Recall that we seek social epistemic mechanisms that are decentralized, permissionless, secure and which carry truth-telling incentives. In our previous blog post, we explored Community Notes' Birdwatch model, and concluded that it cannot be simultaneously permissionless and secure, and that it does not have truth-telling incentives. We point out again that Community Notes has been a massive success, impacting social discourse in a positive and constructive way, even if its underlying model was not theoretically sound. This motivates us to continue our search for better mechanisms, even though finding one that simultaneously satisfies all of our desiderata is an extremely challenging, if not impossible, task.

In this blog post, we discuss a few mechanisms, among them one that recently gained enormous momentum: prediction markets.

Prediction Markets

What distinguishes prediction markets and betting houses is that the former is specifically designed for information elicitation. The price of a security in a prediction market is aggregated knowledge of the probability of a future event. Anyone who has strong beliefs in either direction away from the current security price can, according to their beliefs, make a profitable purchase of either the security itself or of its complementary securities. Conversely, at any particular point in time, no one is willing to bet against the knowledge encoded in the current security price.

While it may be true that trading fees can reduce the accuracy of the encoded probability and that users have different risk profiles and differently sized pools of capital, prediction markets are still the gold-standard of social epistemic mechanisms in terms of security. Truth-telling, i.e., betting on what one believes, is a dominant strategy¹, and forming coalitions is not profitable.

Prediction markets have a long history. Several early prediction markets were used to predict the outcome of elections [14], movie box-office profits [12] and even the time for the delivery of a construction project [18]. Truthcoin [21] is, to our knowledge, the first design of a prediction market on a blockchain, and one of its goals was finding correlations between policy decisions and their outcomes [22]. Using prediction markets to govern decisions is called Futarchy [10], a proposition by famous economist Robin Hanson [11], who is known as the father of prediction markets.

Furthermore, prediction markets have a wide range of untapped application potential: mainstream prediction markets, such as Polymarket [19] and Kalshi [15], deal only with simple securities, usually with only a few, one for each outcome. However, more advanced prediction markets support much larger outcome spaces and complex securities that describe sets of these outcomes. For instance, in permutation or ranking markets, there are \(n!\) outcomes for \(n\) players, but users could bet on \(n (n - 1)\) securities of the form “player \(i\) finishes ahead of player \(j\)” [1] or \(n^2\) ones of the form “player \(i\) finishes in position \(j\)” [5][3]. Other possibilities include tournament markets [6], hierarchical markets [8] and continuous and geometric markets [2][17][13]. Application possibilities are numerous, from more efficient sports betting to earthquake or hurricane insurance.

Unfortunately, the Achilles heel of prediction markets is that they are not decentralized. In order to settle trades at the end of a market, the mechanism relies on an oracle. There have been occasions in which high-stakes prediction markets were resolved against their final-price consensus by their oracles [20]. As a consequence, self-resolving prediction markets have been proposed, and we shall consider at least one of them in a future blog post.

Omniscience

Simply because prediction markets are centralized, it does not mean that they are not useful for moderation in decentralized social media. Vitalik Buterin has considered the use of prediction markets as an extension of a central moderator's capabilities [4]. Essentially, every social media item would get its own individual market, that predicts whether this central moderator, called Doug, will decide to moderate the item or not, when, and if, he looks at the item. Vitalik's insight is that, even if Doug only actually looks at a small fraction of the items, the incentive for traders is to trade honestly in all the markets, and their security prices can be used for moderation decisions. Trades in markets whose items Doug does not inspect are reversed, and the only markets where trades are settled are the ones manually resolved by Doug.

Of course, there is a significant amount of details that have to be filled in, such as how to reverse trades and how to mitigate the opportunity cost of capital lingering in these markets. One detail that we address is how to bootstrap liquidity in these markets, as, even with fees, market creators may have impermanent loss of their initial liquidity. We propose to only start prediction markets on flagged items, because the item author and the moderator are two necessarily disagreeing parties and, each under their own beliefs, are expected to turn a profit. This does require authors to place some collateral on each item, but that can be returned to them if the post ages enough without flags, if the market is reversed or if they win Doug's favor in an arbitration.

This idea is quite useful because it solves the alignment problem between individual moderators and moderation companies (or individuals, such as Doug) offering moderation services. Presently, moderators have very little incentive to stay honest. If and when one of their decisions gets audited, they can claim an honest mistake or simply leave the system, because they do not have much collateral staked. It is thus hard to have a healthy market of moderation services when these services hire from a common pool of moderators. In contrast, applying prediction markets affords Doug an “epistemic extension,” which we call omniscience, and, the more trusted Doug is, the larger and sharper this extension can become. Paradoxically, centralized prediction markets can help decentralize moderation by the straightforward introduction of competition, with many people taking the role of Doug and with many competing moderation policies.

