Prediction Markets: An Answer to

Our Democracy's Shortcomings?

Alex Pinheiro | June 2021

The New York Stock Exchange

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onsider the group of Americans who believe stricter gun laws would prevent gun deaths. Of that group, how many of them believe abortion is morally wrong? What about someone who opposes gun control laws -- how well does that belief predict moral opposition to abortion? In both cases, the views strongly correlate. That’s weird, considering gun control and the permissibility of abortion are logically unrelated (the truth of one doesn’t constitute evidence for the other).

 

In politics, we tend to disagree in ‘clusters.' It’s common to be religious, against immigration, against gun control, against affirmative action, against gender-nonconformism, and against wealth redistribution. It’s about equally common to be somewhat irreligious, pro choice, progressive on gender, pro immigration, pro affirmative action, favor gun control, and sympathetic to the welfare state. The clustering of logically unrelated beliefs shows us that something is going wrong. We would expect beliefs in logically unrelated propositions to be randomly distributed among people reasoning independently, so we know tribalism and bias play a big role. 

 

Sometimes that bias is so strong that beliefs correlate opposite to the way they should. For example, belief that abortion violates a fetus’s right to life correlates with the rejection of animal rights, even though one expects similar arguments for the moral consideration of both fetuses and animals (sentience is what matters, not intelligence, and so on). That’s not to say it’s a contradiction to simultaneously accept animal rights and reject fetal rights (fetuses and animals are different in some respects) but the two ideas should find common hosts more often than they do. 

 

Of course, that’s not even the tip of the iceberg when it comes to irrationality in politics. There’s a widespread failure to update beliefs, disagree calmly, hold beliefs with confidence levels appropriate to the conclusiveness of available evidence, refrain from stereotyping large and diverse segments of the population as evil, and so on. Most people don’t need much convincing of this. 

 

But the irrationality of politics distinguishes it from other domains which aren’t so bad -- and that needs explaining. It’s not obvious why our political beliefs admit stubborn and frequent disagreement whereas, say, our beliefs about our consumer choices don’t. (Most of us are open-minded when receiving suggestions about how our purchasing habits might be altered to save money; we naturally modify our beliefs after reading product reviews and consulting with friends, etc.) Why are we more rational in domains other than politics?

 

Maybe political issues are more morally charged than other issues. If you’re wrong about politics, you’re wrong in a way that makes me think you’re morally deficient -- that your beliefs run the risk of harming people. Maybe that’s anger-inducing in a way that amplifies the influence of tribalist thinking habits. Personal virtue is rarely on the line when there’s disagreement, say, in a math class about the answer to a problem. That probably explains some of it. 

 

But here’s another possibility: maybe people don’t think rationally in politics because it’s a bad idea for them to. That’s the view of philosopher Michael Huemer. He argues that in typical cases where we seek information, we have a stake in the accuracy of the beliefs we form. Need to buy a car? It would be wise of you to do good research beforehand -- otherwise you risk sinking money into a bad product. But what’s the incentive to form accurate beliefs in politics?

 

We don’t bear the cost of our wrong political beliefs. But seeking and processing political information is time consuming. It’s often boring. Being politically informed has a depressingly low return on investment. 

 

Therefore our political ignorance can actually be explained as good decision-making. In math class, if you don’t understand the lesson, you’ll pay the price once the test rolls around. At the store, false beliefs impact you. Not so in politics. 

 

Huemer advances similar arguments to explain why we don’t respond to evidence rationally either (that is, in addition to not honestly seeking it out in the first place). First, a rational thinker doesn't get to believe whatever he or she wants. Their worldview is at the mercy of the evidence. Most people don’t like that -- I sure don’t. I want to believe things that make me happy. We all have belief preferences. I’d rather think the sun will continue burning for eons than believe it will explode tomorrow, killing everyone -- that would be distressing. If someone were to try to change my beliefs about our star’s longevity, they probably couldn’t mount a very convincing case. But to deny I’d be motivated against believing that would be naive. 

 

If we were rational in politics, we would be putting our worldviews at risk constantly. We’re okay with that in several domains, but in politics, we’re more likely to have preferences for our beliefs. They’re tools of social bonding -- we love to dunk on the other side of the aisle. They’re parts of our self-image. And nobody wants to risk alienating themselves by endorsing beliefs which offend their social circles. It’s the same idea: being rational about politics has high costs and negligible benefits. 


