Voting and Vote Splitting in Crypto-economic Systems

Transcript

Let's check. Okay. Okay, so thanks for coming everybody. My name is William George. I'm a researcher with the Kleros Cooperative. Uh so if you're not familiar, Kleros is a blockchain-based dispute resolution platform. It's kind of a blockchain oracle optimized for dispute resolution. And today I'm going to be talking about voting and specifically vote splitting in different crypto-economic systems. Uh so if I said the words vote splitting, you probably think of vote splitting in political elections. Um if I have some election for Parliament or for the National Assembly or for president or something, if you depending on the vote system you use, sometimes if you add similar candidates to candidates that exist already, that can have effects on who will win. Uh so particularly if you use the kind of simplest voting system, uh

the first-past-the-post post voting system or the plurality system, which is used for say British Parliament or US uh elections. Uh so this system where you vote for one candidate and then the candidate with the most votes wins. Uh this generally has the effect that if you have similar candidates to kind of split the vote among each other. Uh and this is illustrated well by this cartoon from the 1912 US presidential election where the incumbent Republican president Taft was running against two major challengers, uh the Democrat Woodrow Wilson, but also a former Republican president Teddy Roosevelt who decided that he didn't like what Taft was doing and wanted to run again.

Uh and unsurprisingly, these two Republican heavyweights split the vote among each other and Wilson became president. >> [snorts] >> Uh so there's been a lot of research over decades in terms of like what what are good voting systems? How do I have voting systems that resist kind of weird behavior, uh vote splitting and others? Uh so this is field is called social choice theory, the study of voting systems. Uh generally, you know, one of these problems is I have similar candidates. How do I prevent them from splitting the vote among each other? Uh and in the world of crypto economic systems, you have some voting that looks like this.

In DAO voting, you have the same the same basic kind of structure. If I'm a voter in a DAO, there's some propositions put in front of me and I want to choose how to vote. Well, I have some personal preferences. Like my vote is based on who I want to win, what proposition I want to win. Maybe I have some kind of economic rationale. It's good for my bags, whatever. But fundamentally, my motivation is I want this option to win the vote. So that it's very similar to political elections and you have kind of the same similar effects.

However, there are other kinds of voting in blockchain world. So particularly a lot of oracles, particularly kind of more crowd-sourced oracles. The Kleros oracle is like this. Others like UMA and then a few others use this sort of mechanism where the oracle is supposed to produce some fact about the world. I have some piece of information that the blockchain doesn't know as part of its consensus algorithm and you're trying to bring on chain. How do you do that? People vote on it. And to give a sort of illustrative example, in Kleros what this looks like, and it's is pretty similar from one oracle to another, is I take some panel of randomly chosen people and they vote. Maybe I have a case, you know, it's a dispute resolution

platform. Kleros is optimized to resolve disputes, bring this sort of dispute information about who's right given dispute on chain. >> [snorts] >> I have a dispute between maybe Alice and Bob. Alice has a small business, she hired Bob a freelancer to do some kind of task, build her a website. She's ultimately unhappy with Bob's work. And like who's right, Alice or Bob? My randomly chosen panel of people are going to vote. And they receive economic incentives based on how they vote using what we call a Schelling point mechanism. So the idea of a Schelling point or a focal point uh, is due to uh, American economist Thomas Schelling, who observed empirically that when people try to play games where they coordinate, uh, in the absence of communication,

they wind up coordinating around solutions that seem natural or special for social reasons. So, that seems pretty abstract, maybe, uh, but like concretely, uh, in the example of these kind of blockchain oracles, the the general idea is the following. Uh, if I have my voters and they look at the case, they look at the sort of thing about to bring on chain. They look at the Clash of Disputes between Alice and Bob, they read the evidence, they think Alice has the the winning case. Uh, they are incentivized to kind of agree with the community. Uh, vote the way other jurors are going to vote. Uh, in Kleros there's like a notion of appeal, you know, they want to go vote the way it's uh, how the the community decides after potentially some future appeals. There can be nuances, but like as a

