### The Wisdom of Crowds

 The (possible) future pricing of a Warren-like candidate in the futures markets.

#### How the Prediction Markets Work

If you've ever been so desperate for new polls that you'll look for anything that will give you a sense of shifts in the political winds then have I got a treat for you: political prediction markets.  Places like Betfair, Hypermind, and PredictIt will allow you to put real money on upcoming races or events, and if your prediction is correct, you get a dollar for every share you buy.  Here's a current snapshot of the Democratic primary market:

 The current Democratic primary market at PredictIt.  At the moment, investors think the most likely nominees are Warren, Buttigieg, and Biden, in that order.
So, for instance, if you buy 1000 shares of Warren at $\$$0.26 and she wins the nomination, you pay \$$260 and get a payout of$\$$1000, a profit of \$$740 (less PredictIt's 10% profit fee, $\$$74 in this case). If she doesn't get the nomination, you get nothing. Of course, down the line (but while the race is still going), you might decide Warren is not the best investment and sell your shares, maybe at a profit, maybe at a loss, depending on what the market has done in the interim. If you don't want to bet (and I don't), and you don't go there for the comments (definitely don't, unless you want to see a bunch of people pumping the market and saying some super offensive stuff in the process), the main advantage of these markets is that it utilizes the wisdom of crowds to try to synthesize all of the data (polls, news, gut reactions, history, etc.) to figure out what is actually going to happen. Because people are betting with real money, the theory goes, it's bad business to simply invest with your heart, rather than what you think will actually happen. That's the theory, but what about in practice. #### They Work! At least in the short term. I collected data from every PredictIt market covering a race since 2016 (as good a starting point as any). To avoid duplication and cross-correlation, I looked at the "top level" market. That is, I only included the 2018 "Who controls the House?" market, and not individual US House races. I found a total of 48 races, and recorded the price 2 days before the relevant election here. It's not the largest dataset, but still, there are some interesting results. For instance, I found that, on average, the market undervalues Dems by about \$$0.04 (but with an uncertainty of$\$$0.05). In other words, the markets may have a small Republican lean... or it may just be noise. But as another test, I could bin up the data, and see, for instance, how often Dems win when they are priced at, say, \$$0.70.  It should be ~70%, right? You know what?  The markets are quite predictive, at least in the short term:
 A fit to 48 electoral PredictIt prices and corresponding results since 2016.  The dotted blue line corresponds to a completely unbiased pricing model. As you can see, it's not exactly perfect.
The higher the price, the more frequently candidates with that price win.  You can also see that, in general, the Dem tended to win just a little more often than their price would suggest.

The Technical Part (you can skip this, if you like)

While in principle, we'd expect that the probability and price should be the same, in practice, they're not. We can estimate the best fit by maximizing the efficiency of the market.  That is, if the cost of a share for an election, $i$, is $C_i$ and the probability function of winning an election is $p(C_i)$ then:

$$E=\sum_i (p(C_i)-W_i)^2$$
where $W_i=1$ if the candidate won, and $0$ if they lost.  The lower this $E$ value, the better the model.

I opted for a simple model, in which the slope of the curve is given by $\alpha$, and $\alpha=0$ for the totally random result (every race is 50-50), and $\alpha=1$ for the case where the share price is perfect.  We then find the value of $\alpha$ which gives the best efficiency:

 The efficiency of various probability function slopes.
The best fit is $\alpha=1.5$, somewhat steeper than a perfectly priced market.

#### Non-technical: What it Means

As near as I can tell from the data, the PredictIt markets provide a pretty good prediction for what would happen if an election were to be held tomorrow -- but with a slight caveat: it's a little conservative.  For a real 50-50 shot, the market will, indeed, trade around $\$$0.50, but markets trading at, say, \$$0.70 really mean that a candidate has approximately 80% chance of winning. Non-binding investment advice I should note that if this trend holds, there's a pretty easy to make money in the prediction markets. Simply buy all candidates trading at$\$$0.60-\$$0.80 a day or two before an election, and on average, you'll make a net profit because the market is under-valuing them.

But more generally, what all of this means is that there is a pretty direct relationship between the value in a market, and how likely the candidate is to win if the election were held the next day.

