Politics transformed? Electoral competition under ranked choice voting with Peter Buisseret

Transcript

we are super excited to continue governance week we have our last two talks today we're going to be deep into the uh mechanics of voting with a lot of interesting implications for web 3 and we're delighted uh to have Peter Boer here from the government government department at Harvard to talk to us about instant runoff voting thank you Peter great thanks very much Andy uh and thank you all very much for an incredibly uh stimulating week that's really broadened my horizons so I'm going to talk about instant runoff voting today just a quick word about terminology some of you may have heard the term rank Choice voting uh used in the US political discourse what they're talking about is what I'm describing today and since I know there's at least one Englishman in the audience I'll also

say that uh the alternative vote is equivalent to what I'm describing today so before I describe how it works and I will give you an illustration let me just give you a sense of where you might expect to see it in traditional elections as well as in web 3 so instant runoff voting I contend is the most rapidly expanding and controversial electoral reform of The Last 5 Years in the United States there's about 13 and a half million voters using it in traditional elections to elect uh offices ranging from local state and federal so notable examples since we're in New York uh include the 2021 Democratic mayor all primary which rolled out instant runoff voting to select Eric Adams to be its candidate

and uh some elections in Alaska which now uses Instant runoff voting for federal Offices as well as for the G uh the the gubernatorial race and I'll talk about uh Alaska quite a bit as a running example uh it's been banned in Florida there's some contention uh about the consistency of instant runoff voting with a state constitutional requirement and I'll comment on that later too um but it's become like so many things quite a partisan uh uh sort of debate um but it's widely used in the US and continues to expand uh it's also used in fact in web 3 so uh ens in September of 2022 uh the token holders approved uh a

proposal to create an endowment out of Treasury and to put out a request for proposals for an endowment manager that vote approved for a working group to select the endowment manager without further participation by token holders but uh the group actually narrowed down eight proposals to three and put them to a final vote of the token holders using instant runoff voting the final three plus an option none of the above uh and maker also uses Irv for its governance polls okay so it's been rolled out in both traditional and web 3 contexts so how does it work I'm going to describe the process you're going to find that description a bit confounding so then I'm going to illustrate it with

an application from Alaska so the goal of instant runoff voting is to select a single alternative from a set what we're going to do is ask voters to rank the Alternatives according to their preference in some applications will compel voters to rank every alternative on the ballot in others will allow them to rank as few as they wish if any alternative commands a majority of first preferences that alternative is going to be chosen and the election concludes otherwise the alternative with the fewest first preferences is going to be eliminated and we'll proceed to a second round of counting in that round we'll keep using the first preferences of candidates who haven't been eliminated but we'll go to the ballots of Voters whose first ranked candidate was

eliminated and see who was second ranked and will award that ballot to the corresponding candidate if anyone has a majority the election ends otherwise we proceed sequentially uh using each voter most preferred alternative from the set of Alternatives that have not yet been eliminated so at some point by construction an alternative will secure the support of a majority of ballots that have not been exhausted so some voters may have stopped ranking after the first candidate those ballots will be tossed away once that first preference is eliminated okay now if that's a little bit confusing let me give you an example from Alaska in 2022 so there was a special election in Alaska for the single congressional seat

following the death of the incumbent and there were three candidates in the general election ballot Nick begic comes from an Alaskan political family of Republicans uh Sarah Palin who I presume needs no introduction and Mary pela who was the Democratic candidate and what am i showing you on this column if you look at my first column I have a ballot that was submitted that ranked begic first followed by Palin second followed by Mary pela or which ranked begic first followed by Palin and failed to rank pela those two ballots are equivalent under the rank under the mechanism and what this tells me is that 27,0 53 voters submitted such a ballot okay so some voters may have only submitted uh a

first preference in favor of a single candidate and how are we going to how are we going to figure out who wins the election so the first thing we're going to do is sum over all the first preferences that were awarded to each of the candidates so all three of first three columns have in common the proper see that begic is the first ranked candidate and that sums to nearly 54,000 we do that for the rest of the candidates and we see that Mary pela wins a plurality of first preferences but she doesn't manage to secure a majority so we eliminate begic who won the fewest first preferences and we proceed to a second count in which pela and Palin continue to win the first preferences of Voters who ranked them first but we now look at the ballots cast in favor of begic we look to see