guiding principle, they want to get in the minds of the other voters and think about what like a generic juror would vote, and what a generic voter would vote. Uh, and then I look at the case, I think Alice has the better argument, and I think, "Okay, like the other voters are probably also going to think Alice has the better argument. Uh, so I'm going to vote for Alice because I think they're going to think that I'm going to vote for Alice. Uh, so like I think they vote for Alice because I think I vote for Alice because I think they vote for Alice, sort of down." Uh, and we all vote for Alice. Alice voting for the truth, uh, is a focal point or a Schelling point. We sort of drift to it it because it's a socially distinguished solution. Uh, and uh, note just in passing, this

structure is also shared by many blockchain consensus algorithms. Uh, this is a point that was raised by Vitalik in a blog post back in 2015, uh, where if you have some kind of fork, uh, and there are two competing blocks to extend a chain, they're contradictory, one like has one version of a transaction, the other one has a transaction that's that's like incompatible, uh, and I as a block producer or a miner, I have to pick one to be the parent for the block that I'm going to mine as like the next block. Uh, which one do I pick? Well, I want to pick the one that's going to get in the chain. Uh, I my rewards depend on my block getting in, at least partially. Like I'm more rewarded if my block gets into the chain.

Uh so, I want to pick the the parent block uh that will be most likely to get me and it into the chain because that that aligns with my rewards. So, the same basic payoff structure. This is just something to keep in mind. I'm going to talk mostly about this kind of like article situation, uh but the blockchain consensus is like the same game and you can >> [snorts] >> like some of the results apply to those Uh and uh okay. So, back to vote splitting. Already vote splitting was a problem in political elections. You know, people talk about this a lot and you know, newspaper articles and columns and such.

Uh I would say that it's probably even worse in blockchain oracle problems uh because imagine that I have the kind of following setup uh where the voters in my case uh are confronted with four options. Three of them are kind of all reasonable and similar. Uh you know, one of them is like give Bob some more time and and you know, give Bob even a little more time and give Bob even yet a little more time. Uh and then there's a distinguished different option which is just wrong. Uh just refund Alice. When Alice doesn't deserve to be refunded. Uh and uh how are the jurors going to vote? Well, like they should ideally vote to give Bob more time because that's the honest answer. Uh and the Schelling point like if we design the system well, should be to for everyone to drift to voting for

the honest answer as a strategy. But, you know, if we use a maybe the bad voting system here, voting the dishonest distinguished but different answer, that can also be a Schelling point. It's also distinguished for social reasons. Uh and you can imagine the voters just sort of all grouping around voting for the dishonest distinguished answer uh and that being an alternative Schelling point. That's really bad. You really want to avoid that happening. Um So um what can we do? Uh a classic thing to do uh in voting system theory in social choice theory is to ask voters for richer information in their ballots.

Instead of just voting like Alice or Bob or you know like A or B, I'm going to ask my voters to rank their ballots. And then how can I once everybody's ranked their ballot, how can I turn this into a collective decision? Well, there are different ways. One way is to use what's called the Borda system. So here you give a certain number of points for each position in your vote. If I put a option first, it gets three points. If I put it second an option second it gets two and so on. And then you count up and you see which option has the most points and it wins. Another possibility is what's called instant runoff. This is used in parliamentary elections in Australia.

And here the idea is we simulate a series of runoffs where you count the number of first place votes that each option gets. And if an option gets more than half of the first place votes you're you're done and it wins. And if no option gets half, then you take the option that has the fewest first place votes, you eliminate it, and you take the voters who voted for that option and their vote defaults down into their second place. And you keep sort of eliminating options like this until somebody wins. So I'm going to use instant runoff as kind of a running example in this talk. So I'll give little more detail full example.

