 My name is Kirsten Elliott. I'm the director of philanthropy at the center for election science and for those of you who are unfamiliar with our work we are a non-partisan non-profit dedicated to empowering voters not politicians by equipping you with a better ballot and really that just means that by using better voting methods like approval voting you can benefit from fairer more representative elections. So today you have joined us to hear from the mastermind behind approval voting professor Stephen Brams and so we're really grateful that he joined us today and he will be interviewed by our board chair Felix Sargent. So just a couple of housekeeping items before we get into the discussion. So everyone should be muted if you become unmuted for some reason I will mute you and please try to stay muted that way we get good audio quality. Once Felix wraps up the discussion portion where he's asking Professor Brams of his questions that he's prepared we'll go to you all for some questions and when we do that we'll ask that everybody just have one question at a time. Ask your question and then I will mute you and then Professor Brams will answer. If you have other questions in the meantime you're welcome to drop them in the chat and if I can answer them I will if not we can try to get to them during the Q&A portion as well. As one final note we are also recording this and we will be putting this up on YouTube so if for some reason being on a recorded call makes you concerned now is your chance to leave. Okay that is all I have as far as announcements I'll be moderating the questions at the end like I mentioned and Felix take it away. Okay hi everyone my name is Felix Sargent I'm the board chair of the Center for Election Science and I am pleased to be joined today by Stephen J. Brams. Stephen Brams is an American game theorist and political scientist at the New York University Department of Politics. Brams is best known for his techniques involving for the techniques of game theory public choice theory social choice theory to analyze voting systems and fair division. He's one of the independent discoverers of approval voting as well as the extensions of approval voting to allow for multiple winner elections to give proportional representations of different interests. He co-wrote the book Approval Voting in 1978 which I happen to have a copy I need to have you sign this and with that one of the first questions I wanted to start off in some ways we're all here because of the work that you have done and the fact that you published this book and you looked into it how did you discover election science what originally turned you on to the topic and and how did you discover approval voting? Well my original field in graduate school was international relations so I worked in that field for a few years after graduating I worked for the office of the secretary of defense and for a non-profit agency called the Institute for Defense Analysis so I was really working in national security international security issues and then after a stint in the defense department and with this nonprofit I began teaching as a visitor at the University of Rochester and I began working with William H. Riker who was the kind of founder of mathematical political science and he was primarily interested in American politics and I got interested in voting and voting theory and what we call social choice theory so he really turned me on we actually wrote an early article together on log rolling in congress and we wrote some other things too so that's how I get started I also like mathematics I went to MIT as an undergraduate and had a lot of science and math like Bill Poundstone who interviewed a few days ago so was interested in applying mathematical thinking to our understanding of voting and elections. Very cool I have to ask what is what is log rolling? Log rolling is when congress people for example trade votes so you care about a particular issue I care about a different issue we agreed to vote for the issue of the other person if he'll vote for our issue okay and that's actually practiced in congress these days. Yeah it absolutely makes sense and I wish it practiced a little bit more so we could get some things out the door. So when Arrow's theorem came out I don't have the date for when Kenneth Arrow ended up publishing his paper was it before or after? Yeah it goes back quite a few years. And so the practice of studying game theory and voting systems had already been created why do you think it took from around 1950 until until your discovery for us to say like hang on a second if we give people just you know pick all the options rather than than ranking them why do you think that that was a big job? First of all it wasn't my discovery alone approval voting goes back to the election of pokes by the Cardinals in the 13th century so the Cardinals gather together and they can vote for as many other Cardinals as they like so that's the first use of approval voting that we know of. A more contemporary use is by the UN and choosing a secretary general countries vote for as many of the candidates as they like so we have precedents as to the use of approval voting that predates my work so I was picking up on these ideas but not really knowing very much about the history I actually started out as an advocate of negative voting whereby a voter can vote either against a candidate or for a candidate but not both but that turned out to be more limiting than approval voting because if you think about it voting against a candidate if there are three candidates is equivalent to voting for the other two or you can just vote for or approve of one candidate but when there are four more candidates approval voting gives you much more flexibility you can approve of two for example which you cannot do with negative voting so approval voting was a natural generalization of negative voting which I first wrote about and I talked to people who introduced me to some of these ideas and then at a conference in South Carolina in Hilton held around 1970 I met my later co-author Peter Fishburne and we began working together on approval voting and that culminated in the book Approval Voting in 1978 and the second edition came out a few years ago it's published by Springer. Very cool. One of the questions I keep on asking myself is with approval voting being so simple why do we use plurality voting by default you know do you imagine that in some theoretical world someone has said like okay rather than everyone pick your favorite everyone pick the ones that work for you and then just all of democracy takes off on on that level that wasn't just a fluke. I wouldn't say all of democracy there are very different systems including proportional representation systems which are largely used in European countries and a few other countries but it's a good question it's a kind of history of science question why did most people fixate when electing a single winner on plurality voting voting for exactly one rather than approval voting I've already given you a couple instances where people organizations decided there might be a different way the popes well the Cardinals voting for a pope and the country's voting for secretary general so people had this idea it was floating around it was in the air so to speak but Peter Fishburne and I I guess were the first to really formalize the idea and give some of the history and then there's more history more recent history which I wrote about in a subsequent book called mathematics and democracy designing better voting and fair division systems and that was published by Princeton in 2011 so that's more a more up-to-date treatment of the history and not only approval voting but variations and approval voting whereby for example you elect more than one candidate which we