Political Prediction Markets

Can they be gamed? Are they being?

The main function of the stock market is allocating capital but it also generates information. If the price of Tesla stock goes up, that tells you that investors, people willing to wager their own money on their prediction of the future and good enough at it so they still have money to wager, believe Tesla will make more money in the future. If, shifting from the stock market to the futures market, you observe that the price for petroleum futures five years out is much higher than the present price of petroleum that is a reason to expect that the price of gasoline will go up, useful information if you are deciding whether your next car should be an EV. In both cases what the market is selling is the opportunity to make bets, but doing that generates information, given away for free.

A good many years ago it occurred to Robin Hanson, then a NASA scientist, now an economics professor at George Mason, that it should be possible to construct markets designed to generate information. He called his proposal “Idea Futures.” If you want to know something — the average temperature of the Earth ten years from now or who will win the next presidential election — create a market where people can bet on it, buy or sell a contract giving the right to collect a dollar if global warming is more than two degrees or if Trump is elected president. The market price of the contract will adjust as other prices do until supply equals demand, until the number that people want to buy equals the number other people want to sell. The price implies a probability. If a contract on Trump winning costs fifty cents and pays a dollar if he wins, buying one is a good deal for anyone who thinks his odds of victory are more than 50%, selling for anyone who thinks they are less. Thus the market price gives you information about what people believe the odds are.

It might be better information than you get from polls¹ or the predictions of pollsters, since it is being generated by people with skin in the game, money to win or lose. The amount they are willing to bet is some evidence of how sure they are and, just as on the stock market or the futures market, people who have been good at it in the past have more money to bet than people who have not. Polymarket, which takes and pays bets for political outcomes and lots of other things in cryptocurrency in order to get around US restrictions on gambling, was started in 2020. Kalshi, as a result of a recent court decision in their favor, now takes them in cash. Robinhood is a new entrant to the business, also taking bets in cash.

The existence of prediction markets that take bets on political outcomes and report the probability implied by the prices raise some interesting issues, in particular the question of whether they can be manipulated to affect elections.

Changing the Odds

Suppose I am a Trump supporter. Further suppose I believe that many people believe the odds implied by the prices on Kalshi are a good proxy for the odds that Trump will win. Finally suppose I believe that being expected to win makes a candidate more likely to win, through some combination of voters wanting to be on the winning side and donors wanting to have the winner of the election grateful to them. It occurs to me that by buying Vance shares on Kalshi, betting that he will win, I can push up their price, push up the perceived odds that Trump will win, and so improve his actual odds of winning.

Calculations

Without my final assumption, this is simply an expensive way of making Trump supporters feel happy — until the election. It is expensive because I am pushing the price of a share above the price implied by the actual odds, making bets on unfavorable terms.

Suppose, for example, that the real probability is .5, reflected in a price of fifty cents for a bet that pays a dollar if he wins, nothing if he loses.² By betting a million dollars on Trump I can push the Kalshi odds of his winning to .6. I am making those bets at odds ranging from .5 for the first bet to .6 for the last, so about .55 on average. If Trump wins I get $1,000,000/.55 = $1,818,182. If he loses I get $0. The actual odds he will win are .5 so my expected return is .5 x $1,818,182 - $1,000,000 = -$90,909. That is, on average, the cost of my fun.

Now put back my final assumption. If the actual probability is raised by my bet to something lower than .55 I am still losing money, although not as much. But if raising the Kalshi probability to .6 pushes the actual probability above .55 I am, on average, making money on my bets as well as increasing the chances of getting my preferred candidate elected.

Implications

On my current set of assumptions, bidding up the Kalshi probability is worth doing for a Trump partisan if the effect on the probability he will get elected via the causal chain

Kalshi Probability —>Probability people believe—>Actual probability

is at least one percentage point in the actual probability per two in the Kalshi probability. It is still worth doing if the effect is smaller than that but the expected loss in money is less than the value to the partisan of the increased chance of winning. It would make sense to bring additional Trump partisans into the project, sharing the cost and increasing the benefit since even if increasing the chance of a Trump victory by a few percentage points is not worth the cost to one partisan, it might be to ten.

There is, however, a problem. The more people are involved, the more likely it is that the existence of the project will leak. Once any investor who is not a Trump partisan finds out about it, it will be in his interest to bet on Trump losing, since he is being offered the bet on favorable terms. Investors who want to make money are going to be willing to bet much more on a gamble with a positive expected return than partisans on one with a negative return (in money), so the project collapses. The same thing happens, without the involvement of investors, if the existence of the project becomes common knowledge, since that will break the link between the Kalshi probability and beliefs about the actual probability. What is required is a conspiracy with very good security.

