Dogenomics: the Numbers Behind the Experiment

It’s not rocket science but it is pretty damn close.

By Stuart James with contributions from William George

Doges on Trial is Kleros’ first cryptoeconomic experiment on the Ethereum mainnet. It’s based on a curated list application, a key area of research within the decentralized ecosystem. Users are rewarded by submitting and challenging images of cats and Doges (you can find out more about the specifics of the pilot here and also learn a bit about user behavior in this Coindesk piece).

Many users have asked about the specifics of how payments flow between users in the Doges on Trial economy. This is just what we’re going to do in this article: show the route of ETH and PNK from image submission to its acceptance or rejection on the Doge list.

Potential Scenarios in Doges on Trial

An image is submitted to the list. Is it a Doge? There are three broad scenarios:

1. The image is not challenged and is accepted directly into the list.
2. The image is challenged, a ruling is made and is not appealed.
3. The image is challenged, a ruling is made and is appealed.

Let’s look into three real cases which have already passed through our Doges on Trial pilot. Alice will play ‘The Submitter’ and Bob the role of ‘The Challenger’.

The Dogelion: a No Challenge Scenario

Alice submits an image and pays the depost fee of 0.06 ETH to do so. Since the image is not challenged, she receives her deposit back in full and no further payments are done. No interaction with jurors or PNK is made. The image is accepted into the list.

Alice’s handsome Doge image accepted onto the list with no challenge.

The Puzzledoge: a Challenged Image with No Appeals

1. Alice submits this image and pays the deposit fee of 0.06 ETH.

Alice’s image. Seems legit? Bob thought not and challenged it.

2. Bob doesn’t believe this is a valid Doge and challenges the image by depositing 0.06 ETH. Now there’s 0.12 ETH in the contract and the image is sent to arbitration.

3. Kleros jurors are called into action. Those who have deposited PNK and been chosen to rule* should now vote.

At this stage, there are 3 jurors who each have 200 PNK ‘locked’. Jurors who don’t vote coherently (i.e with the majority consensus) will see their ‘locked’ PNK distributed between those that did. Also, an arbitration fee (0.01 ETH) will be paid to each juror for taking part (regardless of whether they rule coherently or not).

Below we can see the journey of this very image and the outcome of the ruling.

# of challenges: 1 — Challenged
disputeID: 18
# of Appeals: 0 — No Appeal lodged
Votes (No Vote/Yes/No): — Juror vote results. 
 — 0/3/0
lastRuling: It’s a Doge — Final result

All three jurors voted that the image was in fact a Doge. This means that Alice (the Submitter) won the case. Bob accepted the ruling and chose not to appeal.

This is what happens as a result of this decision:

• Alice gets immediately 0.03 ETH back (these funds come from Bob’s deposit).
• Each one of the 3 jurors is paid 0.01 ETH (these funds come from Bob’s deposit).
• Bob loses his 0.06 ETH deposit (these funds go to Alice and the jurors).
• No PNK changes hands.

The image goes back to ‘pending’ status. As it’s not challenged again, it’s finally accepted into the Doge list. When that happens, Alice gets her 0.06 ETH deposit back.

Other Possible Outcomes

In this case, Alice won the dispute with a unanimous jury decision. But let’s break down other possibilities which could have happened.

Bob Wins

If Bob wins, Alice would lose all her ETH.

Of the 0.12 ETH in the contract:

• 0.03 ETH is used to pay the arbitration fees collected by the jurors (0.01 ETH to each of the three jurors).
• 0.09 ETH is collected by Bob. He gets his 0.06 ETH deposit back and 0.03 ETH from Alice’s (the funds that are left over after the arbitration fees are paid).

The image is rejected from the list.

If Bob loses the dispute he would lose all his ETH.

Again, of the 0.12 ETH in the contract, 0.03 ETH is used to pay the jurors. Now, of the 0.09 ETH that is left, 0.03 ETH would immediately go to the Alice. The remaining 0.06 ETH stays in the contract… for now. This serves as Alice’s deposit in case someone else decides to challenge her image. If the image eventually remains unchallenged for 24 hours, then it is accepted to the list as in case 1 above. Only then does Alice get her 0.06 ETH deposit back.