can talk about later yeah um one of the things that I'm very excited to ask you about um is how do we compare voting methods against each other especially in in your work I think a lot of the things that you know we as as an organization that proposes you know advocate you know we go on advocate for approval voting as a system people always you know want to compare and contrast it with other systems how do you decide that approval voting is you know one of the better systems to use and how do you compare and contrast them so that's another good question and what voting theorists social choice theorists usually do is ask what properties it has that distinguishes it from other systems for example one property which has been prominent in the literature since Arrow's theorem is a Condorcet criterion after the Machete de Condorcet of late 18th century France and he proposed that the candidate to be elected should be the candidate who can beat every other in pairwise comparisons when they're more than two candidates so A against B A against C and so on and if A beats all the other candidates we call him the Condorcet winner the problem is one problem is that the Condorcet winner does not always exist because one can get it to cycles A beats B beats C but C comes back and beats A so who's a winner if each candidate can beat other candidates but be beaten himself or herself so that's an example of a criterion we asked the question does an election system always find the Condorcet winner but there are other criteria such as doesn't encourage people to be sincere versus strategic and probably there have been about 30 or 40 properties of different voting systems that have been proposed and theorists generally ask which ones they satisfied what I consider a very important property is simplicity and I think approval voting is the simplest of all voting systems including plurality voting plurality voting is obviously simple in the sense that you just have to choose one candidate but approval voting in a sense is just as simple because if you don't have a clear first choice then why shouldn't you be able to indicate that more than one candidate is acceptable and that might be easier for people than singling out one candidate as their choice when they're really relatively indifferent or have different reasons for voting for or approving of multiple candidates what do you think about recent attempts to rather than divide voting systems into their their types and the criteria as they fulfill but to instead assign them to a uniform score such as Bayesian regret or voter satisfaction efficiency well some of these criteria don't always take into account the game theory aspects they're what we call decision theory criteria and they don't take into account the fact that voters may strategize and not necessarily vote for a favorite candidate if we're using approval voting but for a candidate who can they think win so they ignore the candidate they sincerely most most favor in order to try to be more effective in getting an acceptable candidate elected and what I think makes approval voting stand out is that one doesn't have to be usually strategic one can vote sincerely for a favorite he or she might be a fringe candidate so it's not going to win but then you can vote strategically for the next acceptable candidate who might be more viable and can win so in a sense you have your cake and eat it too you can vote sincerely and if the sincere vote is unlikely to be the factual vote strategically by approving of a more viable second or third choice this really gets into the dichotomy between ranked versus rated systems where very often I'll hear people who are advocates of rating systems to say well but I do have preferences and those preferences are important and so you know I want to make sure that I express those preferences fully and the you know saying to people well you can sincerely vote for this person but you'll also sincerely vote for this person seems incompatible to them and and in that framework yeah people often want to express preferences and they have a first choice they have a second choice they have a third choice and the rating systems we also call them scoring systems allow a voter to do that the problem is not that you are not the problem is that you can express yourself perhaps better with a scoring system but how do you aggregate the scores you can add them up for example but that's not always satisfactory so and there's another problem that one runs into if there are three or more candidates so you're maybe effectively casting two one and zero votes for your best your next best and your last choice and adding them up then you can get into the cycles which I alluded to earlier that the candidate who comes out at the top can be beaten by another candidate who can in turn be beaten by another candidate and there's a cycle and how do we resolve that cycle and that actually is a basis for arrow's theorem which is one of the famous results and social choice and voting theory that no system can can necessarily find the best candidate just being defined in different ways another way of putting it is the following there's a kind of incoherence when there are three or more candidates that causes these cycles and what arrow show is suggesting five reasonable conditions no system can satisfy all of these but he was applying this to ranking systems that effectively score voting is also a ranking system so rating systems ranking systems are vulnerable to arrow's paradox however when there are only two options to approve and not approve there are no cycles the candidate who is most approved beats every other candidate in pairwise comparisons so this incoherence that you find with multiple candidates in rating them or ranking them disappears with approval voting so yes it sacrifices some expressivity because you can't rank candidates but when you aggregate them you don't get into these incoherence problems that you do that's governed by arrow's theorem so would you say that and especially taking the philosophical implications of such a thing that express expressivity can actually be a detriment to a voting system allowing people to fully map their preferences can lead to unsatisfactory outcomes isn't there just ultimately at some point there's just there are 10 candidates on a ballot and this candidate's going to be the best uh i'm not sure what you're asking sorry um you were saying that one of the advantage so it you made it sound as though arrow's theorem also applies to things like score voting and and and um yeah when you have when you have two options uh one of the two candidates it generally applies whether you're scoring them whether you're ranking them um you get into these problems of incoherence or uh Bill Poundstone said the other night that things can be chaotic so small changes can result in big effects so you don't want that you want a system to be more fluid continuous uh and approval yes go ahead would you say in that scenario that you're actually some people might argue that you're denying choices to voters um is that is that the case that we're limiting voters options to be able to describe their preferences or are those preferences being moved somewhere else well i would argue that you can't express intensity uh indirectly with approval voting so let's say there are five candidates um and you like one or two so you can express yourself for those one or two you can't rank them you can't distinguish them but let's say there's a candidate you despise uh then you can approve of everybody else the four other candidates so in effect you can indicate intensities by where you draw the line between acceptable and non-acceptable candidates and where the gap is biggest is probably uh where you make this distinction and i think that's allowing you