Say I have these five voters. I count the number of first place votes. Nobody won. First round yellow is eliminated. It got zero votes. Second round still nobody won so green is eliminated. And I reattribute green's the growth the vote that voted for green to pink. And now the pink angel wins. So the pink angel wins on the third round. There are other ways that you can ask voters for rich information to like sort of get around these kinds of voting paradoxes and pathologies. There's a system called approval voting which is very popular where instead of asking for rankings I ask each voter to say okay, check yes or no for each option whether it's approvable or not.

That's an alternative thing you can do. You wind up taking the option that has the highest rate of approval. I'm going to mostly focus on rankings here because it's kind of like a classic thing people talk talk about in in social choice theory, but like there are alternatives. Okay now a moral a lesson of decades of research in social choice theory is that there's no perfect voting system. Every voting system has some problems. If you've ever heard of Arrow's Impossibility Theorem, it's sort of in this vein. And social choice theorists have spent decades creating these like elaborate tables where you have voting systems on one side and properties you want voting systems to have on the on another and you can say okay like this voting system has this and this but not that. This one has well it doesn't have this but it has

this and this. These two properties are just incompatible. I have a theorem saying that if you have this you can never have that. And you wind up having to make trade-offs. You pick the voting system that makes the most sense for you. In particular one of these columns here of clone independence is relative well is particularly relevant for vote splitting and I'm going to focus on that and sort of how it manifests itself in blockchain systems. >> [snorts] >> So clones are this idea related to vote splitting that was particularly explored by Nicholas Tideman and he defined clones as as follows where a clone a set of clones is a set of options that are ranked consecutively in all the votes.

So here the angels are clones. Some of the votes put them 1 2 3, some of them put them 2 3 4, but they all put them together like you know some people may think the angel is better or worse than the devil. Some people think that maybe the maybe the devil's better than the angels, but like wherever I put the angels I put all three of them together because I think they're basically the same. And then a clone independent voting system is one where if I delete an alternative from the set of clones basically nothing happens. If the the winner was not in the set in the set of clones before the deletion same winner.

And the winner is in the set of clones before the deletion if and only if the winner is in the same in the set of clones after the deletion. So you can sort of change from deleting a clone can change you from one one clone winning to another clone winning, but otherwise it doesn't have an impact on the outcome. Uh and um in my example with instant runoff voting, I take my five votes from before. I said that the pink angel won in this example. What if I just delete the pink angel? Uh now the green angel wins if you sort of recalculate things. And this is a reflection of the fact that instant runoff, if you take an appropriate tiebreaker, there's some nuances around tiebreakers, instant runoff is a clone independent voting system.

Um okay. So, now back to blockchain oracles. Uh in blockchain oracles like we have these economic incentives. I'm rewarded based on how I vote and how other people vote. Uh and it's not a matter of trying to get my preferences to win anymore. It's like ultimately the system is trying to bring information on about the real world on chain, and you want the system to produce like true information. So, what do my incentives look like generally? Well, I kind of think that like I have some truth. Uh maybe in like a given case the the true answer is the pink angel should win.

Uh and then I receive a signal. Each juror is going to receive a signal. Each voter is going to receive a signal that's like the pink angel winning plus some noise. Uh and the result of that signal is like this fuzzy angel. Maybe I can't quite tell the color. The other clones are all very similar, so I like the true signal was pink and I wound up thinking yellow. Uh it's a little fuzzy. Like I think the angel is the best choice. I can't really tell. Maybe the devil is the one one or is the true signal. And um I wind up with like a probability distribution for how I think each of the options is likely to be the truth based on my signal.

Uh and then what should the incentive function would be? Well, the the system doesn't know who what the truth is either. That that's the point. We're trying to bring this information on chain. So, it'll take each each each voter's vote uh and kind of piece them together and try to come up with his like own probability distribution of how likely a given thing is to be the truth, uh ideally in an attack resistant way, uh and then pay people accordingly. And what this generally looks like, there there's some flexibility in this space, uh is to basically reward people who rank options that are collectively ranked highly, Uh if you rank that option highly, you are rewarded. And if you rank options that are collectively ranked highly quite low, then you're penalized. So here we saw the winning option is the pink angel.

