Futarchy and preferences over variance

i. What is futarchy

Futarchy is a proposed system of governance that combines prediction markets with democratic decision-making. Developed by Robin Hanson (who is at my university!), it improves policy outcomes by harnessing the efficiency of markets. Under futarchy, citizens would vote on desired outcomes or metrics of success, but not on specific policies. Instead, prediction markets would be used to determine which policies are most likely to achieve the voted-upon goals. Traders in these markets would bet on the expected outcomes of different policy options, with the policies predicted to be most successful being automatically implemented. You vote on goals, but bet on beliefs.

What I want to draw your attention to is an unintended, but beneficial, side effect of such a system. Policy will reflect the utility functions of the people, even if they are non-linear. Indeed, if there are no subsidies to the prediction market, non-linear utility functions are the only way in which anyone would trade!

A quick word on what a prediction market is, in its simplest form — you have a security which pays out 1 if it resolves yes, and 0 if it resolves no. In other words, gambling. You are doing the same thing as when betting on whether the Orioles or the Blue Jays will win a baseball game.

Why would you trade on this? If everyone were perfectly risk-neutral and rational, they would know the only reason someone would come along and bet is if they possessed more information about the game. Perhaps they knew the Orioles’ starting pitcher had injured themselves, or the Blue Jays had an outbreak of the flu. You would be foolish, under those circumstances, to bet. In the case of sports, it is because people find it fun; in more boring markets, it is hedging. It is a truism about the world that people prefer the certain to the risky, and that money has declining returns. If a company benefits if an event happens, and is harmed if the event doesn’t happen, then they can buy shares that pay out only when the event doesn’t happen. This way, they change an uncertain level of profit into a certain level of profit. Their hedging will not distort the market away from the true probability of things, because they are one and the other bidders are many. This ought not hold when people’s harm and benefits from an event occurring are not symmetric, however. Let’s explore why that’s an advantage in futarchy, though.

ii. An example

Our society has voted to get the policy which is most likely to achieve a value of .5. (Imagine the value is a rate of GDP growth, which affects everyone). Suppose there are two securities, both of which have an expected value of .5, and achieves that level or better precisely half the time. One always returns a normal distribution tightly centered around .5, while the other one returns 1 half the time, and 0 the other half. If everyone is perfectly risk neutral, then traders will be indifferent between the two, and buy and sell such that the price of them is the same. If the second policy were infinitesimally more likely to resolve 1 then that would be our policy and we would enter a slightly weighted coin flip for our outcomes.

Suppose that everyone is risk-averse, however. A risk-averse person finds losing the .5 of value, when the second security resolves to 0, to be a keener loss than missing out on .5 of value when the second security resolves to 1. Thus, people will not regard these securities, despite paying out the same on average, as having equal real value — the riskier will be lower than the safer. The payout includes not just the value from getting it right, but the value from the government policy, and if the government is choosing policies on the basis of their chance of success, then the policies chosen will better reflect the preferences of the people.

Requiring unanimity is a big jump, though. Is this robust to times where most people are risk-averse, but some people are risk-neutral? Let us say that, in an extreme case, precisely one person is risk neutral. They will see the price of the second security, and bid it up until the price reflects the true rate. Of course, this “true rate” does not correlate perfectly with people’s utility, so we would expect them to be outbid, if funding is not infinite. As we increase the number of people, adding in arbitrary risk-neutral or even risk-preferring utility functions, the price of the securities should reflect the cardinally-weighted sum of all utility functions in the economy. This seems really, really good!

iii. Why it’s a challenge for prediction markets

One of the nice things about prediction markets is that you can simply read off the price of a security on an event as a percent chance of the event occurring. This presumes risk-neutral traders, however. If everyone is hedging in a direction, then the price will diverge from the true probability. Scott Alexander, in his Prediction Market FAQ, in section 4.6.1.1, has us imagine that an export-import bank hedges against Trump winning the election. Other people would step in, then, to arbitrage the possibility away. If you presume that everyone wants to hedge against Trump winning, though, this shouldn’t hold! If there isn’t unlimited funding to undoing hedging, the market price will differ from the true probability of the event. (Why would Trump have a chance of being elected, if people consider his election as a really bad thing in this world? Because voting cannot take into account cardinal preferences, only ordinal ones. Voting is also essentially costless, and so people are free to vote for what they want to believe, rather than what they really believe. This is just a fundamental problem of voting).

Is it such a big deal, though? I would argue that, even while the price may diverge from the true probability, it is still useful at providing information about the world. For similar events, such as bad weather, you could assume that people’s hedging remains roughly constant over time, and adjust accordingly. Even if the information were unpredictably distorted, it still surely provides some value.

iv. A concern

This came up while I was writing — hence, its ugly appendation to this blog. I am concerned that futarchy may lead to excess risk-taking, if people vote for unrealistically high goals. Suppose that people are universally risk-averse, and that the two policies as before (a tight distribution around .5, and a coin flip between 1 and 0) are available to bet on. This time we vote on a goal of .99, however. The first policy will never achieve that, but the second policy will, and so wins — in spite of the fact that we may, as a society, find that the increased risk leaves us worse off than the policy which doesn’t achieve our goal, and that if it were put to a vote, the first policy would win unanimously. There may not be as much of a separation between goals and policy as we would hope — the choice of goal may lead us into sub-optimal policies.

Perhaps this example is unfair, because we are voting on unbounded possibilities, but betting on only two possibilities in this example. Allowing unlimited policies should not help, however, when the goal is not easily achievable. Imagining again that we are trying to choose a tax rate which will result in a given rate of economic growth, perhaps what we could do is have separate markets for each gradation of economic growth. The variance in policy outcomes would be implied by the difference in percentage between markets — so in the prior example, you’d have a market to see if it comes back with .1, .2, .3, etc. We would see then that policy 1 always achieves below .5, and never achieves above .5, and the second policy’s returns are the same (a fifty percent chance) at all increments. We would then need to decide how risk averse society should be, which could be voted on, or decided arbitrarily by some group of reasonable people.

This would probably still be an improvement over our present system. I am concerned, however, that people will vote aspirationally as to what our goals should be, and thus unwittingly harming ourselves. We cannot entirely get away from the foolishness of the voter. If we believe that people will act more idealistically the farther away they are from actually setting policy, then it would be better for people to vote for representatives, who then vote to set goals.