to express intensity uh which in a way uh just ranking candidates uh does not allow you when you just rank candidates and using something that's called the border count where you get points to the candidates um you can't in this case where that biggest gap is uh you just have to uh rank them and uh i think that's a that's a problem so simple as approval voting is it allows you to express yourself quite well without getting into these problems and paradoxes uh that they follow ranking systems and rating systems i'd like to step back and ask you a question a little bit of a different track some of your other work that you've done uh you discovered the first envy free cake cutting algorithm for an arbitrary number of people who are going to be eating this cake or or cutting the cake and then eating it have you ever seen that algorithm used at a birthday and how did it go uh no but i've gotten pictures from people who have you this or tried to use it it's a very complicated algorithm it's a it's a theoretical result um the first theoretical result came in the 1940s in the area of cake cutting that was an existence theorem which is non-constructive which means it's not a step-by-step procedure an algorithm that actually allows you to physically cut the cake with our algorithm which we call the trimming procedure you physically cut the cake but then you might have to paste pieces together so it gets very complicated so we're not recommending this as a practical system on the other hand what came out of this work on fair division were other procedures one for example called adjusted winner and that was patented by my university and why you and was licensed to a boston law firm that does dispute resolution over the internet and that's one reason we i call this newer book from cake cutting to dispute resolution this newer book on fair division because this is actually a very simple system using points and when people have difficulty dividing things such as a marital property and a divorce we think the system is actually applicable so the most general theoretical results on cake cutting led to more practical procedures algorithms that are actually used and we think therefore that this ties in to what i try to show democracy strives for i think there are two essential features of democracy free and fair elections which is all about voting of course but rule of law and due process which is all about treating people fairly equally so this work on fair division i think complements the work on voting because it hits upon the two features of democracy which i think are essential excellent and and do you find that the entry free component works well where uh you know people have left it and said like okay no more cake this is fine yeah when you get down to crumbs people don't care i have seen people fight over crumbs well then you you continue the procedure the basic procedure is you just repeat it so when you get down to crumbs and people are not satisfied then you get down to specs because you divide the crumbs so the so the procedure eventually uh goes to allocating all the cake but it takes a it may take an infinite number of steps so that bothered computer scientists especially and eventually they came up with a procedure uh that does the job completely us does it completely but it might take an infinite number of steps uh so that was an improvement upon average yeah yeah envy has no comparison to sheer boredom where people are like okay fine done well it means envy in this literature means that you think somebody got more than you did yeah so that's why you envy them and i think envy is a very difficult problem to solve because i think all of us at some time are envious of other people or what they have or their looks or something like that so if we can get rid of envy or minimize it then i think we make the world a better place that's that's wonderful i like that i wanted to talk to you about the current state of the movement obviously you know lots of things are happening we're getting ready for fargo to have its first election hopefully if the situation clears up by then and we've just recently found that st louis missouri has placed approval voting on their ballot for the election that's coming up for them probably the presidential election so i mean you know big changes from you know when you first published your book how do you see the movement going well i made an effort to get get approval voting adopted so in 1980 i went back to my home state of new hampshire new hampshire as today is the first primary state i would as caucuses as you know that's somewhat different and i thought if i can get people interested in adopting it in new hampshire that would give it a lot of publicity and might encourage other states to copy it so i so the prodigal son me returned to new hampshire and tried to convince the governor i spoke to him testified between a house and senate committees in the new hampshire legislature which is called the general court and the largest newspaper in new hampshire the majesty union leader also did a story on this but the bill never got out of committee but i wasn't ready to give up so i tried to publicize this in other states i eventually ended up testifying before committees in vermont in new york and bills were written but they didn't go very far and one reason is that i think most politicians are gun shy if they got elected under the current system why should we change and i remember talking to the assistant majority leader of the new york state assembly the kind of house in new in new york and he said well i won with 80 of the vote in the last election because this is a very liberal district for him and he's also jewish it's a very jewish area and he said with the approval voting my opponent would have probably gone from 20 to 20 percent but then i would have gone from 80 percent to 90 percent approval so we both would have gone up and it wouldn't matter so i think this is a good attitude would it help me and generally of course approval voting helps the candidates in the market in the middle because they tend to get support from both the left and the right if we're talking about a unidimensional system along a single spectrum and that was something that i think led to considerable opposition we don't want to try anything new things have worked pretty well for us in the past so it was trying to get people out of this attitude so i would use stories like well when you choose a movie and go out with friends how do you make the choice and when you go to restaurant the same problem which restaurant should we choose and i suggested that it's really approval voting implicitly that what's most acceptable to the most people so making these simple analogies i think is convincing that why shouldn't we adopt this in a voting system so my experience was mixed i wasn't particularly i wasn't successful in getting approval voting adopted in any jurisdiction city of south states but what happened was that when the people saw some of the theoretical work they became interested so several major science and engineering societies did adopt approval voting usually after considerable discussion so today the two major math associations the mathematical association of america and the american mathematical society both adopted approval voting in the 1980s and 1990s the operations research society management science also adopted at the american statistical association adopted it so societies with tens of thousands of members adopted it and a generally elected candidates who were widely acceptable for example in mathematics there had not been a woman president of one of the major math associations before but when approval voting was inaugurated the first woman was accepted now she might not have been the top choice of many people but she was