Solving the value problem in futarchy

Governance has two main problems: the problem of what objectives to pursue (the value problem), and the problem of how objectives should be pursued (the implementation problem). Many think that democracy is the least bad solution to both. In a rare governance innovation, Robin Hanson introduced the idea of futarchy ~25 years ago as a new solution to the implementation problem, still leaving the value problem to the traditional democratic solution.

Futarchy assumes societal values have already been derived by democratic voting and focuses on how to choose which policy to adopt to realize those values. Futarchy’s solution is as follows. First, we derive a metric from the values. Second, we set up two prediction markets: one for the status quo policy, and another one for some policy change. Both markets are defined in terms of whether the policy will achieve some target value for the metric by some future date. At some point in the future (before the settlement of the markets), the government will either reject the policy change or adopt it depending on which of the two markets has a higher price by that time. This way, presumably, the policy considered most likely to achieve our goals is the one that’s selected. That’s it, in a nutshell.

Futarchy has been debated extensively, so I’m not going to discuss its merits in detail here, but suffice it to say that it leans into the strong evidence that markets are great at aggregating information, and that policy choice is just a matter of having the right knowledge or right beliefs: there is a truth to the matter. Importantly, futarchy does not deal with how we arrived at the objectives in the first place, as it does not think there’s necessarily “truth” to the matter of values, so that an information aggregation tool wouldn’t be helpful to decide a truthless matter. In other words, futarchy deals solely with implementation, and leaves objective-setting to democracy. Hence the tagline for futarchy:

Vote values, but bet beliefs

Some of us propose another governance innovation that purports to solve the value problem that futarchy left unaddressed. That solution involves the design of a peculiar mechanism. In mechanism design, one designs a certain mechanism, then let people participate in that mechanism in some environment, hoping that things play out in such a way that a desired outcome is achieved. Probably one of the most famous (and successful) pieces of mechanism design is the Bitcoin network. The Bitcoin network would just be a Rube-Goldberg machine if it wasn’t for the emergent outcome it produces: sound money. Indeed, the design of the Bitcoin network involves random people around the world solving a pointless computational problem by brute force. But the outcome of all this silliness is valuable. Similarly, our idea involves a quirky design, but with the hope of a valuable emergent feature.

Imagine a world where people carry around wallets with various proportions of all existing currencies and trade can only happen by spending all the currencies in one’s wallet at a rate corresponding to their proportions in the wallet. This is the key feature of this world. If we view a wallet as a vector of currencies, the vendor gets some multiple of that vector as payment. Let’s call that vector the wallet vector w.

In turn, the vendor has a private valuation of each of those currencies. This private valuation of each currency is done in units of some reference currency, which can be thought of as a “universal currency” whose units are, say, utils. Let’s call that vector the valuation vector v. In other words, it’s the rate at which the vendor is willing to accept each currency as payment.

So, on the one hand, we have a buyer with a certain endowment in each currency (wallet vector), and a vendor with a certain valuation of each currency (valuation vector). A transaction entails the buyer giving the vendor a vector of currencies and the vendor giving the buyer some good. Let’s call the vector of currencies provided by the buyer in exchange for the good the transaction vector t. That transaction vector is a multiple of the wallet vector (this is just a restatement of the foundational feature of this world mentioned above, namely that trade can only happen by spending all the currencies in one’s wallet at a rate corresponding to their proportions in the wallet): t = s ∗ w.

The term s in the equation above is a scalar multiple, which can be described as the transaction’s scale. Another way to think about this multiple is as the “share of wallet” the buyer needs to shell out. The question is: how is that multiple determined? This is where the price of goods comes into the picture. The price of goods is given by the market as a scalar value p reflecting a number of units of the “universal currency”, i.e. the price is expressed in units of utils. Since the vendor gets t and values currencies as per v, s is obtained mechanically as: s = p ∕ w⋅v.

Indeed, the dot product w⋅v, between the buyer’s endowment and the vendor’s private valuation, reflects the unscaled utility of the transaction to the vendor. That utility needs to be scaled in such a way to equal the market price. We therefore obtain the transaction’s scale by dividing the market price by the unscaled utility of the transaction.

The first thing to notice from the above description is that the only way to modify the distribution of your currency endowments in your wallet is via trade and by tweaking your private valuation of currencies. Indeed, as mentioned previously, the key feature of this world is that you cannot selectively pick which currency in your wallet to use to pay for goods; you have to pay with your whole wallet.

The key insight here is that a vendor’s private valuations will affect which customers they attract. Indeed, a vendor that values some currency highly will result in a lower “share of wallet” shelled out by a buyer who happens to have a high proportion of said currency. Therefore, a vendor’s private valuation can be strategic. But what objective should a vendor’s strategy pursue? Maximizing the utility of their own wallet of course, or, in other words, the value of their wallet.