where pela was ranked second and we award these ballots to pela and in that second round count pela once again wins a majority of non-exhausted ballots there was some votes obviously that didn't flow to either of the two candidates because these votes ranked begic first and didn't Express her preference over Palin versus pela okay so hopefully that's that's clear much more attractive looking sanki chart for the Irv uh application in that endowment vote so in that case uh in the first round none of the above uh had a strong plur ity but over a sequence of rounds of elimination and the flowing of second preferences actually the alternative that came third according to First preferences ultimately won in the final

round against none of the above so Kaki eventually won and this highlights a feature of instant runoff voting that it can be very difficult for people uh to get their head around which is that an alternative that WIS sort of the most first preferences might ultimately not be selected through the mechanism the way I want to structure the talk I'm going to first describe what I call the Social Choice approach to thinking about electoral systems this will not contain any original uh insights from me and by social choice I mean an approach in which we fix a set of Alternatives we come to some agreement about normatively desirable properties of a voting system a means to aggregate preferences or information and we ask

which systems if any satisfy those properties and I'm going to give you a very practical uh aspect ECT of that I'm going to talk about vote splitting and the role of spoiler candidates in elections okay so these are kind of the key headline considerations that are important from this uh approach and then I'll talk about some original work that I've done with my co-author Carlo PR at Colombia which I'll call the political economy approach and I'll tell you more about that shortly so what is kind of the main appeal of Irv uh in terms of voting relative to a traditional plurality rule in which we would just take your first preferences and decide the election winner on that basis the key idea is that Irv can help to better protect latent majorities of Voters from splitting their votes in

ways that are harmful to them and what do I mean by that well imagine that we had taken the votes as cast in this uh ens election and we had simply taken the alternative that won the most first preferences obviously uh if your eyesight is very good none of the above would have won but exp poost a majority of Voters would have preferred for car to have been chosen why would it not have been successful because those who agreed that Kaki was Superior to none of the above disagreed about which of the remaining proposals they liked the most and they divided their votes and this sequential elimination mechanism sort of ensures the majority against that expost disappointment now as it happens uh this outcome has another very desirable

normative property which is that if we had had a pairwise vote between Kaki and any of the other Alternatives Kaki would have won one so in a very strong sense Kaki is a majority preferred option we call it the Condor winner under plurality of course it would not have been chosen so you might be asking well is that a property of which we can be assured in any Irv election and I'm afraid the answer is in general no and to illustrate that I can go back to my Alaskan example suppose that I had taken Sarah Palin off the ballot fix the behavior of Voters okay so presume that this is how they vote regardless of whether Palin is on or off the ballot and imagine that we just sum over the ballots in which a preference for begic

versus pelo is expressed and then we sum over the ballots for which a preference of pela over beget is expressed so we have a pairwise contest between those two candidates we see that Nick begic defeats Mary pela similarly if I had taken pela off the ballot and done the same exercise of a pairwise vote between uh begich and Palin begic would also defeat Palin in pairwise majority voting so bit was in fact the majority preferred candidate in this sense uh but Irv didn't use that information it solicited a full ranking of candidates but begic didn't make it to the second round because of vote splitting amongst uh the majority so you know Republicans divided their votes between uh begic and

Palin somewhat surprisingly uh the Republican candidates in that election some of them encouraged their candidates their voters not to rank the other candidate second so there was quite a bit of uh uh of sort of animosity between those candidates and so a lot of people who who ranked beget first ultimately did not express a second preference what I want to make very clear is that fixing the behavior of Voters the outcome of this election would have been the same under plurality a point not necessarily appreciated in the aftermath of the election so what you talk you allude to discussion after the election what was the narrative that emerged after this um the discussion was let me let me sort of summarize it

horis my my reading of it was people said how can we be electing a democrat in Alaska and uh because Irv was still kind of it was as far as I believe it it was the first congressional election in Alaska since uh Irv had been implemented it was sort of viewed as a progressive plot that would be my that would be my summary so um you know as I say the presence of Palin on the ballot was probably the reason why uh pela one in both the August election and surprisingly enough in November when there was a regular congressional election almost exactly the same outcome these three candidates vote splitting amongst amongst the conservative leads to the election of Sarah Palin through exactly the same Force so that's that