generally acceptable and probably members felt that it was time for a woman to be the president of this math association so that's a little more history on the progress approval voting is made not through public elections as the ces is doing now but through a private election so it's pretty widely known in some of these societies and certainly in political science and political science and the social sciences i was less successful i could not get the american political science association or the international studies association to adopt it but scientists and engineers have a mentality which says this is very logical why shouldn't we be using it so in the end they adopted it or if they were using a different system some were using effectively rack choice voting the american mathematical society uh it was too complicated even the mathematicians uh so they decided to adopt it i also found a problem because one of the rules stated in casting your ballot says if you can rank all candidates you should you shouldn't just vote for a first choice you should give a complete rank order and i found a counter example and if there's anything mathematicians believe it's a counter example to a statement because the statement is therefore not true anymore uh so i think that also helped uh in getting this particular adoption by mathematicians what was the what was the counter statement uh the counter statement my counter statement was really an example showing that it was not true sometimes that uh you can do better by indicating only a first choice and not giving a complete rank right absolutely um one of the things that's come up in in the work that i've been trying to do in my own area and you know i'm on the board of not a member of the staff of the center of election science but i am trying to do what i can to get approval voted and acted uh in the bay area in open where i'm based and uh the fascinating thing is how many cities don't have directly elected mayors but instead have a city council that is elected and the city council is often elected at large uh which for you know those listening in meaning that everyone cast their balance if there are three seats open then they get three votes for you know out of the 10 candidates but then the the top three people that get those votes win which has obvious downsize as i'm sure you'll explain but you've also been a bit strong advocate for multi-winner systems which makes sure that there's proportional representation how you know how have you felt your work evolved to go into into multi-winner systems nowadays and is it something that we should focus more on well i think if you're interested in reform or say city councils or selecting better committees more representative committees then one can adapt approval voting for that purpose but you don't add the votes in the usual way that the person with the most approval then the next most approval wins to get proportional representation you have to use an algorithm such as uh the first candidate elected is the approval voting winner the second candidate elected uh will be the one who gets not necessarily the most approval because when you um when you add up votes and let's say you're a voter who voted for the first candidate and he or she got approved your vote should not count as much in getting a second candidate elected so it's discounted say by 50 percent and the more and more of your candidates are elected the less and less your vote counts because you already have representation so that's the idea behind proportional representation systems the most common system is the so-called jefferson method but also in europe goes by the name of dot and it basically is discounting votes of voters who've already gotten one or more candidates selected and that tends to give you a proportional representation that is parties get seats in proportion to their numbers of votes and you wouldn't get that by just adding up approval votes um so that's already existing um and our innovation i guess uh was to show that look there's a problem here because um should i vote for um the shoo win if the candidate who's obviously going to be elected going to get elected but then i'll be wasting my vote shouldn't i vote for somebody who's uh less certain to be elected and forget about the person who is surely going to be elected uh so one can use approval voting in the same way one uses a single winner elections that you can approve as many candidates as you want if you're electing let's say a committee um but you aggregate the votes differently um and in the case of electing parliaments in most european countries uh you don't vote for candidates you vote for parties and you want the parties to represent the numbers and you do so using these kinds of methods um and the latest innovation i alluded to was that uh you if the candidate is elected with an excess of votes then you transfer the excess to other candidates he or she approves of and it gets a little complicated i admit but there are computer programs that can do this now uh so if you're thinking about reform or um councils or committees and electing a representative set of candidates then i think this is a way to go and it's just really an extension of approval voting and so um uh so you were saying there's uh you know block voting which is often what we have right now for councils but we can use approval voting um or reweighted approval voting or proportional approval voting as a system and then uh if we want an even better method we can use the excess method which is a paper that you had recently published is that right not published it's still being reviewed still being reviewed but if you want copies we can email you for for a copy go sure sure okay um and uh one of the things that's very interesting about um multi-winner systems especially in in california we have uh the voting rights act uh sorry the california voting rights act says that like if there's any kind of minorities which are you know excluded from the city council that they need to reform and the bill explicitly recommends uh switching to district based methods um and in fact in fargo and in st louis um they already have districts for their elections and we we are using approval voting with uh within those districts how would you you know uh how would you evaluate you know should you have approval voting with districts or um you know instead use a true multi-winner proportional system okay well i think if minorities are scattered throughout the electorate uh then you don't want to use districts uh because districts uh generally serve the purpose of helping minorities because the minorities tend to be concentrated in a few districts uh so new york city for example adopted districts several years ago when they lost at the level of the supreme court that said there was a violation of one person one vote the equal protection cause of the 14th amendment and i was involved there was an expert witness um in that particular case uh in the brief that the new york civil liberties union uh filed and eventually got to the supreme court so supreme court ruled that because minorities were not necessarily well represented in just single in the average of voting they could be in a sense drowned out we should go to districts so we have districts now um and that's worked well enough because minorities are somewhat concentrated in different districts in new york city um but when they're not uh when minorities say a 20% majority is scattered over all the districts uh then you're probably not going to elect any of them because the majority is going to prevail uh overall so it depends i think on the distribution of minorities if you want proportional their proportional representation when um uh so the proportional representation systems um i think the the there are a large range