Remember, probabilities are probabilities.  2 days before the 2016 election, the markets were trading with Clinton at $\$$0.78 which (per my model) means that she had something like a 92% of winning. It doesn't matter too much whether she had an 80% or 90% chance, it was still very likely that she would win (at least according to investors – and polls, which told a very similar story). But, either way, it was never impossible that she would lose. For context, the probability of being dealt 2 pair or better in a 5 card hand of poker is about 12%, and that happens often enough for it to be unremarkable. #### A Random Pricing Walk The markets can also tell us something now, even a year out from an election. The future is uncertain, but we can make some reasonable guesses. First, we might suppose that there's a single number (the current national poll average, for instance) which gives us a pretty good insight to the state of the election. Before you scoff about the elections being wrong in 2016, we can make a few quicky corrections, like that the Dem has to win by 2 to win the electoral college (it's BS, but the current state of the rigged system), and that the poll isn't necessarily the final result, but just a guess, with an uncertainty (based on historical errors) of about 3%. With a 4% national lead in 2016 just before the election, the best guess would be that Hillary would have had 2%±3% more than she needed to win the electoral college. For what it's worth, that result corresponds to an 83% chance of winning, basically in line with the betting markets. Secondly, we might further guess that news comes in randomly. That is, that in any given day, poll numbers might go up or down, and that the longer it is before an election, the more the numbers might migrate. This is known as a random walk and it describes all sorts of things, from the stock market to winning runs in a casino. It can produce some very complex looking results (and ones that look like there are patterns). I've simulated one year of "data" at the top of the piece. Here's another: In both cases, our hypothetical candidate (in blue) starts off with a modest, 3 point lead (In practice, for a Dem that would need to be 3 points above the required 2, so a 5 point lead. Yes, it sucks, and is also a little confusing.). The red line is a "now price" representing the fair trading price for a candidate with that lead if the election were tomorrow. However, the election isn't tomorrow. As the shaded blue indicates, there's a wide range of final outcomes, which narrows somewhat as time goes on. But because there's a wide range of final outcomes, the expected market price is closer to \$$0.50 than the "now price" would suggest. In the example above, the "now price" is about$\$$0.90, while the actual price is closer to \$$0.75.

By the way, these probabilities aren't just made up.  We can see how much, for instance, Clinton-Trump polling varied from week to week in 2016, and from there estimate the size of our random walk steps:

 The weekly change distribution in Clinton-Trump polling
The polling only changed about a point or two per week, but because of the math of random walks, that corresponds to about 6 points (typical) over the course of a year.  In other words, the uncertainty because of the random walk (6 points) is about twice the uncertainty of polling (3 points). Random walk uncertainty scales as the square root of the time remaining, so it won't be until about 3 months before the election when the random walk uncertainty is half what it is now, roughly the same as the polling uncertainty.

At least, that's how it should work if the markets are behaving rationally, at least this far out.

So where are we now?

There's definitely an incentive for people to manipulate the market a year out from an election to make a few fast pennies per share, and unfortunately, there doesn't seem to be a database of long-term historical data for these markets.  However, we can say how they should behave.  Here's a snapshot of the "which party will win the presidency" market:

The markets say that the Dems have about a 54% of winning the presidency.  But wait!  It's a year out, and I already argued that that means that if the election were held tomorrow, based on what we know now, they'd have more than a 54% chance of winning.

But even so, the market seems more pessimistic on the Dems than the data would suggest.  Running through the numbers, a price like this corresponds to a Dem advantage of about 0.5%, or adding in the electoral college hurdle, about 2.5-3% overall, based on polling.

But that's bananas!  All of the frontrunners are doing better than that.  Biden is winning by 11.6 nationally, Warren by 7.7, Sanders by 8.8, based on my 2020 tracker.  Those numbers are simply weighted averages of recent high-quality national polls, and they've been very consistent.

Even if we assume that Warren is the candidate, and even if we use her state level polling (which paints a more pessimistic picture), and further assume that her lead doesn't improve after she clinches the nomination (a dubious proposition), the correct price should probably be about 60-40, even this far out. And higher for the other candidates.

The point is, I think there's a degree to which people are letting cynicism about 2016 trick them into believing the Dems are in worse shape than they are.