 

Group Wisdom

A core feature of a democracy is its aggregation of the beliefs of its citizens. A group vote therefore results in good policy more often than would a fillable individual leader with dictatorial control, the reasoning goes. 

 

One formalization of this idea comes from the 18th-century French philosopher Marquis de Condorcet, who proved his Jury Theorem, stating that:
 

  1. If a group of individuals independently reason about some subject, and...

  2. Each individual is more likely to arrive at the right conclusion than the wrong one, then... 

  3. If the group takes a vote, the larger the group, the higher the probability that it votes for the right answer.
     

That’s intuitive. Group votes ‘average away’ the random errors and information gaps that make individuals unreliable. It’s a neat formalization of why groups are wise.

 

Democracies take advantage of that in ways that dictatorships don’t. But point (2) of the Jury Theorem is threatened by the concerns in the previous section about irrationality in politics, and democracies routinely make nonsensical decisions that hurt voters or run afoul of expert consensus.1 There’s a lot to be desired. 


 

Hanson's Proposal

 

The upshot of the previous two sections was that while group wisdom is a powerful tool for governance decisions, democracy doesn’t adequately incentivize the rational formation of accurate beliefs among the people who ultimately authorize those decisions (that is, voters). That’s a challenge. The problem of effective governance is big and important and complicated and lots of people have a stake in it. 

 

George Mason economist Robin Hanson (known by his colleagues for his philosophical and crazy-sounding ideas) has a proposal. He suggests democracy should be updated to a system in which voters express their values by voting, but where the policies to attain those values are selected by the recommendation of a prediction market, not by elected officials. The title of his paper offers a condensed slogan for the idea: “Vote on values, bet on beliefs."

 

In a democracy, we vote to express both what we want (wealth, recreational time, justice) and how to get what we want. But democracies suffer failures at harnessing group wisdom into accurate beliefs. Prediction markets, on the other hand, do so excellently, in part because market participants have a financial stake in their beliefs’ accuracy. For Hanson, therefore, we should replace our elected government’s power to select policies with a market in which bettors predict the consequences of policy proposals, while keeping the democratic voting system that allows citizens to express what they want policies to achieve. The policies which the prediction market deems probable to increase national welfare (as measured by the values which we all voted on) become law. Participation in the prediction market would of course be voluntary. 

 

That’s the sketch of Hanson’s reasoning. But what are prediction markets, and why are they considered such powerful belief aggregators? 

 

 

Prediction Markets

 

They’re stock markets, but instead of investing in companies, one invests in wagers on the truth of a prediction of the future. Political prediction markets are most common, but there are markets for sports, finance, and more (here’s a popular one if you want to check it out). 

 

To illustrate how they work, imagine it’s October 2012 and you’re looking at the webpage for a prediction market titled “Who Will Win the Upcoming Presidential Election?” There are two buttons on the page. The first button buys shares of “Obama will win the election” and the second purchases “Romney will win the election.” Suppose you buy shares of Obama -- if you hold onto them until the morning after election day, then if Obama wins the website pays $1.00 for each share you bought. If Romney wins you get nothing, having lost the money you spent purchasing the shares. Individual shares may be bought and sold to other participants in the market and cost anywhere from $0.01 to $0.99 (obviously nobody would want a share priced higher than 99 cents). Supply and demand push the price around until it reaches an equilibrium. 

 

Just like the real stock market, the price of a share in a prediction market fluctuates a bit moment-to-moment, and as new evidence comes out which influences the probability of the predictions, the prices can change dramatically. When COVID began ramping up, the price of Trump winning the 2020 election declined significantly, probably because the coming economic slowdown was evidence that the incumbent was in for some election trouble. 

 

Here’s what’s crucial: the equilibrium price of a share in a prediction market represents an aggregated, probabilistic prediction of the future. 

 

Here’s why. The website sells you shares -- assets with the value of $1.00 if the prediction comes true. The value of a share therefore depends on the buyer’s level of confidence in the truth of the prediction. If a bettor is willing to pay no more than $0.80 for a share in X, that suggests the bettor has 80% confidence that X will occur. Suppose in our 2012 election market the price of one share in “Obama will win” is $0.65. What types of people will regard this as a profitable wager? Anyone who thinks that Obama has a greater than 65% chance of winning the election. 