to choose from how do you evaluate the complexity that's involved in having a a system trying to explain to people how you know how the the mathy bits of having it um divided off as i had to in front of the san bruno city council uh their eyes kind of glazed over you know how do we educate people that these systems are fair while they're so not simple uh well you promise that there'll be a computer program that does all the difficult calculations but you have to explain the i don't know if that helps no i don't think it does that's what makes this approval voting pretty easy because you don't need a computer programs to do the telling usually uh except to do to keep account of things but some of these systems do get kind do get complicated the pr systems proportional representation systems uh which we call apportionment systems like hamilton and jepperson and webster they all have different ideas about what's best so you again look for properties that they satisfy those are the criteria for making a choice so one system may give you proportional representation and another be slightly off this is true in the apportionment literature but you may have other criteria which kind of balances so it's a complicated subject like voting and one has to dig into the details so i don't think i can summarize uh these no i i understand the hard thing about asking hard questions and uh for for my last question um the you know we talked a little bit about districts um but i know you're also focusing on gerrymandering and a lot of that kind of is the same same question of of how do we you know talk about representation when we also have to talk about geography um tell me about some of your current work on on gerrymandering well there's actually a very good film i saw about a week ago um that stream called slay the dragon and it chose the huge distortions that gerrymandering can make so um a party can win more than 50 percent of the vote in states and get maybe only a quarter of the seats in the legislature it's a big problem and uh the republicans were very successful uh after two 2010 in gerrymandering several states so that's why they're quite dominant in state legislatures especially a state like wisconsin uh in which a majority voted democratic so um mathematicians have gotten into this in a big way and have uh developed criteria for determining the degree to which a state might be gerrymandered it's not necessarily crazy lines you can make pretty straight lines and still gerrymander uh that's one of their findings what i proposed was um the following system which is pretty simple actually um you look at the congressional vote in the last election say in 2018 and let's say in a state it was 55 percent democrat 45 percent republican um and it was roughly that in pennsylvania um but uh republican were prevailing until recently um so you let each party um get its proportion of seats there were 18 seats this is for us house the us house in pennsylvania and um that means if it's 5545 that the majority party the 55 party gets 10 seats and the minority party gets eight and you divide the state so that it's um got that proportion uh 10 to 8 5 to 4 and you got uh the majority party gerrymander 10 seats and the minority party uh gerrymander eight seats so you divide the state uh proportionally and then you got each party gerrymander it's pot um that's not an ideal are you making the state into a cake at this point yeah there's a little relationship to that and we use some geometry to talk about how you divide the state into uh we use a version of i cut you choose uh in one case um but having done that then um it's really a pragmatic solution you'll allow each party to gerrymander part of the state so that's much better than having a party uh like the republicans in 2010 gerrymander a whole state and get uh far out of proportion to their uh of the seats in proportion to their uh congressional vote so that's the um that's the solution i propose i even call it fair gerrymandering that might sound like like a can't contradiction in terms but it's fair in the sense that each party gets its proportion to gerrymander makes sense all right and with that i'm going to hand it back over to christen for us to be able to have some questions from the audience perfect well thank you both so much for an exciting discussion so far we've had a lot of questions come in the chat um i'm going to take a couple of questions from the chat while i let people start raising their hands so if you go over to um the control bar on the side you should see an option to raise your hand and that's how i will know to call on you and if you raise your hand i'll unmute you and let you ask a question one question uh to professor brems and if you have another you'll have to get back in the queue all right uh one of our first questions was from callan weaver and callan asks what are the weaknesses of sincere voting systems i'm not sure what a sincere voting system is most voting systems are manipulable and you can vote in sincerely even with approval voting uh so i'm really saying there's no system that encourages you always to vote sincerely but some systems are less strategic inducing than others and i would say approval voting is at the top of the vest it's more difficult to manipulate approval voting than it is practically any other voting system okay perfect i see a hand that it's someone i actually was about to read a question from so i'm going to pitch it to david rosenberg and let's see if i can unmute you there you go david i think i just got on mute so the question is actually the same one i asked in the chat that is i don't understand how with average score voting cycles can occur can you explain how uh average score voting could produce cycles that would be difficult without an example but i have examples like that in an article called the paradox of grading systems published about a year or two ago in the journal public choice no that was published about five years ago called the paradox of a grading system so i think you can find the calculations there i don't have a simple explanation but basically the idea is you can get into these cycles where uh a you get an ordering like abc in terms of the grades adding up the grades across all voters but when you try to determine the condor say winner the one who can beat everybody else you get a cycle rather than a single winner so that's the paradox so that's not a good explanation but you can check the details in the paradox of grading systems felix and i both dropped that into the chat so if you're interested in learning more that's available for you there all right um again if you would like to ask a question raise your hand otherwise i will keep reading through the chat uh jeff wants to know is anyone using multi-winner approval voting yet uh no not that i know uh it's really i think a new idea and a number of computer scientists have written on this um but i don't know of any uh anybody actually using multi-winner approval voting okay we have another question live i will unmute you now go ahead and ask a question oh is this this is me yep it is you yeah thanks um i'm wondering you know you're looking at different kind of systems there's board account there's condor set there's approval voting um one that you haven't mentioned is the possibility that you might give voters more than one vote uh let's say they had 10 votes they have five votes and they can allocate all of those votes to the same candidate or distribute it among two or three candidates seems to me that that would give you uh the possibility to share more information than just approval voting has what's the rule on that one what have you got to say about that actually has a name it's called cumulative voting that it's used in a few small cities in the united states pure