Why Kleros Needs a Native Token?

The Pinakion (PNK), a crypto-token for creating the right incentives and preventing Sybil attacks…

At Kleros we are building a blockchain-based, crowdsourced dispute resolution platform. An essential part of the mechanism design is the native pinakion token (PNK).

A Pinakion from Ancient Athens. These small bronze plates on which citizens’ names were written were inserted into a randomizing machine that selected for participation in juries and certain civil service roles. The name of the token used by Kleros is a reference to this practice.

For each dispute that is arbitrated by Kleros, some number of jurors are required. A jury as small as three people may provide an initial ruling of a dispute. Then if one of the parties decides to appeal the ruling, the number of jurors in subsequent rounds increases.

PNK holders can stake their token in a Kleros court to indicate their availability to serve as jurors. (In our current MVP, there is only one court. However, eventually, we will implement specialized subcourts and PNK holders will be able to choose which subcourts to stake their token in). In order to select the jurors for a case, random PNK are drawn from among those which have been staked, and the people who hold these PNK are the jurors.

A short explainer video on how Kleros works.

Why Does Kleros Need its Own Token?

First and foremost, PNK is a protection against Sybil attacks. In order for an attacker to flood the juror pool, they need to buy enough PNK so that they are selected enough times to be a juror for the same case in order to change the outcome. Generally, this means that the attacks needs 51% of the total (staked) tokens.

An attacker may get lucky in rare circumstances and be selected for two of three juror spots with only a minority of the PNK. However, in order to maintain the attack through the appeal process, it would need to be selected for the majority of the juror spots on larger and larger juries, which will only be possible if the attacker actually has a majority of the PNK. Hence, substantial economic resources are required to perform a 51% attack.

So far, this would still be true if we had potential jurors stake ETH instead of PNK. However, using a native token offers several key advantages for minimizing the risk of 51% attacks versus using an external cryptocurrency.

PNK makes an attack hard

If would-be jurors were drawn based on how much ETH they had staked (rather than PNK), it would be much more viable for an attacker to try to buy enough ETH to outspend the rest of the market. If an attacker wants to obtain 51% of PNK, market liquidity will dry up. As the attacker buys PNK , it will start to become scarce and each additional PNK will cost more and more. The attacker may not even be able to find 51% of PNK for sale on the open market at any given time.

In contrast, consider the situation of an attacker who wants to buy enough ETH to make a stake that is greater than whatever would be already staked in Kleros courts at a given time. There is a lot of ETH floating around, and Kleros will presumably only represent a part of the broader Ethereum ecosystem.

Current 24 hour market volumes for ETH are hovering around 2–3 billion USD with all time highs near 10 billion. If someone wanted to buy enough ETH to overwhelm whatever is staked in Kleros, it probably wouldn’t take them all that long. Moreover, the market for ETH is much deeper than the market for PNK will be. So, while a large purchase of ETH might move the price of ETH a bit, market liquidity effects woudn’t come to Kleros’ defense in the same way as they do by having a native token.

PNK makes an attack expensive

Imagine that someone does buy 51% of the PNK in an effort to attack Kleros. Maybe their attack will be subtle and go unnoticed. However, more likely the community will realize that it is under attack, particularly if the attacker uses her new PNK to commit obvious miscarriages of justice. In this case, Kleros would lose credibility as an arbitration platform and the value of PNK would decrease. Then the attacker would take a substantial loss on the PNK she bought, representing a high economic cost to carry out the attack.

On the other hand, an attack on Kleros would presumably not have that large of an impact on the price of ETH. So, if stakes were made in ETH, an attacker could perform her attack after which she could sell her ETH without taking too much of a loss.

The price of Bitcoin Gold (BTG) over a recent period where it suffered a 51% attack. In Kleros, performing a 51% attack requires holding 51% of the tokens, so the attacker should take a hit in value on each one of her tokens.

PNK makes Kleros forkable

Finally, in the extreme case of a successful 51% attack, by having a native token, it is possible to perform a last-ditch defense of forking the system to remove the attackers’ holdings. Then the market would sort out which version of PNK should be used going forward. This would of course be highly disruptive as any pre-existing contracts designating Kleros as their arbitrator would continue to use the old version of PNK by default. Still, it would offer the community a path forward out of disaster that would not be available without a native token. This is similar to the ultimate appeal mechanism of Augur.

On the left, an attacker has managed a 51% attack and starts carrying out obvious miscarriages of justice. The community decides to fork the token removing the attackers’ holdings, and most of the users migrate to the new version of PNK.

Ultimately, the integrity of juries is the essence of what the Kleros protocol aims to provide. As such, it is key to maximize their defense against 51% attacks. This is why Kleros needs its own native token.

Why Would Users Want PNK?

Many models that attempt to price crypto-tokens look at the velocity of those tokens — namely the average amount of time that a token is held before someone being used or spent. Then, these models appeal to the equation of exchange from classical monetary theory to try to derive a value for the token. This is particularly valid way of analyzing medium of exchange tokens, namely tokens that are the underlying currency of some marketplace.