that's the discussion I think there's a there's just a strong sense that uh you know in a state that traditionally elects Republicans if we choose a new system and it doesn't elect a republican there must be something going wrong and there are versions of that across the Spectrum uh to be to be clear yeah there's a question at the back how often is this true at the B like my understanding is that most of the time in Practical elections the Irv doesn't make a difference that's correct so for some reason the number that comes to my head when you say that someone said they had looked at some elections over the last 10 years and it was something like 15% of cases it made a difference obviously in the Kaki example it made a difference but yes very often it does not make a difference to the outcome

okay but it could uh and that's a point that's not not kind of the desirability of it doing so is not universally appreciated yeah that's right but empirically it is pretty rare if you look at all the New York uh races that were conducted under instant instant runoff voting a very very small fraction hypothesizing that the voter behavior wouldn't have changed across the two rules uh the outcome is almost the same in is the same in almost all of those cases so what am I talking about the political economy approach so the social Choice approach emphasizes selection from a fixed set of alter natives we don't know how the Alternatives arose we presume they're there and we ask how should we make a decision what I'm going to call the political economy approach emphasizes

that alternatives are strategic objects they're chosen by interested parties for example political parties or individual candidates or maybe stakeholders that respond those choices to different strategic incentives generated by electoral rules now you might say well why are you Hawking the political economy approach first of all of course it's my Lively Hood but second of all uh many Irv enthusiasts in the United States believe that um the implication of introducing IV is that it will moderate the kind of proposals that candidates offer in elections and let me give you a kind of Fly by Night intuition for why they think that's true in a plurality rule election I as a candidate can only

benefit from the support of Voters who rank me first okay that's just a mechanical property of the rule that's a very demanding Criterion especially in polarized elections where bases are kind of aifi around candidates in an instant runoff voting election I can benefit from the support even of Voters who don't rank me first okay they might rank me second and their preferred candidate might be eliminated and so the intuition Loosely goes the ability to Win Second preferences should create an additional margin of competition that will somehow encourage candidates to reach out more broadly from from their bases okay so actually to address that you need to think about the strategies of the candidates and what I'm going to do today is give you a

very stylized model that I that we wrote for the purposes of this talk to ask is that intuition necessarily true and I'm going to show you that the conclusions from the social Choice approach the idea that protecting majorities from vote splitting is an unambiguously desirable thing may turn out to be falce okay so that's what I'm going to do next so here's a model this is what we call a just so model in the business so it's a model that is Con con structed around the goal of pushing an incentive that we think is very important to the four it's not designed to be a general conclusion about the nature of instant runoff voting okay so I'm going to make some impose a lot of structure and then we're going to we're going to solve the model so I'm going to have a unit mass of

Voters who have to make a collective Choice a okay and a is going to be a number between minus one and one the voters payoff so if I'm voter I my payoff can be decomposed into two components what you can think of as an IDE iCal component where each voter is going to have a preference type which we're going to think of as her preferred policy a subi and she's going to be more and more unhappy as the winning alternative is further away from her ideal policy okay so that's what this picture is intended to indicate and you can think of ideology in terms of progressive versus conservative um or you could think of it as something like how much concentration

of authority do I want in my organization minus one is you know web two and plus one is web 3 and we'll have an additively separable term which I'm going to call Quality which is designed to capture common value aspects so regardless of our disagreement on ideology we all want for example projects where the cost is lower it will be fine in our framework for you to think of the quality as belonging to the proposer who will implement the policy and then you can think about it as their competence and I'm going to assume that voters are differentiated in their ideological preferences and that they uniformly distributed Ed over minus one1 to get us further along in the analysis I'm going to assume that there are two proposals that are already on the table I'm going to call them X and Y very

evocatively and you can think of them as proposals that reflect the positions of established political parties so it could be there's the Democrats and the Republicans or it could be you know conservative and labor that have established their positions over many many electoral cycles in which they can't change in any given one or it could be that there are groups of stakeholders whose positions are well known uh and who have already sub proposals for a vote and I'm going to focus on the choice of a strategic proposer who's going to introduce a third proposal onto the table which I'm going to call Z proposer is free to choose any location she likes and I'm going to assume that her objective is solely to maximize the probability that her proposal is adopted okay so you could think of this as a third party

candidate trying to enter okay or you could think of it as you know a small stakeholder trying to introduce a third proposal into an otherwise polarized environment okay and I'm just going to fix each of the two uh existing proposals at minus one and plus one and I'm just going to set the quality of those proposals equal to zero I'll assume that the quality of proposal Z is a random variable it won't be known to the proposer at the time that she chooses I'll assume that it's uniformly drawn between minus one and one so you can think of Q as the quality of the proposal or indeed the quality the net quality over the two status quo Alternatives making it random just ensures that the outcome of the election ction is uncertain from the proposer perspective when she chooses policies