illinois um americadero new mexico um and it's designed to give minorities proportional representation in the following sense the minorities can throw all their votes say 10 votes each on a single candidate if it's a 10 minority they assure themselves of getting that say one representative elected the problem is that it's difficult to coordinate voters on voting for a particular candidate or two or three candidates but in these small cities it has given a proportional representation to minorities so it's another pr system but it has certain coordination problems because you have to have sufficient discipline to get voters to focus not on electing a whole council but electing their proportion of council members great okay we have another question in the chat uh this is from jonathan he wants to know he said you were originally in favor of negative voting have you written anything about why you changed your mind uh yes uh i think i mentioned negative voting uh in the first article in the american political science review with peter fishburn uh and why approval voting is more flexible because basically approval voting can do everything negative voting does and more uh so if you in the case of four candidates uh approve of two uh you can do so of course or disapprove of the other two but with negative voting you have to make a choice for whom do i vote against which of the two do i vote against so that's why we abandoned negative voting and went for approval and they're they're equivalent in the three candidate case for the reason i mentioned voting against the candidate is equivalent of approving of the other two but there are three more than three candidates uh they're not equivalent and approval voting gives you a much more flexibility okay and i'm going to take a moment for moderator privilege here to ask jonathan's follow-up question because it's linked uh he also asked what do you think of combining the two called combined approval or balanced approval voting with approved neutral disapprove ballots well you're talking now if you have disapproval as well as approval of not a two-tier system of grading but a three-tier system of grading uh because uh presumably you can also neither approve nor disapprove so you really have three levels of approval um approve uh neither approve nor disapprove or disapprove and that gets you back into the problem of possible cycles uh and incoherence which approval voting with only two tiers uh prevents okay great um i am not sure i'm going to say this right but keith no i'm going to unmute you now so you can ask for question hi um yeah sorry that's it's keith edmunds it's my name but mushed together when i wrote that out apparently anyway um so in multi-winner PR systems do you think approval ballots carry enough information to do the proper reweighting for subsequent winners or should score ballots be considered like if somebody voted uh only was so so on somebody they could that might count for like as much as if they were very strongly in favor is that in that situation we want more information well again uh that's getting to the incoherence problem and cycles uh with multi-winner as well as single-winner elections um i think it would be a sufficient innovation to say in uh i think you know a country like germany let's say germany actually has a pretty good system which i could say something about but okay let me take another example almost any european country uses proportional representation and you don't vote for candidates you vote for parties and when you vote for parties uh you're often uh conflicted because let's say uh you are more conservative you want to vote for the christian democrats but you're also an environmentalist you want to vote for the green party so the ability to vote for the green party and for the christian democrats is a big innovation and i think that's as far as we probably should push this rather than worrying about how much you weight the green body versus the social the christian democrats uh so that's why i prefer to take the step of just allowing approval voting and not different but weightings okay call in had a question in the chat the call in asks it seems clear that no voting system satisfies all hypothetical issues but in practice what are the biggest observed empirical shortcomings of voting systems already in use today that's a big question because there are several different methods here yeah well i think the biggest problem with plurality voting which we use today is that spoilers may upset elections and uh i think the best example a recent example is the 2000 election in which 537 voters uh were effectively electing um bush in florida rather than goa but if the native voters the uh liberal voters uh had been able to approve of a second candidate they for the most part would have gone with goa or over bush and would have had a different winner in florida and that would have been a different president beginning in 1980 or 1981 um so i think that's an example of a big failing of our current system in the united states the electoral college complicates this of course and i could say something about its biases perfect all right um we have another question in the chat where can the most progress be made in moving away from the simple voting systems we have what are the most effective things individuals can do to make progress i think education is key and uh i think in the case of approval voting it's pretty easy to educate people to think in terms of uh not one person one vote which artificially restricts you to voting for one candidate but uh i actually would change the slogan to one candidate one vote and make a judgment about each and every candidate is he or she acceptable so you just go down the list and check off those who are acceptable um that seems to be just as consistent with the idea of equality being able to express yourself um equally as artificially restricting voters to casting one vote why shouldn't you be able to vote for as many candidates as you like if you consider uh to a more acceptable and you may consider them acceptable for different reasons i pointed out earlier you may have a sincere choice but a sophisticated choice who can actually win but you may be genuinely genuinely indifferent between two candidates and for different reasons the environmentalist stands versus the centrist stance of these two parties i mentioned earlier so that seems to me uh something that voters can be educated about and be convinced perhaps that a change is necessary great um katlyn who is one of our colleagues here at the center for election science has a great question she asks is there an argument to be made that approval voting increases representation for women people of color and other minorities i don't think we have empirical evidence of that yet uh because there are relatively few studies surveys or certainly elections uh in which we can put data together that says that but one point i haven't made which i think is important is that approval voting would tend to uh draw out centrists which uh who are not drawn out before so i think that the democratic primaries and caucuses that we've had this year uh we've had many more women candidates because they think they can they have a chance now it doesn't look like a woman it's almost certainly a woman is not going to be the democratic nominee but a woman is going to be the Biden wins the vice presidential nominee now approval voting did not have an impact in this particular case but i think when the candidate feels he's a centrist but he's going to get hit from the left and right then he can rest assured that that's not necessarily going to be fatal because candidates on the left and right can also approve of him or her now an example of that i think would be uh Mayor Bloomberg who of course ran unsuccessfully