If I put the pink angel first, I jackpot. You know, the net the voter in the middle put sort of the pink angel in the middle, but like their angels at the top, they did okay. And the person who put the devil first, even though the angel won, they they get nothing. Maybe they're penalized. And that was like an exact very simple example of a payoff function like that that I'm going to use as like a toy example that for like the following couple of of observations and examples is the following. So this is an extremely simple payoff function. If I put the winning option last, I'm slashed. If I put the winning anything other than the winning option last, I'm cool.

Like no effect on my payoffs. This is an extreme version of this kind of like payoff function where I'm trying to put like the winning option as high as possible. And now this is an example. Suppose that I receive this following signal, fuzzy angel, and I'm voting between yellow angel and devil. I have two choices. And I'm trying to see how the other voters are going to vote. And I think because I saw the angel, they're probably more likely to see the angel than not. However, in this case, just just for the sake of example, I think that the other jurors are like other voters are better better informed than me. I think they're more likely to see the truth. They'll have less noise in their signal. Maybe I'm new. This is the first case I've ever done and like I

I sort of realize I'm not so great at this yet. And the other people are experienced. They they know what they're doing. So I I don't know whether they're going to put angel or devil first, but I think they're going to pick the same answer. So I think maybe 55% chance they both pick the angel, 45% chance they both pick the devil. And then what's my incentive to do? Well, that's you know, I'm going to vote for the angel because like I binary choice, the angel seems like it's more likely to be the devil. Um So, I was incentivized to vote my signal. Uh basically with any payoff function or voting system that's even remotely reasonable in instant runoff plus the simple payoff function before, like I would be incentivized to vote for the the angel first. Now, what happens if I add a clone? Now, I have angel plus

two devils. Uh and the same signal as before, except that I don't really know how the other jurors are going to vote for the clones. Uh I think there's a 55% chance they'll see the angel first. Uh and then well, like you know, between the two devils I think it's as likely they put one before the other than the other. Uh you know, so basically I split the like 55% chance that I think the angel is first into four equal categories of 13 and 1/2% where in one case they both put the red devil first, in another case they both put the blue the the purple devil first, and then there are like the mixed cases that are also equally likely where they sort of one puts the red one puts the purple first. Uh same thing for the 45% chance where I think that they

put the devils first. Uh and now I have this like augmented signal. Same idea as before, but with these three options two of which are clones. Uh and here what happens if I calculate my max like my maximum expected return for all the different ways I can vote based on how I think other people are going to vote using instant runoff voting and the simple payoff function, my expected value is maximized by putting one devil first, then angel, then then other devil. So, separating the clones. Like voting for the clones together is not a Nash equilibrium. Even though the other two voters put the clones together, the two devils together, it's not in my incentive to do so. I'm I have I'm incentivized to like game the system somehow to like pull the clones apart.

Why did this happen? Well, like basically like instant runoff is a very top-heavy voting system. Like who you vote first counts a lot. Uh your your second-place vote only ever matters if your first place is already eliminated. So, your first-place vote is very valuable. Uh this payoff function is obviously very like last-place heavy. Uh it only cares about who you vote last. So, by doing this sort of mixed vote, I can basically have my cake and eat it, too. Uh, where I can have the advantages of putting a clone first uh and impacting like which of the two clones is likely to win, if one of the clones is likely to win. By putting the red devil first, it's like really likely to be the red devil. Uh, and by putting the purple devil last, I can kind of take advantage of like the fact that I think the clone

the the purple devil the devils in general are less likely to win than the than the angel. Uh, so like already I kind of want to have one of the devils last. And by putting the red devil first, I have sucked away winning chances from the purple devil so that like really there's not so much chance the purple devil wins. Uh, so that's not great. Uh, so uh in some sense like even though instant runoff was a clone independent voting system, it's not resistant to these kinds of manipulations once you include economic economic incentives. Uh, however, we have a serum that's in the the paper that I submitted for the proceedings there uh that in like a very fairly simple case with that very simple power function before, all the same sit setup except if you change the voting system for a different voting system called ranked pairs, it's

