Presidential prediction markets

Who will be the next president of the United States? The best answer to this question is found at prediction markets such as Polymarket and PredictIt. As of August 2, both PredictIt and Polymarket agreed that the probability of Trump winning had greatly fallen since July 21 (when Biden withdrew). However, Polymarket had Trump favored to win, while PredictIt had Harris favored. Further, the PredictIt prices seem mathematically impossible since the prices of Trump and Harris sum to greater than 100. How can we explain these facts?

Prediction markets for winner of 2024 presidential elections as of 7am August 2

The table above gives PredictIt and Polymarket prices as of August 2, plus the RealClearPolitics aggregate that includes those two markets plus three other betting sites. I also show the August 1 model projection from Nate Silver, which is a statistical prediction model that mostly relies on polling data.

There are two ways to interpret these prices. First, you can treat them as probabilities: PredictIt says there is a 50% chance that Trump will win. Second, you can treat them as binary option prices: the PredictIt price of 50 means that if you pay $50 today, you will get $100 if Trump wins in November and zero dollars if Trump loses.

Let me summarize the state of the race as reflected in this table:

• Before Biden dropped out, PredictIt and Polymarket agreed that Trump was favored to win. But since then, they have diverged. Either PredictIt is too bullish on Harris, or Polymarket is too bearish on her. Alternatively, you could say the PredictIt has over-reacted to Biden dropping out, or Polymarket has under-reacted.
• It is not surprising that the Silver model favors Trump compared to markets, since his model is based on trailing poll numbers and thus cannot incorporate recent good Harris news in a forward-looking manner.
• Looks to me like the race is about 50-50 as of August 2.
• I’d trust Polymarket slightly more than PredictIt, but they both have potential problems.

What’s the problem with the PredictIt prices? If you interpret them as probabilities, they violate the rule that probabilities of discrete outcomes cannot add to more than 100% (I reject the idea that there is a 5% chance of a Harris-Trump co-presidency). If you interpret them as tradeable securities, they are a violation of the law of one price (LOOP) and a seeming arbitrage opportunity. I will discuss the details later, but it is generally true that PredictIt prices sometimes violate LOOP.

Prediction markets

Here are the available methods for predicting the next president:

1. Bloviating pundits
2. Polls
3. Statistical predictive models based mostly on polls
4. Prediction markets

Now, I think it should be obvious that choices (3) and (4) are best. Polls are trailing snapshots which answer the question “if the election were today, who would win?” This question, while relevant, is not what we want to know.

Let me make a comparison to predicting the volatility of the stock market. What are the choices?

1. Bloviating pundits
2. Trailing realized volatility
3. Statistical risk models based mostly on trailing realized volatility
4. Implied volatility from options prices (like the VIX Index)

Now, there are many reasons that option implied volatility is not a perfectly accurate forecast of future volatility, but in general it is the best forecast around. The same is true for prediction markets.

We have a surprisingly long history showing the accuracy of a version of prediction markets for presidential elections. Last year, six senators wrote a letter to the CFTC saying that prediction markets were “a clear threat to our democracy” due to the danger “that the democratic process is being influenced by those with financial stakes”. [1]  Well, if prediction markets really are a threat, they are a threat that America has faced since its founding, according to Rhode and Strumpf (2004):

A large, active and highly public market for betting on elections existed over much of U.S. history before the Second World War. Contemporaries noted this activity dated back to the election of Washington and existed in organized markets (such as financial exchanges and poolrooms) since the administration of Lincoln. Although election betting was often illegal, the activity was openly conducted by "betting commissioners" (essentially bookmakers) and employed standardized contracts that promised a fixed dollar payment if the designated candidate won office.

This activity peaked in 1916 during the Wilson/Hughes election and was subsequently suppressed or driven underground. Rhode and Strumpf (2004) find that:

The resulting betting odds proved remarkably prescient and almost always correctly predicted election outcomes well in advance despite the absence of scientific polls.

PredictIt vs. Polymarket

In the past few decades, prediction markets have been in legal limbo in the U.S., with ongoing disputes between markets and regulators about the range of legally permitted activities. Over time, many trading venues have arisen, become popular, and then have been shut down by regulators.

PredictIt is an experimental academic market operated by New Zealand’s Victoria University. Unlike real financial markets, PredictIt imposes trade size limits so that individual traders cannot trade as many dollars as they want. Thus, PredictIt prices reflect more of an equal-weighted than a dollar-weighted aggregate. It is currently legal for U.S. citizens to trade in PredictIt although PredictIt (like Polymarket) has a long-running legal battle with the CFTC.