okay so the timing is that my proposer will choose her proposal again to maximize her probability that her option is chosen Q is going to be realized publicly observed and I'll assume that everyone votes sincerely that's not a trivial presumption in the three candidate election but let's put that aside for for now and then the winner will be determined under plurality and under instant runoff voting and my goal is going to be to try and use this framework to investigate this incentive to propose moderate policies under one rule versus the other okay so everyone clear yeah can you say for people what you mean by vote sincerely yes exactly so what I'm going to assume is that the ballots that my voter submit is a true

statement of their ranking so if you prefer Z over minus one you rank Z above minus one when you submit your ballot you don't try to strategically influence the outcome of the election by reversing the order of preferences when you submit your ballots thank you okay Peter is the model of with the linear preferences is the model of Uncertain quality equivalent to uncertainty about the medium voters yes you can do this exactly so you could assume that um you could instead have assumed that there's a mean of this distribution and the mean is subject to some aggregate uncertainty it was just easier to get through the analysis fast so this is this is the equivalent of stochastic veillance and

uh it just makes the outcome of the election uncertain that's exactly right good I also prefer this formulation because it's very clear what it means to moderate in a model where the ideological preferences of Voters are are known so that's just a stylistic preference so preliminary steps in our analysis the first claim is that it's without loss of generality to look for a best response of my strategic proposer from zero up to one why is it without loss of generality there's a lot of symmetry built into this model and if and only if some Z in zero or one is a best response then minus Z will also be a best response remember minus one and one they're at the same they're kind of at opposite ends of the spectrum they

both have the same quality so I'm just going to look for an optimal Z between 0 and one and in parentheses if I find such a a z remember that minus Z and plus Z will both be best responses nice feature of this setup is that the decision of a voter to cast her first preferences is quite straightforward in particular if I'm a voter whose ideal policy lies somewhere between minus1 and0 I'm going to claim that the only possibility for my first preference is that either I like minus one the most or I like Z the most why is that the case minus one and plus one by assumption both have a quality of zero so they're equivalent in terms of this second uh component but minus1 is closer

to my ideal policy than plus one and so I'll always rank minus one ahead of plus one the only possibility is either that Z is close enough to my ideological preference that I like it on ideological grounds or the realization of its quality might be large enough that I'm prepared to accept it even if in spatial uh uh terms it's worse for me so if I'm a voter with an ideal policy AI between minus1 and zero my first preference will either go to minus1 or Z and by the same argument if I'm a voter with an ideal policy between 0o and 1 my first preference will either go to plus one or it will go to Z I haven't said anything about second preferences yet second claim I'm going to be able to identify for any choice of Z and any realization

of q a cut off type of voter between minus one and zero possibly at the boundaries such that the first preference decision rule is to vote for the alternative minus one if my ideological type is to the left of that threshold L and to vote for Z as my first preference if my type is to the right of that threshold and I'm going to find that by looking for an indifferent type a voter who is exactly indifferent between those two Alternatives and I'm going to get a formula for that and just as a sense check if Q were realized to be zero okay so that all three proposals were equivalent in terms of quality the indifferent type is just the midpoint of the two platforms remember voters have these symmetric loss functions okay and

obviously as Q gets bigger and bigger this guy is going to get pushed further and further over here because there are more voters who are willing to support Z despite its inferiority in terms of ideology because the quality realization was more favorable and again I'm going to find a threshold which I'm going to call R such that a voter with a type to the left of R and to the right of zero will support Z and a voter whose type is closer to one on the right side of R supports plus one same logic okay if Q is equal to zero that cut off type is just the midpoint between the two platforms and as Q increases it's going to push further to the right so you can think of L and R as kind of Swing voters they're the kind of marginal preference

type that demarcates the support for Z versus each of the two more extreme proposals so finally we can start asking the interesting question so what is the optimal proposal under a plurality rule mechanically it's going to be the one that maximizes the probability that the alternative Z is chosen which means the alternative Z getting more votes than each of the other candidates on the table okay so what does that mean all we care about is first preferences what is the vote share of of alternative Z it's just the CDF of all the types between R and L so those are the ones who are supporting Z remember that my ideological preferences are uniform so it's just R minus L / 2 and that's going to have to be greater than or equal to