another famous voting system. Uh, like then this doesn't happen. Uh, now voting the clones together is a is a weak Nash equilibrium. Uh, so like this setup, you know, even though the incentives are the same, I just changed the voting system is more resistant to these kinds of clones effects. Um, I think I'll skip over telling you what how ranked pairs works. Kind of running low on time. Uh, but uh it's interesting that ranked pairs was the voting system that was originally proposed by Tideman uh when he was writing about clones. Uh, it's sort of like when he was trying to like come up with like what's a clone resistant voting system, like that's that's what he was thinking about. Uh, and even though there are other voting systems that are clone clone resistant, uh this this

ranked pairs voting system that um like was designed with clone in clone independence as like a motivating property is somehow like maybe more clone resistant. It has these like it has these new clone resistant properties that like it's still holding this kind of economic setting for blockchain articles. Uh so generally uh before I showed you this giant table of like different properties and different trade-offs in voting systems, I think that in this field we can expand that table uh and have like columns for for blockchain oracle voting properties, the kinds of things we'd want in being resistant to kinds of manipulations and attacks in the world of blockchain oracles. Uh and here, you know, we have these like two notions of clone independence. Uh like the classical voting system clone independence and

this like do you are you incentivized to separate your clones? How well does my system hold up when I have clone options and economic incentives? Um so just to conclude, um we saw that clone options have different impacts in sort of governance preference voting versus the incentive voting that we have in the world of blockchain oracles and consensus algorithms. Uh and that interestingly, even when you like have a fixed payoff function. Everything's the same and the only thing you change is the voting system, uh that can change stuff. Uh and it's not just enough for that voting system to be clone independent. So there are these like very subtle interactions between voting systems and payoff functions uh that I think there's a lot of space to explore.

Uh so maybe I can take some time for questions. >> [applause] >> I take the mic in case you guys have questions. Yes. Could you hand it up? Hi. Very good talk. Thanks. Um I had a question that I wasn't quite clear about one point. You have this signal that's coming through to the voters.

Where does that signal come from? So in the world of of blockchain oracles, we imagine that there's this like information that you know, like an observer could see, but the blockchain consensus algorithm could not see because, you know, it's not like saying whether someone default like saying whether it like rained in a given place or whether like who was right in a commercial dispute. These kinds of informations about like things that you can see off chain are not available to they're available to to observers.

So basically it comes from from reality. In the case of Kleros where I have like a a dispute resolution platform, it's an oracle related disputes. Basically it's a matter of looking at who like the evidence of a commercial dispute and making up my mind about who I think is is right in that dispute. Okay thanks. Any other questions? Yeah, thank you so much for the presentation. I was wondering like based on which criteria do you select the properties of the mechanism that you would want to favor in your in the system.

So can you can you elaborate like Because you said that different voting systems have different properties and then the question would be like I mean for each particular use case based on which process or like based on which method do you select the mechanism or the properties that you're looking for? Is it purely a trade-off between the properties that you're looking for or are there any other approaches to this? Yeah, I mean it depends somewhat on the like the setup that you're in. So for example, you're already in the world of of like clone resistance. Like how much how much do I care about clones as as a property?

