Futarchy is usually formulated using multiple continuously running markets, which raises questions about how to introduce liquidity, when to introduce it, and who will do so. Robin Hanson (the inventor of futarchy) recently proposed how to handle some of these details, but they seemed to me a bit inelegant. I instead propose reformulating it to use a sealed-bid auction with no liquidity added. I will only be covering the joint-stock company version of futarchy, not the government policy version, which I'm not sure how my proposal would generalize to. The joint-stock company version is relevant to effective altruism as a possible component of a market for altruism.

Consider a hypothetical joint-stock company named The ACME Corporation with one million shares.

Proposals and bids

Once a month, the public can submit proposals. A proposal can either be:

1. A CEO replacement: replaces the current CEO with the proposer, under terms of a legal contract included with the proposal. If the proposal takes place, this is immediately effective and legally binding. The current CEO is considered fired. (Given that they are only guaranteed to have their job for a month, most candidates will include a decent severance package as part of their compensation.)
2. A company directive: instructions that employees should follow. It is considered company policy to follow these. If these are consistently ignored, future proposals should propose replacing the CEO with one who will enforce them.

For example, let us consider proposals A, B, C, and "Change Nothing".

The next step is that people submit sealed bids. There are two types: buy bids and sell bids.

Buy bids

Any member of the public (including current investors if they wish to increase their investment) can submit a buy bid, conditioned on a given proposal passing. The bid contains a maximum price and a number of shares.

Note that first they must put money in escrow. They can submit multiple bids. For any given proposal, the total amount they bid on that proposal must not exceed the amount in escrow. However, the total amount of bids across different proposals is unbounded, since only one proposal can pass. So if a buyer has $10 in escrow, they could bid up to $10 on A, and up to $10 on B, and up to $10 on C, and up to $10 on "Change Nothing".

Sell bids

Each current investor can, for each proposal that they dislike, submit a sell bid. The bid contains the number of shares they wish to sell, as well as optionally the minimum price they would sell for.

For each proposal, the total amount of shares being bid for sale must not exceed the number of shares they own. However, the total amount of bids across different proposals is unbounded, since only one proposal can pass. So if a current investor has 5 shares in escrow, they could bid up to sell up to 5 shares on A, and up to 5 shares on B, and up to 5 shares on C, and up to 5 shares on "Change Nothing".

Proposal value

After everyone has submitted their bids, we go through each proposal and calculate the price that would clear the market for the bids conditioned on that proposal, as in a double auction. This price is known as the proposal value. The proposal with the highest value is called the winning proposal.

All bids associated with proposals other than the winning proposal are immediately voided (whether they should be published or not is a detail I have not thought about). All the bids conditioned on the "winning proposal" are treated as live bids, and trades are executed at the proposal value according to the double auction we simulated for it. Then the winning proposal is implemented. (For the "replace CEO" this means that the proposed CEO is now legally considered the CEO. For "company directive" it just means that the employees should begin following it and the CEO should enforce it.)

When do we predict the probability that a proposal will succeed? Never!

Normally in futarchy, with the continuously running market, we are also predicting which proposal will succeed, unconditionally. We skip this step: the proposal values represent conditional prices, conditioned on the proposal. We never bother predicting things unconditionally.

Sell-by-default as a solution to frivolous and malicious proposals

How do we determine who can submit proposals?

In past formulations of futarchy I have read, there was a need to limit the number of proposals submitted due to the limited liquidity.

As currently described, allowing unlimited proposals would be problematic: if there are too many proposals for the investors to review, there could be proposals such as "burn down ACME" or "ACME gives all their money to the proposer" that no investor issues a sell bid for (since they didn't have time to review it). Then that proposer submits a bid to buy 1/X shares for $X, where X is in arbitrarily large number. They only need to put $1 in escrow, but the proposal value is then $X.

To fix this, we just add a simple convention: if a investor doesn't review a proposal, we assume that they are submitting an unconditional sell bid. For the proposer to force their bid through, instead of 1/X shares, they must instead submit a bid for one million shares and have $X million in escrow. If their proposal wins, they are essentially buying the entire company, and thus can do what they please with it.

If there are a large number of proposals, the investors would just review the most promising (or at least serious) ones, which they would learn about via a coffeehouse or similar mechanism.

Fundraising proposal

Although not strictly necessary, as a bonus we can consider a mechanism where proposals can automatically raise funds for the company. Indeed, this leads to the idea of self-fundraising: if the proposal directs the company to do a project that requires extra capital, instead of directing to first raise capital the proposal can itself raise it!

A fundraising proposal is like a normal proposal, except it also includes a "funding required" amount. For example, let's say that proposal C says to buy a warehouse. The proposer could add to the proposal "funding required: 2 million dollars".

Then when calculating the proposal value, we include the company itself as a seller. Its bid is a bit special: instead of selling a certain number of shares, the bid says to sell a number of shares worth 2 million dollars. This changes the calculation a little but it is still easy to find a market clearing price with a bid like this.