 

And everyone else will regard the wager as losing. That is, the price of the share is equal to the confidence level you must have in the prediction for you to regard it as a break-even bet. If you have a higher confidence than the price, then you should buy shares. If you have a lower confidence, sell them. 

 

 

Are Prediction Markets Good Belief Aggregators? 

 

Yes -- to an astonishing degree. It turns out that aggregating the views of people who are willing to put their money where their mouth is is a powerful setup.

 

Keep in mind that the accuracy of prediction markets in absolute terms doesn’t matter. What matters is whether their predictions constitute an improvement over the other information institutions against which they compete (the media, academia, pundits, computer programs). 

 

We have strong evidence that prediction markets indeed outcompete those institutions.2 They outperform polls and pundits when predicting election outcomes.3 They outperform tipsters in predicting the outcome of soccer matches.4 They improve upon immunologist’s predictions about the spread of disease.5 They outperform the predictions of racetrack experts. Markets predicting Florida orange juice sales outperform professional predictions of the weather.  Prediction markets even outperformed HP’s own forecasts 6 times out of 8 at predicting HP’s printer sales. Hanson’s conclusion: they’re the best information aggregation tools we’ve got. 


 

Returning to Hanson’s Proposal 

 

So why not harness their informational power to solve one of the most important problems we’ve got -- that of making good public policy decisions? Here’s how it would work in a bit more detail.

 

Recall that citizens would vote on values to communicate what they want, while an official prediction market would handle the formation of beliefs regarding the efficacy of possible policies at achieving those citizen-selected goals. 

 

This raises the immediate question of how the markets would assess the policies exactly. Markets must bet on unambiguous propositions in order to yield useful information. You can’t create a useful prediction market that bets on the proposition “If the federal minimum wage were raised to $15 per hour, the consequences would be good?” You need to define “good” in a way that’s specific and measurable enough that the market could reliably pay the bettors who turned out to be right. 

 

Defining “good” is therefore the task of elected representatives. Hanson suggests that for most big policies, representatives should create an index estimating the nation’s aggregate well-being. Hanson suggests this index would be a number computed by a formula which weights GDP, amount of recreational time, satisfaction with their personal relationships, and so on. That index would be a number called GDP+, and would roughly represent the cumulative welfare of the country at any given time. Prediction markets would then bet on propositions like “If an open borders policy were enacted, GDP+ would rise” and the bettors would be off to the races. (That formulation of the proposition is an intentional simplification to illustrate the idea -- the best statement for speculators to bet on depends on several factors to ensure the market yields the desired information, which is a complication in its own right. The proposition must specify a fixed amount of time after enactment when GDP+ would be measured, for example.)

 

When the prediction market reaches equilibrium at a price which suggests that an open borders policy probably increases GDP+, that policy becomes law. After some time, the nation’s GDP+ would determine which bettors were correct. If the market says the policy would cause GDP+ to fall, the policy does not become law and the bets are canceled (remember, they were placed as predictions on the growth of GDP+ conditioned on the passage of a policy under consideration). 

 

Smaller measures could be used for policies that wouldn’t be big enough to influence the welfare index. Suppose there was betting on a policy of banning firearms in grade schools. Such a policy would have a negligible effect on GDP+, so it might be wiser for the market to predict something like “If the gun ban were enacted, yearly gun deaths would increase.” (again, simplifying a lot here). 

 

While we have strong reason to believe prediction markets are good information aggregators, Hanson’s proposal is radical and untested. He’s not an idiot; he doesn’t endorse overthrowing our democracy overnight and replacing it with a system he theorized in a journal article. But the idea shows promise, so he proposes we test it in local contexts while continuing research on prediction markets of public policies. 

 

What I like about Hanson’s proposal is how well it targets the problem outlined in the first section. Citizens in a democracy lack an incentive to hold informed, rational political beliefs. Enacting policies at the recommendation of disinterested members of the public who lose money for making incorrect recommendations is a wonderfully elegant idea that holds bettors financially accountable for their wrong beliefs. And by expressing values through elections, Hanson’s system retains democracy’s responsiveness to the interests of the public.