It might occur to a Harris supporter, after reading this analysis, that he can lower Trump’s odds of winning by starting a rumor that his partisans are bidding up the Kalshi probability — even if it isn’t true. If voters believe the rumor they will interpret the Kalshi probability as a proxy biased in Trump’s favor, conclude that his real odds of winning are lower than that and become less willing to support him. If investors believe the rumor they will bet against Trump, pushing down his Kalshi probability and so, by the assumed causal chain, his actual probability.

Isn’t strategic behavior wonderful?

One Step Farther

I have, for simplicity, been assuming that Kalshi collects no house cut, that if the Kalshi odds are .5 a winning bet either for or against Trump pays two dollars for every dollar bet. I now drop that assumption, substitute the assumption that the more is bet on the election, the greater Kalshi’s profit. It is now in their interest to do whatever they can to encourage partisans of both sides to spend money trying to distort the Kalshi odds, to push them up or down. Doing that works less well the more likely it is to be discovered, so Kalshi would be well advised to maintain a high level of secrecy about who is betting what for which side.

How Expensive Is It?

How much it would take to change the Kalshi odds depends in part on the size of the market, how much money is being bet or can be. Kalshi claims that, currently, more than a hundred million is being bet on it on the presidential election. That is a lot of money to you or me but not much compared to the amount at stake in a presidential election or the assets of some partisans of each side.

But the amount bet on Kalshi is not the right number. If the Kalshi odds are .6 and the Polymarket odds are .5, an investor can make money by arbitrage, bet on Trump on Polymarket, Harris on Kalshi, and make money whichever candidates wins. Doing that pushes the odds on the two markets back together, although not necessarily all the way since there are some transaction costs. Since arbitrage links the markets, what really matters is how much money is available for all of them combined. The most recent number for Polymarket, the largest platform, is $2.7 billion, so the total on all platforms is probably about three billion.

Suppose an additional billion bet for Trump would raise his betting odds from .5 to .6 and that doing that would raise his probability of winning from .5 to .51. That would be paying a billion dollars for a .51 chance of winning $1,000,000,000/.55, an expected value of $927 million, making the net cost $73 million. That is the cost of an increase of .01 in the chance of Trump winning. If a Trump victory is worth more than a hundred times that, $7.3 billion, to a wealthy partisan or a team of wealthy partisans able to keep what they are doing secret, that’s a good deal.

If raising the betting odds, all linked by arbitrage, to .6 raises actual odds above .55, the cost goes negative and it is a very good deal indeed.

And if both sides are playing the same game, we could have a tug of war, with millions, perhaps billions of dollars thrown into it on each side.

Is it Happening?

From Maxim Lott and John Stossel’s Election Betting Odds site:

Trump’s odds are (bid-ask):

Kalshi: 56-57%

Polymarket 61.1-61.2%

Pollster Nate Silver: 55%

Election website FiveThirtyEight: 53%

Which might mean that Trump partisans are pushing the odds up a little, that people willing to bet are off a little, or that the market is a better predictor than the polls and Trump’s odds are a little better than the pollsters think. Given how close the odds, based on either polls or markets, are, the election result won’t tell us much about which prediction was right or why.

But there might be leaks.

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1. "Prediction Markets Vs. Political Polls: Forecasting Election Outcomes"  is an article by someone who used the 2020 contest for the Democratic nomination to test prediction markets against polls. The author’s conclusion:

Both the Real Clear Politics polling scores and the PredictIt contract price data correctly predicted the winner of the 2020 democratic presidential nomination, but the polling scores leave a smaller margin when compared to prediction market data. Generally, prediction market data had a larger response to micro events and towards the end of the race correctly forecasted the future winner by a larger margin. The biggest contributor to prediction markets being able to forecast future winners with higher margins is its ability to aggregate information more quickly when compared to political polls.

Idea markets are a new idea but betting on US elections is not. A recent npr article by Luke Garrett describes the history. It quotes NPR's former gambling correspondent and current editor Keith Romer:

Of the 15 presidential elections between 1884 and 1940, the betting market correctly calls the race in 11," Romer told NPR's Planet Money. "It's too close to call in three. And they only get one wrong.

2. To make the calculation easier I assume no house cut, which fits what Kalshi claims about its terms.