How is one supposed to value one’s wallet? There are many ways one could go about that. One way to find out the value of one’s wallet is by imagining that you spend all your wallet on one vendor, which gets you a certain number of copies of the good sold by that vendor. Now multiply that number of copies by the public’s demand for that good. This gives you the total utility of your wallet if you were to empty it at that vendor. Now do that for all vendors you could spend your whole wallet on and take the maximum. That number is your wallet’s value. This particular algorithm isn’t necessarily the “one true algorithm” to value your wallet. It makes several assumptions such as the fact that your actions have no impact on the public’s demand for the goods, or the fact that you spend it all on one good, ignoring diversification objectives. Notably, this methodology does encompass savings, since one of the goods you could be spending your wallet on could be a savings vehicle, including buying currency from a currency issuer.

Importantly, this valuation process reflects the objective value of your wallet, in turn reflecting a public value of the currencies in your wallet. It is a given, not the outcome of strategic reasoning. This is in contrast to the private valuation v that we talked about earlier as the rate at which a vendor is willing to accept each currency as payment, and which has a strategic component. To put it in a pithy manner: how much a currency is worth to someone can be different from how much they value the currency.

Where do the currencies come from? They are issued by organizations pursuing some cause expressed as a public good. Those organizations produce a public good (non-excludable and non-rivalrous). Just like any other vendor, the causes raise funds in the form of transaction vectors. In return, the donors receive utility proportional to how well the cause is funded by the community and how much they care about that cause. A cause thrives more if there is a high demand for their currency, and so it thrives more when people want to hold their currency.

Therefore, people, alongside their strategic, fluid, private valuation of the currencies, also have non-strategic, more fixed, private valuation of the currencies, since they are connected to public causes. This creates an interesting tension between people pursuing wallet value maximization in a purely strategic fashion, and their attachment to public causes.

The main difficulty in mechanism design is to predict the optimal strategy for the players, and what equilibrium that leads to. One approach to deriving the optimal strategy is to simplify the environment in such a way that it becomes mathematically tractable to derive a closed-form solution for the optimal agent strategy.

We could also do agent-based modeling of this game, using reinforcement learning agents. This frees us from the need to overly simplify the environment to make the derivation of optimal policies mathematically tractable. It also makes it easier to tweak the design and study the equilibrium outcomes. Without agent-based modeling, you are constrained to keeping your environment simple and you might need to re-derive the mathematical closed-form solution every time you tweak your design, slowing the feedback loop in mechanism design between mechanism features and equilibrium outcomes.

The game is to assess the value of one’s wallet and take action to increase the value of one’s wallet. The action space, i.e. what you are in control of, is the private valuation of currencies. This private valuation, though, is also constrained by your attachment to the causes that each of those currencies is linked to. The environment is the strategic behavior of all the other agents, as well as prices. The game’s reward is the value of one’s wallet. What is the equilibrium of that game?

We can build an agent-based model of that game and observe the outcomes. Those agents can be modeled as neural nets using reinforcement learning (RL). RL is characterized by states, actions, environment, and state valuation functions. So our world maps very nicely to a RL setting:

• State s: an agent’s wallet.

• Environment: other agents and market prices.

• Action a: private valuation of currencies.

• Reward: wallet value.

In RL, an agent aims to learn a policy θ that maps states to actions: a = θ(s). An RL agent learns by optimizing its policy. The first step to optimize a policy is to know how to evaluate it. Once we know how to evaluate a policy, that becomes our optimization objective.

Now why on Earth would one think up a world like that? What is the point?

The point is that, when we model the game as suggested above, there’s some evidence that people tend to converge in their values, as reflected by their private valuation of the various currencies. In other words, a simple design change to our world (trade can only happen by spending all the currencies in one’s wallet at a rate corresponding to their proportions in the wallet) may have the surprising consequence of aligning people’s values.

We don’t yet have a proof that index wallets lead to value alignment. But they have some mathematical models that are suggestive. The next step is to devise an agent-based simulation and study its equilibrium outcomes. After that, perhaps a real-life experiment.

So this could solve the long-standing “value problem” of governance: the problem of what objectives to pursue. As explained earlier, the other big problem of governance is the problem of how objectives should be pursued, arguably solved by futarchy. As such, futarchy and index wallets may be natural partners in “solving governance”. A world of “solved governance” is a world where causes issue currency, people support causes by holding their associated currency, compromise on causes via trade, and bet on policies to advance those causes in prediction markets.

What I find inspiring about both futarchy and index wallets is that they are real innovations in the field of governance studies. Such innovations are pretty rare. Governance is typically thought of as philosophy: nothing ever new under the sun. Economics studies the existing mechanism, but rarely tries to alter it. What I admire in the crypto ethos is that true governance innovation is being actively pursued, new mechanisms are being designed and tried (eg: quadratic funding), which I expect to usher in an era of Governance Revolution. That is the right mindset: one should not think that our current democratic system is the end-all be-all of governance. Governance can be subject to engineering and tinkering.

This post was also published on Medium.