 

Rejoinders to Hanson

I’ll conclude by spelling out a few objections to Hanson’s proposal, and some replies to those objections advanced by Hanson and others.

 

Objection 1): Bettors in prediction markets are, on average, unqualified to judge complex policies, so markets would produce poor recommendations. 

 

Reply: First, in democracies laypersons also submit input on complicated policies by voting. They just do so with no incentive to hold accurate beliefs. 

 

Second, this concern is not borne out by the experimental evidence, which suggests that prediction markets reach equilibrium at probabilities which resemble actual frequencies of events in the world.6 They also generally outperform field experts, so if some counter-proposal wanted to privilege experts in some way it would probably produce worse outcomes than the market recommendations. 

 

Third, uninformed voices are weeded out of the market over time because they lose money by making worse-than-average predictions. Yes, the Dunning-Kruger effect is powerful, but it’s liable to be outweighed by financial incentives. 

 

Objection 2): Special interests could manipulate the markets to enact their preferred laws. 

 

Like any market, prediction markets are sensitive to supply and demand. That means a wealthy person or group with a special interest could sink money into one side’s shares until the market falsely appears to recommend it. 

 

Reply: It remains helpful to compare Hanson’s system to the democratic alternative. It’s easy now for interested parties to use their wealth to gain political influence. The question is not whether Hanson’s proposal is flawless, but whether a prediction market system would churn out better policies than a democratic one. 

 

In any case, evidence suggests that prediction markets are difficult to manipulate. Think of bettors in a market as falling into two classes -- wolves and sheep. The wolves are betting pros. They’re informed on the subject and highly attentive to new evidence. Maybe they’re experts in the market’s topic. They win money over time. The sheep are the opposite. They lose money by making bad bets. It turns out that the more sheep there are in a market the more accurate the market’s prediction. That’s because a market full of sheep attracts wolves to exploit them. With more sheep in the market, more wolves can profitably trade at higher volume. And the sheep cancel each other out since their betting behavior is, at worst, equivalent to making random predictions. 

 

Market manipulators are, by definition, sheep. Their betting behavior in the market reflects something other than their beliefs about the future. Think about it: their strategy is to lose money in the market by making bad bets in the interest of manipulating the market’s prediction to the point that their desired policy is recommended. But the existence of market manipulators attracts hordes of typical bettors to make free money off of people willing to give it away on a bad bet that the manipulator is only making because of a side interest. Those typical bettors will outweigh the influence of manipulators as the market returns to its true equilibrium. Empirical findings bear this out -- prediction markets anticipate manipulation in their equilibrium price. 

 

Finally, in any political issue, there will be special interests on both sides. Manipulation efforts will partially cancel, meaning it’s only the difference between the two which must be outweighed by the hordes of regular bettors. 

 

Objection 3): Markets would recommend so many different policies that it would overwhelm the budget. 

 

Reply: Adopting policies that exceed budgetary constraints would hurt national welfare, which speculators would account for. 

 

Objection 4): It’s impossible for markets to accurately yield a verdict on the efficacy of long-term proposals. Betting on a policy’s effect on national welfare in, say, 20 years would be impossible because many policies will be passed in the interim.

 

Reply: True, predictions get more difficult the farther into the future they are. But this temporal decline in accuracy does not mean that markets provide no information whatsoever -- it only means that some recommendations can be less conclusive (likewise with all information institutions). We should nonetheless expect large policies to cause a discernible effect, on average, on the trajectory of national welfare.

 

In Conclusion

 

America is divided and voters are irrational. Many argue that solutions to our political divide lie in opening channels of cross-partisan dialogue; others claim that if we merely switched to a system of ranked-choice voting, political life would be less contentious; still others merely advocate for splitting the country in two. Yet prediction markets, with their encouragement of dispassionate betting, might just be the solution, detaching us from the drug of partisanship and incentivizing us to focus explicitly on the efficacy and outcomes of various policies.

Alex Pinheiro  is a rising junior at the University of Michigan studying Philosophy and Cognitive Science. His interests include philosophical topics including rationality, existential risk, minds, and more, which he may choose to study in graduate school. Outside of MC he obsesses over learning and playing online poker.

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