If the proposal wins, new shares get issued, diluting equity, but the company receives 2 million dollars directly from the buyers.

Shareholder oppression

The main advantage of futarchy for joint-stock companies is to eliminate shareholder oppression. Let's observe how this works with this formulation.

If shareholders are perfectly unanimous, they can control the company

Let's start with the opposite problem. If the shareholders were perfectly in unison about a proposal, could an outsider force the company to do something different?

The answer is no, because the shareholders can use the following strategy: they agree to not submit any sell bids on their favored proposal, and then one of them submits a bid to buy an additional 1/X shares for $X, where X is in arbitrarily large number. This only requires $1 in escrow but makes the proposal value $X.

What if only one shareholder defects? The beautiful solution of futarchy

Let's say the majority shareholders has a proposal A that the market thinks is worth $100 million, but a shareholder named Lola with just a single share came up with a proposal B that is estimated to be worth $500 million. Lola claims that the majority prefer A because of conflicts of interest. The majority claim that B is just a bad idea. How do we resolve this?

Well, the question comes down to this: does the majority with the 999,999 shares believe that proposal A is worth more or less than $500 million?

1. More: None of them sell on proposal A, except Lola who puts in a sell bid for $500. One of the majority investors puts in a buy bid for one share at $501. Proposal A wins! Lola does not get to see her proposal come to fruition, but she does get to see the benefit: she gets $500 in cold hard cash, the same thing she predicted would happen if her proposal succeeded. The majority shareholders are also fairly happy: they only had to pay half a grand to get Lola out of their hair, and they can what they believe is a fair trade out of it (they traded $500 for a share which they think is worth more than $500).
2. Less: The majority shareholders all put sell bids on Lola's proposal B at $500. The market now must put up $500 million (minus Lola's $5) and completely buyout the company. The majority shareholders are pleased, since they got more than they thought the company is worth. Lola is also pleased; her proposal is getting implemented, and we get to see whether or not Lola's idea was correct!

(In practice the majority shareholders will both be putting sell bids on B and some buy bids on A.)

Interaction with a stock market

Technically, with this system we do not require a separate stock market. The system itself functions as a stock market! To buy a shared, just submit a buy bid on every proposal. To sell one, sell on every proposal.

Nevertheless, if a separate stock market does exist, here is an interesting way we can interact with it.

When calculating the proposal values, we consider every buy bid on the stock market to be a buy bid on every proposal in the futarchy, and every sell bid on the stock market to be a sell bid on every proposal in the futarchy. When a proposal passes, we actually trade with the stock market as we fulfill all the bids.

This ensures that the proposal value isn't just the predicted price. It becomes the actual price after the proposal is selected, because we actually buy and sell with the stock market to force the price to match.

Interactions with a prediction market

Let's say some third-party finds a source of liquidity and sets up a prediction market for predicting which proposal will succeed. They could setup the following service:

If a forecaster named Elmer has a prediction contract paying $1 if proposal C wins, the prediction market can offer Elmer the following deal: it can place $1 worth of buy bids conditional on C on his behalf. If C wins, they will use his prediction contract winnings to pay for the bid.

In theory this could offer unlikely proposals a lot of leverage. If the prediction market says that C only has a 1% chance of winning, folks favoring C can pay $1 and put $100 worth of buy bids on C. Then if C wins, those folks both get the satisfaction of their proposal winning and they got shares in the company at a huge discount! But something seems fishy, isn't this bad overall? What if C is foolish (which is why it had so low a probability to begin with)?

Well, kind of, but it is not the futarchy's problem. The only way this works is if Elmer can find a counterparty to take the otherside of the bid. If C is foolish, we can expect that most of the investors put sell bids in.

So the counterparty paid the current investors a good price to give the company to Elmer, who then ruins with his foolish proposal C. In particular, the price must be higher the proposal value of any other proposal, or C wouldn't be the winner. So the prediction market participants are the losers, and the investors make out fine!

Of course, if the prediction market is functioning well it will not be so foolish, and will likely actually benefit the futarchy with free information. But if the prediction market is poorly functioning for whatever reason, our futarchy mechanism still does its job!

Conclusion: How did we make do without a liquidity adding mechanism?

Although I hope the above arguments show why this system works, there still appears to be a paradox. How can something like this work without liquidity when futarchy usually requires such? Have we created some sort of "perpetual motion machine", with the problem subtly hidden? 

I don't think so. Let's first review why stock markets are more popular than prediction markets. When a business owner owns a business, they hold a lot of financial risk. Being risk-averse, it benefits him to decrease this risk. Selling the company on a stock market decreases his risk, and spreads it across my participants.

A prediction market, on the other hand, creates risk out of thin air for both parties. So we need to "bribe" them with liquidity to get them to participate in the first place. 

Normal futarchy also has this problem, but it is not necessary. In the sealed-bid formulation, we carefully removed the need for risk creation mechanisms. Risk is moved around but not created. Thus, we don't need to incentive people to participate.