the maximum of the votes uring to minus1 all the types between minus one and L and all the preference types between R and one quick phase of algebra and we're going to get not surprising a threshold on Q is a function of Z above which the alternative Z is chosen so my problem thus is to uh minimize this constraint to make it as undemanding as possible I want to make that threshold Q as small as possible if my goal is to win and why must that imply that the optimal choice is zero suppose I start from zero and I move my proposal z a little bit to the right there are two effects I move this swing voter further to the right because I'm appealing more

on ideology okay so I'm making a voter who was previously indifferent between myself and one at a given Q now strictly prefers me so that's good in the sense of helping me to defeat one but I'm tightening the constraint on defeating minus one because I'm also moving this voter this indifferent voter type further to the right this was now this was a type that was indifferent between me and my opponent and now I've upset her by moving away now she strictly prefers minus one okay and to balance those two incentives I want to put my proposal smack bang in the center where each of the two constraints on winning is exactly as tight as the other okay so Z equals z is my best response voters are uniformly distributed right we

didn't have a this is always what's going on a because the support of the distribution of Q is so big that I'm running up into the the boundaries so there is an implicit presumption which is correct that at the threshold where the candidate wins both L and R must be interior to minus one and Z respectively and uh Z and one respectively so I know that at the threshold I know I'm not for example in the situation where R is strictly to the right of one but no so so I've got Z at zero and I'm I'm getting I'm getting I'm getting all the voters between L and Q that's right and now I consider a marginal move to the right that's right and L and Q move the

exact same amounts exactly right we have uniform distribution that's right and I'm still getting everybody in between those two that's right but it's the extremes that I'm changing so in a two candidate election yeah the vote share that I'm getting is the same actually with the uniform because I'm you know I'm waiting them by the density but the density is the same but as I move to the right I'm also increasing the votes of this person at the rate at which I'm decreasing them for that person and so those two forces are pushing me in opposite directions in terms of winning out against the most demanding of those two I see and I'm getting in expectation of getting a third of the vote the Symmetry that's exactly right that's exactly right uh good so what do we see from this and by the way I'll show you

what the planner would choose so if someone just wanted to maximize the welfare of all of the voters in this model I'll tell you what they would choose uh uh in in a minute but moderation is the name of the game in fact under plurality the reason is that in some sense the threat of vote splitting is quite dangerous for candidate Z it might be that Z is majority preferred but as she moves further to the right she's opening up the opportunity for L for minus one to win uh and she knows that she can't count on the support of any voter between R and one okay those votes for R and one even if these voters prefer Z to minus one they can't express that in the ballot uh and so vote splitting is quite dangerous and it's a form of discipline

and that's a theme that I'm going to return to later on so what about instant runoff voting what is the optimal proposal under instant runoff voting for sure the alternative Z is not going to win if the alternative minus one gets a majority of first preferences remember that under instant runoff voting if anyone wins a majority in the first round that alternative is going to be selected otherwise the candidate with the fewest first preferences will be eliminated and her second preferences will be redistributed so a necessary condition for Z to win is that this cutoff Type L had better be to the left of zero cuz if it's to the right it means that everyone between minus1 and 0 is voting for one and it's winning a majority so necessary condition is that

this cut off Type L be strictly less than zero and I'm going to assert that's equivalent to the condition Q is bigger than something a function of Z it turns out and here I'm going to wave my my hand and say trust me that whenever that condition is satisfied I know that plus one is not winning a majority okay because it could be that plus one wins a majority uh in which case you know I also lose but I know that under the conditions that minus1 fails to the alternative plus one doesn't and Z is in a very privileged position in the sense that anyone who supports either of the two extreme Alternatives with respect to First preferences will give their second preferences to Alternative Z by virtue of the fact in some sense that it's the

moderate alternative okay so what does this tell me what is z problem Z just needs to be chosen to kind of maximize the probability that minus one fails to win a majority and Z gets at least the second highest share of the vote in the first round getting the second highest share of the vote in the first round and denying minus one a majority is sufficient to trigger a second round in which Z has to win it's going to get the second preferences of anyone who supported the alternative that was defeated okay so we have now a necessary insufficient condition Q strictly larger than Z minus one and if you remember under plurality the only difference with