Polymarket is a cryptocurrency-based market based in New York and backed by venture capital. Unlike PredictIt, there are no dollar limits to trading. Thus, Polymarket can have whales (large traders) while PredictIt cannot. Polymarket has experienced a surge in trading volume in the past month.

For two reasons, the population of Polymarket traders is different than the general population of investors. First, Polymarket requires that traders use cryptocurrency to fund their account. Second, Polymarket is illegal for U.S. citizens to use, although the law is widely evaded.[2] So Polymarket oversamples law-breaking crypto-loving investors.

These facts suggest there are two potential reasons that Polymarket and PredictIt prices might diverge:

1. Polymarket traders are more Trump-friendly and believe there is a higher probability that their favorite candidate will win (Trump has recently proposed making the U.S. “the crypto capital of the planet”).
2. PredictIt’s trade limits make it more inefficient, and the PredictIt prices for Harris are just wrong.

I don’t know which of these explanations is correct; perhaps both are partly true.

Arbitrage opportunity?

The table of prices reveals two possible strategies. The first is cross-market arbitrage. Suppose I sell Trump on Polymarket and buy Trump on PredictIt; this gets me a profit of 4 today with no subsequent risk. The second is within-PredictIt arbitrage. If I sell both Trump and Harris, I get 105 today with a maximum future loss of 100 in November. In theory, both cases are arbitrage opportunities.

In reality, these calculations are unrealistic; to properly assess alleged arbitrage opportunities, we’d need to consider bid/ask prices and various fees charged by PredictIt. Stershic and Gujral (2020) carefully calculate net profits, and they do indeed find many arbitrage profits available on PredictIt.

However, these profits are tiny, due to PredictIt trade size limits. Stershic and Gujral (2020) find the biggest dollar PredictIt arbitrage profit you could have made in the 2020 elections was only $85.

So to summarize, there are probably no economically significant arbitrage opportunities on PredictIt. Nevertheless, the LOOP violations casts doubt on the reliability of PredictIt prices.

Prediction markets as probabilities

Should we treat prediction prices as true probabilities? There are three reasons why they might deviate: risk premia, behavioral biases, and manipulation.

Risk premia

If Polymarket traders were risk-neutral, then we might expect that Trump’s price of 54 represents a 54% chance that Trump will win. But if traders are not risk-neutral, then their valuations will deviate from their beliefs. Economist call this “hedging demand” or “risk premia.”

Suppose hypothetically that traders believe there is a 60% chance that Trump will win, and that if he does win, he will lower taxes and regulation, causing rising corporate profits and thus a rising stock market. In this world, a bet on Trump is not risk-reducing; it does not hedge market risk, it amplifies market risk. Thus risk-neutral traders would be willing to pay 60, but risk-averse traders will only pay 54. Trump has a positive market beta and thus a lower price. This argument is perhaps even stronger for the crypto-loving traders on Polymarket; if a Trump win benefits crypto, Trump has a high crypto beta and should thus have a low price.

Similarly, implied volatilities from option prices are not necessarily unbiased measures of future volatility, due to a possible variance risk premium. If investors are willing to pay a risk premium to own options, implied volatility will systematically overstate future volatility.

So, which way does the risk premium argument go? Is the probability of Trump overstated or understated? I have no idea. It depends on whether investors want to hedge against Trump or against Harris, which investors are trading in which markets, and how many dollars each investor has. I’d think that crypto-related hedging would drive down Trump in Polymarket relative to PredictIt, which is not what we observe.

Behavioral biases

Let me discuss two behavioral biases.

The first is long-shot bias, as discussed in the context of gambling by Thaler and Ziemba (1988) and documented by many studies before and since. Long-shot bias is the fact that extremely unlikely events are overpriced in prediction and betting markets. This bias is not relevant for the Harris vs. Trump contest, but we certainly see it in prediction markets generally.

As of August 2, Michelle Obama winning the presidency is trading at 1% on Polymarket while Gavin Newsom is at 1% on PredictIt. In my view, these are absurdly high numbers. The presidential election of 2020 was held on November 3, but as late as November 20, Trump was trading at 12% on PredictIt, leading Nate Silver to comment:[3]

Lot of dumb money out there, and I mean that quite literally.

