certainty" on outcomes. You can make a copy of this calculator for PredictIt to see the effects.

This problem is somewhat ameliorated by people making multiple sequential bets (this amortizes the 5% withdrawal fee over more bets -- in the limit, I think that if you made an infinite number of (on average winning) bets, the 5% withdrawal fee would become just a fee on profits), but I think it's a significant issue in the tails.

Regarding the inflation/opportunity cost, I'm curious as to its effect in a more efficient market. If I believe that the probability is $q$ but the market currently values the share of YES at a price reflecting some probability $p<q$, then I should believe that the market will update itself upward. That is, I expect my personal information and considerations to be eventually discovered by other people and the price to reflect that (especially if after I buy I'll also share my information and considerations). This would mean that I don't have to wait a long time before the price goes up, and by then I can sell. 

However, I don't think we should expect the price to go all the way up to $q$. In the simple case where everyone believes the probability is $q$, and that it would remain $q$ until the market closes, and everyone is rational and risk-neutral, the price should reflect the expected benefit considering the opportunity cost, so that one would value buying YES and investing in other alternatives equally. 

In such an efficient market, at the limit, I'd expect no difference between holding on to some stocks compared to buying and selling any time at whatever the price is. Therefore, the price $p_t$ at each time $t<T$ (the closing time) should really be such that the following holds:

$q\cdot 1-p_t=p_t{r}^{T-t}$, where $r$ is the interest rate. Equivalently, 

$p_t=\frac{q}{1+r^{T-t}}$.

I can confirm that for this reason, and a few more, a prediction market mechanism works much better in a well-designed virtual market economy where bets are not denominated in a monetary currency. In fact that's why I sold Redmonitor, a real money prediction market I founded in 2004 only 4 years later, in 2008 and started a virtual one.

Augur used to have a set of markets called "Chad Edition" where you could wager Ethereum instead of USD

 https://augur.net/blog/augur-ce/

Just to highlight a particular example: suppose you have a prediction market on "How much will be inflation of USD over the next 2 years?", that is priced in USD.

So think the outcomes point is the strongest here.

When I'm thinking about how seriously to take their prediction market percentages I consider:

• Do the outcomes have the right incentives
• Is there sufficient liquidity to think the number is a proper representation (maybe $1000 or M$1000)
• Is the probability over 95% or smaller than 5% (in both cases it becomes much less clear)

Outside of that using prices as probabilities is fine.

Again your hedging bit is right but just rarely happens in the kinds of markets people quote on this forum.

Thanks for writing. I think you are technically right which is good.

Regarding the question of locking up money for so long, do prediction markets generally require bets to be 100% funded? That seems like it makes these bets unnecessarily capital-intensive.

In futures markets bets are generally margined and marked to market daily (or more often). If the market moves in your favor, you could withdraw money accordingly, but if it moves against you then you must add more capital or else liquidate your position. Overall this allows placing trades (sometimes long-term trades) without having to put up as much capital.

The amount of margin required for a particular bet generally depends on the liquidity and volatility of the market in question.