this expression is that we had a Max here because under plurality you have to get the most votes when you enter in between the two alternatives to win here you just have to get you know not the strictly fewest votes okay and this is the key difference so vote splitting is very problematic to the cist alternative under plurality no problem under instant runoff voting instant runoff voting is kind of ensuring the proposer against the risks of vote splitting by helping to coordinate the majority around her in the second round of counting I'm going to argue that this creates a bit of a an indiscipline which will ultimately be harmful so rewrite this condition and now instead of a Max we have a Min and if I'm going to look for the Z that minimizes this constraint

that again makes the threshold Q above which I win the election as slack as possible is to choose Z equal to 1 12 and what's notable about this is that it's exactly the opposite of the intuition that I proposed or that I've filtered for you from other other proposals it suggest that IV is encouraging the proposer to choose less moderation than under plurality how do we compare these rules and which one is better let's let W of Zs denote the average payoff under rule s so either plurality or instant runoff voting when the proposer chooses Z so the idea is you know fix the rule pick a particular Z write down you know for every possible quality realization who's the winner and

what the associated payoff of each voter is average over quality average over all the voters that's welfare and then compare those two across the two rules Insight one is that if you just give me a fixed alternative and I'm going to call this the social Choice insight for any fixed Z it is always better in terms of average payoffs to use instant runoff voting versus plurality and it's exactly the social Choice Insight that I highlighted earlier instant runoff voting protects the majority from vote splitting and it helps the more moderate proposal to beat out one of the more extreme proposals okay so fixing the you like instant runoff voting more however the bad news here and I'll comment on robustness in just a second is that that conclusion reverses when

you evaluate average welfare under each rule at the proposer optimal choice so if I evaluate the welfare under plurality at the choice of zero and I compare that to welfare under instant runoff voting at the proposal's optimal choice of 1 half the value reverses why there's a direct and an indirect effect the social Choice Insight is in this calculation so you know fixing the proposals instant runoff voting is creating a boost to the more moderate proposals chances of winning but there's an indirect effect which is that the proposer is taking advantage of that to make the moderate proposal less moderate because the proposer knows the only way she can benefit from second

preferences is if she defeats the candidate who's holding them okay so the more General kind of force that's going on here is the proposer says the fact that I Cann your second preferences doesn't mean I need to go after them I can only benefit from those second preferences if I defeat you in the first round of counting so now my problem is not to kind of make sure that I stop minus one from winning a plurality my problem is to defeat proposals whose supporters are likely to rank me second in order to benefit from this dividend of second preferences is this the right comparison so you've you've written a model where you're forcing a third a third party candidate to enter and I think like a standard kind of thought would be under plurality rule

where where they can't get better than a third of a chance of winning right entry is like it's very hard to get a third- Party candidate to enter whereas under Irv where they can get a high probability winning it's true they're less moderate in equilibrium but you're going to get way more entry um and you've stacked the deck in some sense by forcing entry 100% so a comment I was going to make um but you've exactly anticipated is suppose that you now wanted to build on top of that the alternative not to propose in the first place and suppose that uh making a proposal is costly okay so whether it is indeed costly we probably depend on the application but certainly in the context of electoral systems one of the reasons that third parties in the UK are quite fond of instant runoff voting the liberal democrats for example

uh made a condition of entering coalition government with the conservatives the holding of a referendum on it is they think it makes it easier for them to kind of run candidates and have a chance of winning imagine that there was some cost of Entry such that the candidate or the proposer is only prepared to place Z on the table if the probability of winning is big enough that will generate an interval of costs where under plurality Z will not be chosen uh and under Irv Z will you will enter and you will have this more moderate proposal and then things get a bit trickier but in fact even in this setting uh the assumption that Q is uniformly distributed on minus one to one heightens the rhetorical power of this example because indeed it is the case that payoffs are worse under

instant runoff voting but in general there would be a trade-off between the indirect and direct effect and the force that you're highlighting would just stack more in favor of the direct effect which is we want to stimulate entry so I completely I completely agree my claim is that this is more of a Sandbox for an intuition on which you can you can have exactly these kinds of insights you can think about strategic entry exactly as you suggested final nugget uh which I didn't anticipate but which I think is quite interesting you might ask the question if my goal were to to uh maximize average payoffs by choice of Z under each of the two rules what would I want to choose now the choice of Z is zero is kind of very appealing in the sense that it minimizes the average loss okay so from a in a spatial sense Z