Now what happens with the jurors? We saw that whether Alice or Bob wins, each juror is paid 0.01 ETH for their time. Additionally, each juror had 200 PNK ‘locked’ pending the outcome of the case.

(The amount jurors choose to deposit in order to be chosen can be any amount above 800 PNK. 200 PNK of this amount will be locked until the case has been ruled).

So for one dispute at the ‘Challenge’ stage the contract would look like this.

0.12 ETH Locked (from Submitter Alice+ Challenger Bob) + 200 PNK * 3 locked for jurors.

In total: 0.12 ETH + 600 PNK to be redistributed.

2–1 juror decision

If the decision is unanimous, PNK is not redistributed as all jurors voted the same way. But what happens if there’s a 2–1 vote?

Each juror still gains 0.01 ETH in arbitration fees. Now there are two coherent jurors and an incoherent juror. The coherent jurors (2) each receive their 200 PNK back + the PNK of the incoherent party.

So in this case, the two coherent jurors would receive 200 PNK + (200 / 2) from the incoherent juror meaning each receives 300 PNK and the incoherent juror loses 200 PNK.

The Cuteness Controversy: a Case With Multiple Appeals

Let’s take a look at the image which sparked a double appeal in its journey through the Doge list.

Very cute… but is it a doge? Our submitter believes so lodging two appeals.

# of challenges: 1
disputeID: 3
# of Appeals: 2
Votes (No Vote/Yes/No):
 — 1/0/2 = Challenge
 — 0/0/7 = Appeal one
 — 1/0/14 = Appeal two
lastRuling: Not a Doge — Final result

This image has been challenged, ruled on and appealed two times by the submitter Alice. Let’s go through the numbers behind the appeal process. First we will look at the flow of ETH between Alice, Bob, and the jurors.

When Alice or Bob makes the decision to appeal, the jurors have already been paid their 0.01 ETH each in arbitration fees, but the remaining 0.09 ETH is still locked in the contract. Also, the PNK redistribution will not have happened yet, so each juror still has 200 PNK that is locked.

Appeal Round One

To the 0.09 ETH still locked in the contract, the appelant pays fees of 0.07 ETH. So now the balance of the contract looks like:

0.06 + 0.06 (initial challenge) - 0.03 (cost of intial round arbitration) + 0.07 (appeal fee)= 0.16 ETH

There are 7 jurors present in the ruling. Each will be paid 0.01 ETH for their efforts. That leaves 0.09 ETH left over.

Imagine there had been no second appeal and the round one ruling stood. What what would have happened? As in the initial ruling, if Alice (the Submitter) wins, she gets 0.03 ETH, and the image can be re-challenged, so the remaining 0.06 ETH stays locked up as a deposit. If Bob (the challenger) wins, the image is immediately rejected from the list and Bob receives the entire 0.09 ETH.

However, there was another appeal, so that ETH stays locked up into the next round. Furthermore, each of the 7 jurors from the first appeal has 200 PNK that stays locked up (in addition to the 3 jurors from the initial ruling who also still have their 200 PNK each locked up).

Appeal Round Two

Right after Alice triggers the second appeal by submitting 0.15 ETH in appeal fees the amount in the contract is:

0.06 + 0.06 (initial challenge) - 0.03 (cost of initial round arbitration) + 0.07 (first round appeal fee) - 0.07 (cost of first appeal fee arbitration) + 0.15 (second round appeal fee) = 0.23 ETH

There are 15 Jurors present in the ruling. Again, each will be paid 0.01 ETH, and once again that leaves 0.09 ETH left over. As in the initial round, if Alice (the Submitter) wins, she gets 0.03 ETH, and the image can be re-challenged, so the remaining 0.06 ETH stays locked up as a deposit. If Bob (the Challenger) wins, the image is immediately rejected from the list and Bob receives the entire 0.09 ETH.

There were no more appeals, and the Challenger did, in fact, win. The image was finally rejected from the list and Bob received the 0.09 ETH.

Now, at the end of the last appeal, when the ruling is being finalized, we finally consider what happens to the locked PNK of the jurors who voted over the various rounds. As it turns out, all of the jurors who ruled that this was not a Doge. So none of these jurors lost their deposits, and no PNK was redistributed to them from incoherent jurors.