There are two other methods to achieve the omniscience effect, both mentioned in a thread [7] started by Konstantin Kladko [16] as a response to Vitalik.

Robin Hanson's Double or Nothing Lawsuits

Robin Hanson proposes a simple mechanism [9] to disincentivize wrong behavior even when the maximum harm caused is small, making litigation unattractive. He proposed using a randomizer “office” or machine, in which a legal claim could be doubled or destroyed, with 50% chance of each. This way, the value of the claim doesn't change in expectation, but small claims could potentially become large claims worth legally pursuing, even though only with a tiny probability. The brilliance of this scheme is that litigation would only occur in a small fraction of claims, with its cost amortized, while the expected loss from misbehavior would be closer to the damage restitution, rather than to zero.

One challenge with this idea in social media is that some users have close to zero collateral, and they would not be able to pay an amount that has been doubled many times. However, maybe moderators can. Doug could require his moderators to deposit a significant collateral \(C\) (say \(10^6\) sats) for taking part in his moderation company. Those moderators would then get the power to take down items on behalf of Doug. Item authors that believe they have been wronged by a moderation decision can buy a small claim of \(c\) (e.g., \(10^4\) sats) against the moderator for a much cheaper price \(p\) (maybe \(500\) sats), and, rather than repeatedly doubling it, they can directly increase it to \(C\) with probability \(c / C\). Only these large claims would require intervention from Doug. If the author has Doug's favor, he receives \(C + p\) from the fired moderator's collateral and the initial purchase. Otherwise, if Doug is not summoned or favors the moderator, the moderator is paid \(p\).

Under this scheme, a Bayesian moderator has an incentive to work for Doug as long as his decision accuracy is more than \(1 - p / c\), and a Bayesian user has an incentive to buy claims when their judgment accuracy is at least roughly \(p / c\). Thus, there is considerable margin for the choice of the parameters \(c\) and \(p\), accommodating other risk profiles.

Moderation Poker

One downside of the previous approach is that the damages from the removal of a particular item are not accounted for, only the average damages. Thus, an ideological moderator still has the incentive to censor only the items he opposes that are gaining significant traction, since the social cost to him of the success of the item outweighs his expected loss in the mechanism. To some extent, this issue can also affect the first approach with prediction markets, because the moderator could bet on Doug not inspecting the item.

To overcome this issue, we need to allow every dispute to potentially escalate to Doug. Like in our proposition on how to bootstrap liquidity, when an author posts an item, they deposit a small amount of collateral, which can be refunded to them later. In order for a moderator to flag the item, they have to also commit collateral, which becomes the item's pot. Then, starting with the author, each side takes turns at least doubling the pot. If a side folds and does not double the pot, the other side takes the whole pot and the right over the moderation outcome. Otherwise, eventually the pot size will become large enough, say \(P\), to merit the intervention of Doug, who resolves the dispute and gives the pot and the moderation outcome to the winner.

One advantage of this scheme is that third parties besides the author and moderator can contribute to the dispute, helping increase the pot. At the end, the pot would be split proportionally to contributions to the members of the winning side. However, still, in order not to depend on others, authors have to keep about \(kP / 2\) capital available in order to unconditionally defend \(k\) of their items, and that is also the sum that honest moderators have to keep to unconditionally defend \(k\) moderation decisions.

Besides this capital inefficiency, there is also the issue of Denial-of-Service, where a whale trying to disrupt the moderation system escalates \(n\) disputes, where \(n\) is much larger than Doug's throughput in several decades. While eventually the whale might lose up to about \(nP / 2\) in capital, the moderation will stop and users will have their capital locked in for unreasonable amounts of time.

Conclusion

We have explored oracle-dependent mechanisms to epistemically extend centralized moderation in order to enable a free-market of moderation services. We found that, even under the big assumption of a trusted oracle, incentive issues still remain, particularly around the exogenous value of moderation decisions, which are hard for mechanisms to account for. While the mechanisms described are expected to work effectively and efficiently for most items, making sure that they work for items of high exogenous value is still elusive.

In practice, the assumption of a trusted oracle is rather brittle, since power corrupts, and there are always lingering threats of bribery, blackmail, exit scams and ideological co-optation. In some sense, the success of systems based on centralized oracles can be their downfall, as the more capital it manages, the bigger the target they are and the bigger the risk of these threats.

Addressing this concern, in our next blog post, we will delve into the area of Information Elicitation Without Verification (IEWV), which considers epistemic mechanisms that do not necessitate oracles, and yet still maintain truth-telling incentives.

References