for the democratic nomination but he didn't run in 2008 and uh he didn't run in 2016 because he thought he would be taking away from the democratic candidate and he would split for the democratic candidate if there had been approval voting i think Bloomberg probably would have run in both 2008 and 2016 and may even have won as the moderate between uh the democrat and the republican i mean now he's a democrat but uh on the conservative side so i think it's going to draw new candidates in who otherwise would opt out and i think that's important then some of these candidates are likely to be women thanks for that question katelyn all right uh we are approaching six o'clock but professor brams said he's happy to stay a little bit later if anybody has any additional questions so if you do i'm going to give you just a couple of minutes to either raise your hand or drop your question in the chat uh while i'm waiting on that i did want to let you know that if you have any general questions about the center for election science or opinions or just things you want to share with us on friday we're going to be doing what we're calling a team town hall which will be another zoom meeting but it'll be a very informal discussion and you can join our staff and ask any questions or share your feedback with us so we'd love to have you join us there's a registration link in the chat now all right we have one more question from amy brown would you implement approval vote approval voting for both the primary and the general election uh certainly for the primaries because as uh 2016 and 2020 demonstrated we can get 20 or more candidates running and therefore their vote tends to get quite finely divided and we're not necessarily going to elect the candidate who's most acceptable to the most voters and i think that uh has been proven more or less in the 2016 election uh trump it appears could have lost to uh moderate republicans in a one-on-one contest and uh i think that is often the case and uh it's i think quite unacceptable so it relates to spoilers and this is why the strongest candidate doesn't win and approval voting largely eliminates and he largely eliminates the effect of spoilers uh and i gave examples of that great uh keith i see your hand raised i'm going to go to a couple of folks in the chat who haven't had a chance to ask a question um first we have tom tom would like to know would approval voting be integrated into the electoral college or would it be a national popular vote great question well i favor national popular vote uh and if we get the national popular vote then i think we can then go to approval voting especially if there are more than two candidates running which i think they're likely to be just as we see in primaries um and i think we're not going to get the national vote by a constitutional amendment because that's very difficult to enact uh but uh there is this new idea of what that uh states can vote for it for a compact and if states with a majority of electoral votes vote for the compact to institute voting for the national popular vote winner then the national popular vote winner wins and we don't need a constitutional amendment it's kind of an end run around the constitution to get uh the national popular vote winner elected and i think it's important because we've seen in recent elections at the national popular vote winner uh in nineteen in 2000 uh that was gore and in 2016 that was clinton lost and i think the electoral college is an anachronism that definitely should go and at least 70 to 80 percent of americans feel that way so maybe we need a device like the national popular vote plan to do it so just let me explain the idea that states enact a law that says instead of casting all their electoral votes for the um popular vote winner in the state they cast their electoral votes for the national popular vote winner so if the states with a majority of electoral votes pass this law it becomes enacted that's what the proposal says and therefore we automatically elect the national popular vote winner but we're several states away from getting that majority of electoral votes and it's all democratic states who passed such a law so i'm not sure we're going to get there very quickly yeah and just to um tack on one little thing there to what professor brams was saying um the really nice thing about approval voting is that um obviously it's kind of getting to like there's no reason that it wouldn't work at the electoral college even if you favor national popular vote um the same can't be said for some more complex voting systems so that's a really nice feature there right but there's one point i want to make and that is if some states use approval voting and other states don't then you have to have a way of standardizing uh the candidates uh that use approval voting and basically would be i think their level of approval standardized to the number of voters in the state all right i'm going to unmute Keith again hi i'm a bit of a technical question um in your excess method you you say you favor the jefferson um sequential proportional approval voting over the webster uh rewriting scheme and i would start on the other side and and i would think about it as if you consider a two-seat race with two factions uh red and blue assume red is the larger party so it gets at least one of the seeds and the fraction of votes that red would need to get the second seed would be three quarters in webster so halfway between the half and the full amount of votes but it's two thirds in jefferson and this always seemed obvious to me that that makes it the correct choice is am i wrong in my math or is there another thing that i'm not considering right and there are proponents of the webster method which has a different name in europe and there are proponents of the jefferson method uh and each can make arguments there's a well-known book by bolinski and yang called their representation which says the webster method is most appropriate in determining the representation of states in the united states and the jefferson method in electing parties in parliament so their arguments are both sides that support one or the other of the two methods so the excess id i can be applied to either either you're going to get an excess of votes for the most popular candidates and you can transfer those to the other approved candidates and you can use at that point either the jefferson or the webster method so i'm not particularly arguing for the jefferson method the webster would also be i think applicable great looks like felix had a question felix do you want to just ask your question yeah i feel like it's unfair but i want to know is it possible for us to mathematically model the harm generated by the spoiler effect in a plurality voting could we actually put a dollar number on the inefficiency it creates oh i don't know whether you can measure these things in dollars i'm not sure uh exactly it's my economics agree talking okay uh i mean there are different measures of something like inefficiency but inefficiency in economics usually means that there's something better for everybody out there that makes something inefficient so i think we have to be a little more careful about how we define efficiency to make that clear okay um rudolf has his hand raised i'm going to unmute you now rudolf okay hello um so in most of these models like the ye diagrams that i've been seeing uh there's like this there's this assumption that the voting population on a political spectrum is normally distributed and so i guess my question has a a empirical and a theoretical component to it which is uh like is that assumption is that assumption curts uh a valid assumption even like even out if like plurality is a polarizing kind of system does itch is there empirical proof that uh