This little guy was rejected from the list. May be cute, but not a Doge, according to jurors.

The Doge-Cat Dilemma: a Case With Jury Disagreement

Let’s now look at a case that sparked disagreement among the jurors and consequently involved PNK redistribution. It was all triggered by this image.

This case provided some shifting perspectives. First it was ruled as a Doge and upon appeal that decision was overturned.

# of challenges: 1
disputeID: 1
# of Appeals: 1
Votes (No Vote/Yes/No):
 — 1/2/0
 — 0/3/4
lastRuling: Not a Doge — Final result

In the initial ruling, this image was ruled as a Doge. Two jurors voted that it was a Doge and one juror did not vote. However, Bob the Challenger appealed.

Let’s go through the numbers behind the appeal process. First we will look at the flow of ETH between Alice, Bob, and the jurors.

When Alice or Bob makes the decision to appeal, the jurors have already been paid their 0.01 ETH each in arbitration fees, but the remaining 0.09 ETH is still locked in the contract. Also, the PNK redistribution will not have happened yet, so each juror still has 200 PNK that is locked.

To the 0.09 ETH still locked in the contract, the appellant (which in this case is the challenger Bob), pays appeal fees of 0.07 ETH. So now the balance of the contract looks like this:

0.06 + 0.06 (initial challenge) - 0.03 (cost of intial round arbitration)+ 0.07 (appeal fee)= 0.16 ETH

There are 7 jurors present in the ruling. Each will be paid 0.01 ETH for their efforts. That leaves 0.09 ETH left over.

As in the initial round, if Alice (the Submitter) wins, she gets 0.03 ETH and the image can be re-challenged, so the remaining 0.06 ETH stays locked up as a deposit. If Bob (the Challenger) wins, the image is immediately rejected from the list and Bob receives the entire 0.09 ETH.

In this case, the Challenger won his appeal. So Bob received the 0.09ETH, so he is better off than if he had given up after the initial ruling and not paid the 0.07 ETH of appeal fees.

The ruling in the appeal round was 4–3 in favor of Not being a Doge. So 3 jurors lost their 200 PNK and this 600 PNK was split evenly between the 4 coherent jurors from this round. So each coherent juror from the appeal round receives 150 PNK.

What happened to the 2 jurors from the initial ruling who voted that this image was a Doge? As they were ultimately incoherent with the final ruling, they lost their 200 PNK each. There were, in fact, no coherent jurors in the initial round to redistribute this PNK to. So instead it returned to the contract govenor. For now, that address is controlled by the team, but in the long run, left over PNK like this will be put under the control of the liquid vote governance mechanism.

To Conclude

The take-away from this is that for the flow of ETH, there are a few basic principles:

• A Submitter places a 0.06 ETH deposit with an image she hopes is added to the list. If there is a Challenger who does not believe this image is a Doge, he also places a 0.06 ETH deposit.
• If a Submitter’s image remains unchallenged for 24 hours, the image is added to the list and she gets her 0.06 ETH deposit back.
• Each juror who rules is paid 0.01 ETH, regardless of appeal round or outcome.
• The Appellant (which might be the Submitter or the Challenger) who wants to overturn the previous round’s decision pays an amount of ETH to cover the cost of arbitration for the appeal. If the ith appeal is being triggered, as this appeal has 2^(i+2)-1 jurors, the Appellant pays (2^{i+2}-1)* 0.01 ETH.
• If the Submitter ultimately wins the dispute (regardless of how many rounds it takes), she gets 0.03 ETH in stake from the Challenger and 0.06 ETH remains in the contract as a deposit for future challenges or until 24 hours pass and her image is added to the list.
• If the Challenger ultimately wins the dispute (regardless of how many rounds it takes), the image is rejected from the list and the Challenger receives 0.09 ETH immediately.

For the flow of PNK:

• Jurors that are incoherent with the final decision lose 200 PNK each.
• That lost PNK is evenly redistributed to the coherent from the same appeal round (if there are any).

Rewards

All successfully accepted images onto the list will split 1Million Dogecoins between the users.

Get a cat image onto the list as per our payout policy and you could win 2 ETH + a Cryptokitty.

For more information on the payout policy click here.

If you have any more questions feel free to join our Telegram or Slack channels and speak with the team directly.

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