equals z is a really good compromise and indeed the planner would choose Z Star equals z under plurality surprisingly at least for me the planner would not choose Z Star equals z under instant runoff voting the planner would like the would indeed like the proposer to shift her propos a little bit to the right okay to take advantage of getting those second preferences and helping the moderate proposal to be elected and the planner would be willing to trade off the degree of moderation in order to give even more of a boost by helping this proposal to defeat plus one okay however the planner would not want all the way to one half okay so it's still the case that the proposer is choosing kind of too extreme in a proposal

relative to what would be chosen in the first B best so in the final moments let me just uh of quickly give you some want say insights but maybe Reflections on instant runoff voting from traditional elections that may have some relevance for web 3 considerations so one thing I hear a lot and I've heard it this week is that participation is a big problem uh and one of the arguments made by proponents of instant runoff voting is that it increases people's propensity to participate that somehow having more candidates I can rank gives me a higher sense of efficacy unfortunately the evidence does not favor that so the elections that we have turn out has not increased after switching from plurality to instant runoff voting another

interesting problem or kind of conceptual challenge is that there are extensive and intensive margins of participation in instant runoff voting in a plurality election you either turn out or you don't but in an instant runoff voting election conditional on participating if you have the option not to fully rank the ballot you also have to decide how many candidates I want to rank and if you're worried about inequities in participation and if you think that that intensive margin of participation also varies across different kinds of stakeholders then um your your concern might be justified so in that Alaska election that I told you about only uh you know two-thirds of Voters ranked more than one candidate and of those who only ranked a single

candidate 75% said it was because it was the only candidate I liked Carlo and I put a survey at the end of the mayoral election in New York and we got very similar results so many voters chose not to rank the candidates and they said oh I I didn't know who they were or I just didn't like them enough this audience probably will be aware that confusion about the system and indeed execution errors can create a lot of space for doubts about legitimacy so you may remember that during the uh first round of results for the New York mayal race the New York Board of Elections released results prematurely there was some test ballots kind of bundled in and uh it really shook a lot of faith in in the operation of the system it was an example of an election in which the

candidate who won a plurality in the first round ultimately won a majority but had that not been the case uh there could have been a lot more blowback I highlighted that strategic voting might be a consideration so there are incentives when you have three or more candidates to sometimes uh submit a ballot that does not reflect your true ranking of candidates for example in Alaska uh if you wanted to help uh Mary pela win you might have thought that one of the two other candidates had a better chance of being defeated by her you might want to have ranked that candidate first to help them get into the second round where you believe that your preferred candidate would win so those incentives exist but it's really hard for voters to figure out what to do

there's some experimental evidence I can talk about one novel feature of the Dow applications that I highlighted at the beginning is that you have public voting over a period of time where you can see how the results are shaping up and you have the opportunity to revise your vote uh before the end which is something I you know don't see in real world elections or traditional elections but is a very interesting feature and more broadly Thinking Beyond instant runoff voting to voting rule choice in general I think there are two features of design that are often conflated but which should be conceptually distinct the first is what information do we want to elicit from voters what do we want to learn about their preferences that's what we would call ballot structure in plurality we just ask you to give us the most

preferred alternative preferential voting methods which include but are not limited to instant runoff voting you know effectively ask you for all pairwise rankings okay you submit a list and another some assumptions about the structure of your preferences that list conveys all the possible information that you could give me okay all ordinal information a second question is how should you use the information that voters submit to choose a winning candidate okay an Irv puts a big wedge in between one and two because it elicits all this information about pairwise comparison that is ultimately discarded by the aggregation mechanism and there are ways uh to modify and fine-tune instant runoff voting that would fix some of the pathologies I

described earlier okay so there are there are very simple ways to change instant runoff voting that are on the table that would kind of do better in at least some applications with respect to point 2 and so my view at the end of the day is that in the traditional world of Elections Irv reflects a kind of compromise between the parsimony and the Simplicity and the transparency of the principle of plurality voting that whoever gets the most votes uh wins versus perhaps a desire to make more use of the information that is revealed by ballots okay and without knowing exactly where that trade-off should go in web 3 my feeling is and this is just my view whatever you think that trade-off

calibrates to in a traditional election my feeling is that web 3 could go more in favor of two could do more kind of fancy things really because first of all the participants to these elections are quite sophisticated reading the discussion that followed that vote uh people had some very very sophisticated ideas about why the system might work and some of its shortcomings and then of course the obvious one is that execution is a lot less error prone when it's done through smart contracts so thank you very much happy to take any questions now or afterwards and thank you again for such a stimulating week [Applause]