However, it should be pointed out, PNK is not a medium of exchange token. It is not the currency of a market as would be required to apply the equation of exchange. In particular, PNK is not spent to buy arbitration services.

Instead, holders of PNK can stake their tokens, giving them the opportunity to be drawn as jurors and rule on disputes. They lose this stake if they rule incoherently with the other jurors, but if they rule coherently, they can gain rewards from the lost tokens of the incoherent jurors. Also, the users are compensated for their time and effort arbitrating cases from the fees that were paid by the parties to the dispute. (As fees are refunded to the winning party, this payment ultimately comes from the losing party to the dispute.)

The mechanics of PNK in Kleros are quite similar to that of the Augur REP token. (As such, PNK falls clearly in the cateogry of “work tokens” in this classification of types of utility tokens.)

Let us investigate what it is worth to an honest user (USR) to stake a PNK.

We denote the following variables:

f — the fees charged to arbitrate a case

— the fees charged to arbitrate a case K — the number of PNK that are drawn to rule on the cases in a given period

— the number of PNK that are drawn to rule on the cases in a given period r — the prevailing interest rate per arbitration period, namely the average interest rate that someone could obtain, for example in a bank, during the time it takes to arbitrate a dispute

— the prevailing interest rate per arbitration period, namely the average interest rate that someone could obtain, for example in a bank, during the time it takes to arbitrate a dispute N — the number of PNK that are staked

— the number of PNK that are staked w — the cost to the user to arbitrate a dispute in time and effort

Remark that while f, K, r, and N are the same for all users, w varies from user to user.

We make a couple of simplifying assumptions:

Note that f, K , r , N , and w can all vary from period to period, and in the case of w , even from case to case within a period. For now, we assume these variables change slowly enough to be approximated as being constant.

, , , and can all vary from period to period, and in the case of , even from case to case within a period. For now, we assume these variables change slowly enough to be approximated as being constant. Sometimes jurors will rule honestly and will nonetheless be in the minority.When this happens, they will lose PNK as a penalty. On the other hand, in other cases jurors will gain PNK from jurors in the minority, whether those jurors are failed attackers or honest jurors who got unlucky. We expect the gains and losses of PNK to mostly average out for an honest juror. For the following computations, we assume these gains and losses exactly average out, and that an honest juror keeps the same amount of PNK from one period to the next.

If w>f, it is not worth a user’s time and effort to be a juror and she won’t stake her PNK.

If f>w, USR essentially receives value of f-w each time she is drawn as a juror. As K tokens out of N are chosen with replacement, the number of times that USR is selected as a juror per period X is distrbuted as X~Binomial(K,1/N).

Then, adjusting these values for interest, we compute:

The interest rate r is an external variable to Kleros. Similarly, how much effort is required to arbitrate a case, w, will depend on the users themselves and cannot be directly controlled by the system. On the other hand, the fees f will be adjusted through governance. Specifically, we intend to use a liquid vote, where PNK holders can vote directly on governance decisions or delegate their vote to another party. See our whitepaper for more details.

As fees increase, it is more worthwhile to rule on any given case, but if fees are increased too high the platform will become a less attractive platform for arbitration and K will decrease. The liquid voting mechanism will be tasked with finding the balance between these effects.

K is a measure for how much arbitration there is to be done, both in terms of how many total disputes and how often they are appealed. All else being equal (if the fees don’t change, etc.), as K increases or decreases — meaning PNK holders have the opportunity to arbitrate more or fewer cases — the value of PNK should increase or decrease accordingly. Namely, the value of PNK should reflect how much the platform is actually being used to provide dispute resolution.

A Bit More Detail…

To be somewhat more precise, as mentioned above, we intend to create a system of subcourts designed to handle specific types of cases. Then, in addition to staking their tokens in a general court, users can choose which subcourts to participate in, where they have the incentive to choose those courts where they are specialists. The above calculation holds for each subcourt in which a user participates, where the fees, number of cases, and effort required by a user to arbitrate a case vary from one subcourt to another. Then, the total value of the token to the user should, in fact, be the sum of the values for each their chosen subcourts.

All of the considerations above were applied to a single user USR. Another user USR’ who is more or less skilled in arbitrating these disputes will have a different w’. Accordingly, what a PNK is worth to each of these users will vary. If there are M total tokens in circulation, we might expect the market value of one PNK to fall into an equilibrium that corresponds to the w of the Mth most skilled would-be juror, namely the Mth lowest w in the pool of users.

Note that one user can obtain multiple PNK. However, due to the marginal utility of their time, the cost of the time and effort to perform arbitration, namely their w, will increase from one PNK to the next. (Hence, one may just model this person as a different user for each PNK.) Particularly, if K increases, the user may get drawn for the number of cases that it is worthwhile for her to arbitrate using less PNK than was necessary before. In this case, she might want to sell (or maybe somehow lend) the excess. See “Scaling Work Token Networks” in this analysis of utility token models for a discussion of these kinds of effects.

To summarize, Kleros needs its own token as a defense against 51% attacks. This token gives users the ability to be selected as jurors. As such, users should have an interest in holding PNK tokens because of the opportunity that these tokens represent to receive fees and rewards for coherence for arbitrating disputes.