The second is partisan bias, the tendency of Trump fans to overweight his chances and Harris fans to overweight her chances. It’s related to familiarity bias: I buy stocks of companies that I am familiar with. It has long been noted that investors suffer from home country bias, overweighting their own country and underweighting other countries. This behavior may partly reflect patriotic feelings. Morse and Shive (2011) find that more patriotic investors are more likely to own home country stocks and shun foreign stocks. Similarly, historically many employees have overweighted own-company stock in their 401k accounts, a dangerous form of anti-hedging that led to disastrous results for Enron employees.

Morewedge, Tang, and Larrick (2018) discuss identity signaling, “a desire to preserve an important aspect of the bettor’s identity.” If your favorite NCAA basketball team is Auburn, you will never bet against Auburn. They report experiments where they offer NCAA fans a free $5 bet against their favorite team, but 45% reject the offer. They discuss another case where an Auburn fan lost $50,000 because “he felt weird about betting against his team”:

Although we examined hedging in relatively low stakes contexts, people may be reluctant to hedge desired outcomes even when stakes are high. For instance, Auburn fan Mark Skiba refused to hedge a 500 to 1 bet he fortuitously placed on Auburn to win the 2014 BCS National Championship that would have paid $50,000 if Auburn won. By hedging, he would have been guaranteed to win thousands of dollars more than the initial $100 he paid for the bet on Auburn, whether it won or lost the game. Despite these high stakes, Skiba ultimately decided not to hedge …

Partisan bias is not necessarily irrational if it reflects preferences. If Mark Skiba is willing to lose $50,000 in order to avoid feeling weird, that is his business. However, partisan bias might impact prices, if the betting markets are populated with many Mark Sibas who are hypothetically willing to overpay for bets on Auburn.

The idea of partisan bias is not new. Here’s a discussion from The New York Times in 1924, quoted in Rhode and Strumpf (2004): 

Wall Street is always the place to which inside information comes on an election canvas ... [and] it is a Wall Street habit, when risking a large amount of money, not to allow sentiment or partisanship to swerve judgments—an art learned in stock speculation …

...any attempt to force odds in a direction unwarranted by the facts will always instantly attract money to the opposite side, precisely as overvaluation of a stock on the market will cause selling and its under-valuation will attract buying.

So to summarize, if Polymarket is populated by Trump fans and PredictIt is populated by Harris fans, partisan bias can explain the relative pricing. One can also imagine partisan bias causing momentum in prediction markets akin to the disposition effect. If Harris fans bet on Harris, and the price of Harris rises, these fans may be reluctant to sell because it would “feel weird” to exit.

Manipulation

Any small and illiquid market is subject to manipulation, but in prediction markets, we have the additional concern that trading will somehow impact the election outcome. There are two ways that elections might be influenced: via prices or via direct action by malevolent traders.

In prediction markets, we might see manipulation of prices motivated by the desire to influence the outcome of the election. Rothschild and Sethi (2016) find that a single individual seems to have manipulated 2012 prediction markets, spending seven million dollars in an attempt to prop up Romney prices and lower Obama prices. The idea seems to have been to prevent bad information from decreasing the morale of Romney supporters. Whoever this person was, their seven million dollars were spent in vain.

We might also see attempts to fix the election, similar to sports bettors who bribe athletes. According to Zitzewitz (2021), PredictIt eliminated some contracts related to Andrew Yang tweets after Yang received death threats from traders in order to change his tweeting behavior.

Here are the conclusions of Rhode and Strumpf (2004) about manipulation:

But these concerns were also evident in the historical wagering on presidential elections, with partisans serving as active participants and contemporary fears of election tampering. Although large sums of money were at stake in the historical presidential betting markets, we are not aware of any evidence that the political process was seriously corrupted by the presence of a wagering market.

Prediction market prices are good

So, should we treat prediction market prices as probabilities, or at least as a summary of the beliefs of informed investors? Wolfers and Zitzewitz (2006) examine both theory and evidence, and say:

In most cases we find that prediction market prices aggregate beliefs very well. Thus, if traders are typically well-informed, prediction market prices will aggregate information into useful forecasts. The efficacy of these forecasts may however be undermined somewhat for prices close to $0 or $1, when the distribution of beliefs is either especially disperse, or when trading volumes are somehow constrained …

Winston Churchill supposedly said that democracy was the worst form of government, except for all the other forms of government. I will say the same for prediction markets: the worst method of prediction, except for all the other methods.