that maybe there's a bipolar distribution with regards to the countries through the bipolar distribution uh for example israel uh there are two major issues that separate the parties uh and they're not necessarily coincidental the issue of socioeconomic development and the issue of national security and people don't necessarily align the same on these two issues and i think there are other countries in which uh there are there's more than one issue but for the convenience of modeling many theorists start with the uh unidimensional the single dimension assumption about the distribution of voters and uh often it's an assumption that it's normally distributed so it's um bell shaped um but you're right that that is not necessarily accurate all right does anyone have any last questions for professor brams before we let him go if you do feel free to raise your hand now or drop it in the chat and just one more sorry john john howard willhelm is raising his hand in oh in real life okay perfect thank you for letting me know john howard willhelm i am unmuting you and so nice to have you join us john uh thank you very much i would like to make a comment about uh several things if i may one is in uh two thousand uh september two thousand i submitted a uh op-ed to the financial times on uh approval voting and the american editor came back to me and said how about condensing it into a letter what they published at that point i thought that it might be a good idea to contact professor brams and to talk him into doing the same assuming that they would uh respect him much more than i got uh i think he did the same but it was the beginning of a wonderful of exchanges i've had with him over the years and i think he's done a real uh service to the nation by trying to raise this issue there there are a few thank you john a few points i would like to make one is that and is uh it's my understanding i believe professor brams knows this because he was copied in on the email exchange united russia in its single member uh primaries use the approval voting to elect its candidates they're open primaries uh that isn't generally explained in our press and the russian voting system gets very negative things as a result of it but on the issue of getting of the uh electoral college and getting around the constitution i don't think you need to get around the constitution article one section 10 and i'm i'm just summarizing the relevant part says no state shall without the consent of congress and then it says enter into any agreement or contact with another state that means it is part as i've been maintaining as a uh congressional act to institute approval voting in our elections congress can also authorize the states to engage in an interstate compact that would be constitutionally valid i think that's possible uh i don't think it's likely um so that's why i think the states are doing this on their own and the hope that it survives constitutional challenges if uh states with the majority electoral votes enact this national popular whole plan which i hope is the case i think they're about 60 percent there um but it's all democratic states uh so i don't think the chances are great that it will work but it's an it's a new idea which i think is worth airing and um trying to get started because i think getting a constitutional amendment is near impossible that abolishes electoral college people have been trying for over 100 years i'm seeing a couple more questions come in now um that i missed earlier colin asks how does voting reform possibly remain non-partisan in today's political world uh i think approval voting is a non-partisan reform it's not geared to help a particular party it might help uh the republicans in one state it might help the democrats in the other but what it will encourage is centrist candidates to run uh a bloomberg for example in 2008 2016 and i think that's an important feature because many of i think the most eligible and most qualified candidates don't run because they think you have to be relatively extreme to win in primaries and i think approval voting would largely negate that review and uh i i think therefore it's actually likely to make politics less partisan okay i see let's see there's one more question in the chat i see and then rudolf has his hand raised um so i'm going to call it on those two questions uh if you have more questions after this i hope that you will join us for our team town hall on friday and we'll try to get to those um so before i call on rudolf keith asks i've heard the access method is not clone proof is this true we actually didn't investigate that question it's a good question i think we have to look into that that's a technical question i think that uh needs some uh serious thinking great and uh i also put in the chat if you're interested in keeping the conversation going particularly if you like voting theory uh we have a room in our discord where you can discuss these topics so we hope you'll join us there uh rudolf i'm going to let you close us out with your question okay this one should be a little simply um um if uh do voting system would a voting system so if plurality is polarizing would uh would approval be able to depolarize the political views or is that more of an empirical question that needs uh that doesn't have enough info yet i think approval voting would uh unpolarize the electorate because uh it would tend to induce uh candidates who are centrist to win because they could better win under approval voting than they can under plurality voting so if you're pushing more centrist into the race uh you're i think uh making views less polarized so i think that's a good reason why uh approval voting would uh help in that regard and i think this is a big problem today uh there are red states and uh blue states and not so many purple states and i think there'd be more purple states that could go either way with centrist candidates great well again thank you all so much for joining us professor brams thank you so much for discussing all these topics with us and taking all these questions um as i mentioned we have a bunch of events coming up um we're really trying to provide a lot of virtual programming for you all so in the next couple of weeks we'll be doing some talks with folks from bargo north dakota you can ask them about what it's been like trying to get approval voting adopted there we'll be discussing open primaries and we'll also be doing some hands-on trainings for those of you who are interested in getting approval voting adopted in the city near you um we'll be doing some on how to start a chapter how to talk to folks about approval voting and we'll also be doing a letter to the editor writing workshop so if you go to electionscience.org slash events we'll have all of those there um any last words professor brams or felix well i appreciate the questions and uh i think if you have follow-ups that you want to uh you want to write me about then i would be glad to try to answer them um i'm at nyu new york university and uh my email address is steven with a v dot brams at nyu.edu perfect i just want to say um sorry i just want to say thank you very much um professor for for joining us in conversation it's been fascinating i've learned a lot and i want to say thank you so much for everyone who is here for for joining us for supporting the center for election science and here's to getting more cities and maybe even states and hopefully the country to start using approval voting absolutely and if you want to i would not be doing my job if i didn't make the pitch that if you want to support our work in more ways in the chat there is a leak electionscience.org slash donate help us bring approval voting to the next american city or state thank you all again for joining us have a good night and stay healthy bye