The Challenger's Dilemma: Decentralized Law Enforcement

Kleros is a general purpose dispute resolution system. As such, it can be used as an element of a wide variety of applications where there is the possibility for some kind of disagreement. For example, one can use Kleros as part of an oracle, resolving disputes about the accuracy of off-chain information being brought on-chain. Similarly, Kleros can be used in the creation of curated lists to resolve disputes about whether elements belong on the list or not.  

The fundamental participants in any Kleros-based system are the jurors. Kleros is essentially a crowd sourced jury service that executes on a decentralized layer. Using the idea of “Schelling Points”, jurors are financially incentivized to rule coherently on cases.

A lot of thought has been put into how to incentivize the jurors to take the time to properly judge a given case, so that the coherent ruling is also likely to be the honest ruling. Indeed, the Kleros appeal system is built in such a way that jurors should remain incentivized to put in this time even as there is the possibility that appeals pull in more and more jurors. This incentive structure – once you allow for subcourts to tune parameters – should be generally adaptable to the full variety of possible cases they might have to consider.

However, there are other participants in the network, and what kinds of actors these are will vary signficantly with the specific use case that Kleros is being used for. So it's important to think about what the incentives of these other actors will be, and how to properly encourage them to act in a way that results in the desired outcomes.

In the basic use case that we often use to introduce the idea behind Kleros – to allow an escrow service for participants in a contract that has a built-in dispute resolution mechanism, such as when Alice's small business wants to hire Bob as a freelancer – the parties to the dispute are themselves important actors. Their incentives should be structured so that it makes sense for them to raise disputes or appeal when the alternative is an unjust outcome.

However, when making these decisions, they presumably already know the case pretty well, and any additional time and effort spent thinking about whether they have a winning case or not is probably marginal compared to their interest in the outcome.

In other use cases where Kleros can be used to resolve underlying disputes, it is not necessarily the case that there are honest participants who have a good knowledge of the case, or who would be willing to put in the effort to share this knowledge without an incentive.  

In the escrow use case, the two parties to the case can raise a dispute in Kleros by paying necessary deposits. In this setting, we can think of the two parties “taking each other to court”. In contrast, in cases where we depend on some incentivized third party to flag an issue that requires dispute resolution, these third parties are playing a role more akin to “police”.  

Specifically, in our curated list model, as used in the Doges on Trial pilot, we allow “challengers” to flag submissions that they believe do not satisfy the conditions of the list, subsequently causing this submission to be considered by a group of Kleros jurors as a dispute.

This challenger places a deposit that can cover the (first round of)  arbitration costs, so that if the jurors ultimately rule that the submission was correct, the challenger's deposit can cover the cost to be paid to the jurors. The challenger's deposit may also include an additional amount that can be given to the submitter as a compensation for an incorrect challenge.

On the other hand, if the submission is rejected, the (first round) arbitration fees are paid out of a deposit placed by the submitter, and the remainder of this deposit is given to the challenger as a reward.

In Theory

Fixing notation, and following a similar structure to this model,  one can imagine that  

e = effort that challenger makes

p = probability that challenger reaches the “correct” evalutation of a case after making effort

J = cost of arbitration that will be consumed by (the first round of) jurors in case of dispute  

C = reward that a challenger receives if he correctly challenges a submission that goes on to be rejected

S = compensation that a submitter receives if she is challenged, but goes on to win

y = probability that a challenger challenges a given submission

u = percentage of submissions that are hostile  

For simplicity, suppose that there is only a single challenger participating at a given time and that if a submission is challenged, Kleros jurors give the “right ruling”, potentially after some number of appeals. Then, the payoff for this challenger to analyze a given case is:

A rational challenger makes the calculation of whether it is worth his effort e to review a given case.

Similarly, the payoff for an attacker to try to make a given malicious submission is:

Then, (if C is large enough to avoid some degenerate cases where it is never worth the challenger's effort to participate), this leads to an equilibrium where:  

We can think about this result in the context of our metaphor where we think of “challengers” as “police” that find potential attacks and put them before the jurors.

When the crime rate is high, governments have an incentive to increase police resources to bring the crime rate down. If the crime rate is very low, it can be difficult for a police department to justify its current level of resources, and democratic governments may be tempted to make cuts. Then the crime rate will rise as there are fewer police. Even if you have only rational criminals, if the resources of the police adjust to their perceived need, it can be difficult to maintain a 0% crime rate.

A sufficiently proactive real-world police department can cut through this dilemma by simply funding police activity at a high level, even if the crime rate is very low. Indeed, according to the broken windows theory of crime, popularized due to its influence on the policing policies of Bratton and Giuliani in New York City in the 1990s, one might hope that policing crime to the point where even minor offenses are caught and quickly dealt with sends a signal to potential criminals that any attacks are unlikely to succeed, which acts as a deterrent to any future attempted attacks, creating a virtuous cycle. However, maintaining such a high level of policing requires an influx of external resources.

In the context of a Kleros curated list, the money that is put in comes from submitters and challengers who challenge those submissions. If we want to guarantee that honest submitters get their deposit back, then the only money that goes to paying challengers comes from attackers. Hence, you can never expect to have a 0% rate of attack.

Moreover, if all incorrect submissions come from rational attackers (note this is a pessimistic assumption; sometimes legitimate disagreements can lead to a submission that is ruled incorrect), there will be no attacks unless there is some expectation that an attack may sometimes succeed.

Thus, the fee model of a Kleros based curated list is somewhat similar to that of law enforcement of a jurisdiction like Nevada, “where fees for misdemeanor offences, like traffic violations, have [also] become a primary revenue model for state and local courts and affiliated programs, and have been for decades”.

Self-funding police departments may have dubious consequences in the context of a democracy, but this model is less problematic in the opt-in world of blockchains, particularly when applied to situations which are not otherwise adequately addressed.  

Ultimately, one should choose the various adjustable parameters: C, S, etc., such that an acceptably negligible percentage of the list consists of malicious submissions while still being worthwhile for honest parties to submit to the list.       

In Practice

Finally, there is an indisputably clear image of a cat that without any doubt, meets the terms of our payout policy present on the Doges on Trial list.

The attacker behind this image did not manage to corrupt the votes of the Kleros jurors. Indeed, this image did not win any disputes. No elaborate bribe was required. Rather, it went unchallenged. The “police” did not catch it during the “pending” period.

This is somewhat ironic when compared to our theoretical discussion above. We saw that the difficulty in incentivizing (perfectly rational) challengers is that if the percentage of hostile submissions is too low, it will not be worth their effort to sift through the submissions looking for the rare submission that is worth challenging.

However, since the cutoff for the payout of Dogecoins on October 31^st, there has been less of an incentive to make honest submissions versus attacker submissions. Indeed over the past few weeks a much higher percentage of all submissions have been cats, so challengers should be strictly more incentivized now compared to the period before October 31^st.

However, in reality, it is not that surprising that the collective responsiveness of challengers has now declined, allowing such a breach to happen. The pilot has been live for a while now, and it is normal that participants are less enthusiastic.

Future Kleros based curated lists will allow for the possibility of making a submission that de-lists an entry that has already made it on to the list (with this de-listing submission being itself challengeable), which should mitigate this phenomenon.

Regardless, this experience reinforces the importance of building and engaging with the community, so people are excited to perform roles like that of the challenger.  

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