It sort of depends on the the setting that I'm in. In political elections, if I'm deciding whether I prioritize it or not, like if it's really easy to get a candidate on the ballot, then you probably care about clones more because it's easy to like have an attack where you okay, I only need like 100 signatures or something to get my name on the ballot and I can like flood the ballot with all these like similar candidates Uh, um you know, that might impact how the how the how people vote in that election where as if the threshold to get on the ballot is really high, it's like, okay, I'm only going to have like three or four fairly distinct candidates anyway, clone resistance isn't so important. Um, so whereas the other properties in the table have different kinds of manipulations, you know, things about

like if I do um, like if I keep my first place vote the same, but I like uh, change options later on in my vote, like what impact can that have? If I like move an option up, like you know, like option A wins, you know, I put it third place out of five, and then I move it to second. Uh, it would be weird if that causes option A to lose, but you know, in some voting systems that happens. Uh, and uh, it winds up being sort of like a UX question for your voters in in a in real election or your users in a blockchain oracle that like what kinds of manipulations are they going to like find natural? What things are they going to be like cautious about and like anticipate, maybe I shouldn't do this because I realize there's there's some

effect. One more. I thought that you wanted one more, sorry. Thank you, great presentation. I really liked it. Um, how do you see voting system interacting with AI agents? So that you feel like will um, um, I mean, of course, voting is uh, cumbersome for humans. Uh, it takes time consuming, you have uh, status seeking uh, behavior as well. Uh, like just other works of politics but just on chain. How do you think AI agents can can help with that?

Yeah, um, so we definitely think that AI agents will be voters in systems like this. Uh, the the sort of question is whether the voting theory when the voters are agents is different than the voting theory when the voters are humans. Um, I'd say that's an interesting open question. Uh, we've run some experiments on sort of past Claros data where we gave past cases to a bunch of LLMs and we saw the rate at which they vote voted for different options. Uh and they winded up they winded up voting fairly similar to human beings. Uh they disagreed at the same rate as human beings like among each other and with the human beings.

Uh and uh I mean there were there were sort of like some interesting differences uh but um you know, it at a first approximation it seems that all this theory is like probably going to be relevant whether the voters are are AI agents or human beings. Um in uh how much you care about clones, well, sort of depends on like what kinds of disputes you're having, what kinds of questions you have. Uh and particularly uh for AI agents I can imagine that we'll have a lot more like to kind of like small commercial uh disputes where like one AI agent is paying another AI agent. Uh and uh these like kind of like task disputes have actually not been so common in in Claros so far. We've more had like disputes that have winded up being binary for for various reasons.

Whereas like if you're an AI agent is hiring another agent, you may it's more likely to have the things that are sort of what I was showing where like Alice bot is hiring Bob bot uh and you know, the question whether Bob bot deserves more time is is is is is like very relevant. Uh so in those disputes like clones are are more important. Like you know, whether like it's basically it's hard to say but probably the theory applies similarly. Thank you. More questions?

I have a final one from observations in voting design. Uh for some reason humans tend to be very focused on the voting rule. So I have never seen a system where the voting rule was defined based on the ballot. And um I mean it you're also pointing in a direction where um why don't we define the voting rule once we have the ballot? End case by case. And here I think agents make a huge difference because they simply adapt. They can use whatever voting rule. Whereas this I don't know how it works at Kleros. I guess you have a very well-defined

system with a dedicated voting rule. I don't know if you even offer alternatives or if you have different cases, different voting rules. How does this work in practice? So in V1 we have a fixed voting rule. It's actually plurality. Uh but uh in V2, which is now in beta and is gradually becoming live, uh we uh allow different modules which have different voting rules for different types of cases. Uh so uh but you still would generally pick the module that your case is going to use uh before there would be a dispute. Um like the idea of like having people vote or, you know, like the dispute's already live and then picking the voting rule, you know, it's going to be potentially hard to do that in a decentralized context uh where like in some sense you maybe you like pick a

voting rule at random. You have like a bank of voting rules and you pick one random. That that could potentially work. Uh and could suppress strategic behavior. Um but um like if the people have to agree if the parties in the dispute have to agree on the voting rule when there's already a dispute, that could be complicated. Sure. All right. Thanks so much, William. Another round of applause for this awesome talk. And next on stage is a talk by Eleonora Okene Gado. He is going to talk about legitimate overrides in decentralized protocols.

This is also related to governance, but um we chose this talk because it