 if you decide to sign it, too. There's a lot of things, but I'll just let you talk. So Steve Jobs, the chair. Thank you, my head. Thank you for organizing this session, which is five other speakers, and we're each going to speak only 10 minutes, one virtual, and the other four here, besides myself. Because this is billed as an historical kind of retrospective, I want to say a little bit about the history of approval voting. It goes back a long ways, when it was not called approval voting, back to at least the 13th century, because hoax were elected using approval voting, and seemed basically to still be so. If you don't know what approval voting is, it's a voting system in which voters can vote for or approve of as many candidates as they like. And the candidate with the most approval wins. So besides the election of hoax, it's been used, for example, in the election of the Secretary-General's of the United Nations and in a number of societies. So I'm briefly going to recount my history and some of the places that are using approval voting, and then the other speakers will supplement. So I became acquainted with something called negative voting proposed by somebody named Bohm, the OVHM, who was referred, who Oscar Morgenstern, who had retired from Princeton, referred me to. And he wrote a little paper on negative voting. And the idea was, with negative voting, that you could vote against a candidate, or you could vote for one of the other, too. But it doesn't generalize for four or more candidates. And about the same time that I was thinking about negative voting, I met Bob Webber, who will speak a little later, at a conference at Cornell in 1976. It was actually a workshop. And he had come up with the idea and the name of approval voting and went on this. And then I went to another meeting, subsequently at Hilton Head Island, where a number of social choice theorists came together. And then Peter Fishburne there, who was a, and still is, an eminent mathematician who's worked on voting and social choice and many other things. And we agreed to collaborate. So we wrote an article in 1978 called Just Approval Voting, published in the APSR. And then in 1983, we wrote a book called Approval Voting. And did quite a bit of analysis of different aspects, which I don't have time to talk about now, and promoted approval voting. I guess I'm more than Peter. And we got adopted in a number of professional societies. I first tried to get it adopted in New Hampshire's presidential primaries in 1980. I'm a native of New Hampshire. I went back. Particle sun returns, but I wasn't received all that well. Although I did testify before House and Senate committees in the general court, the legislature of New Hampshire, I spoke with the governor, Manchester Union leader, ran stories in atorials. So I got a lot of publicity, but I never got out of committee in either the House or the Senate. So I was unsuccessful there. But then other people, particularly mathematicians, became interested, and we eventually got it adopted in the two major professional societies of mathematicians, the Mathematical Association of America and the American Mathematical Society. There are stories behind that, and Jack will probably tell something about the biggest society he looked up. But then, we dig a lot of approval voting was the IEEE Institute of Electrical and Electronic Engineers. So those are some of the societies that were adopted at the beginning in the 1980s. And it seemed to work well. And then, what comes out of the woodwork in a situation like this is those who think they have a better system. So Don Zairey, David, the board account, and wrote about that. We had an exchange in the late 1980s on the board account versus approval voting. And other people have proposed other systems like the hair system, a single transfer of the vote, and there's an organization called Bebo in Washington that promoted that for 25 or so years. Jack is associated with that. And therefore, there's competition as to who can reform a system which is basically, in my opinion, broken, using basically plurality voting, the person with the most votes wins. So more recently, there has been discussion of what if we want to elect more than one candidate. So there's no work on multi-winner approval voting. So the aggregation of approval votes is not the same as with single-winner approval voting. Mike Gilgore will talk about that. And then a number of people elsewhere have gotten interested, particularly in France. So they've been experiments with approval voting, which asks people how they would vote under approval voting right at the polling places. And those have shown that there may be significant differences. And we've also done some retrospective analysis of poll data to show how approval voting might have worked if it hadn't actually been instituted in some important election. We talked about some of that early on in our work. That's a signal at five more minutes. There's also been opposition to approval voting by more recently, a couple mathematicians, Polinsky and Larakie, French mathematicians. And they've argued that the winner should not be the one who gets the most approval. It should be a kind of median. And it's a little complicated to explain the definition of a median winner because there may be ties in who gets the most votes. But the argument is that the median is less vulnerable to manipulation. And that's probably a good thing, but it's a little complicated to explain. And I definitely do not recommend approval voting in electing more than one winner because the, let's say, the five-member council that is being elected might be, basically, cones of each other when, presumably, in a council and a legislature, one wants a diversity of opinions. So that's why I think it's useful to think about different ways of aggregating approval votes. So it's still basically the same simple procedure. You just have to approve and not approve the candidates. But by aggregating them in a different way, approvals in a different way, one can get that diversity of opinion in a council which approval voting generally would not give if it were used straight. Okay, so that's, very briefly, a little background. And I must say that the societies that we have tried that have not seen approval voting as a guiding light are mostly social science societies. Political scientists, including the APSA and international relations specialists, including members of the ISA, I'm going to the meetings tonight there, have not seen fit to use approval voting to elect presidents, for example, though the more scientific engineering and math societies have. So it's not a tidalist success story with these kinds of societies. Let me conclude by saying that in our book in 1983, Fishburton and I predicted that approval voting would become the election reform of the 20th century, just as the Australian ballot, the secret ballot, had been the reform of the 19th century. Well, the century ran out on us. And now we're hoping in the 21st century that approval voting not only survived, but thrives, and is more widely adopted and used because I think it's a natural system in choosing candidates in multi-candidate situations. And now I think the recent work on multi-winner systems indicates that it has a bright future there as well. Okay, let me go on, and I think we'll take comments at the end. So the next speaker is Ma Kilgore, who will talk on the multi-winner aspects, I believe. I should say that I was around in the 1980s. In fact, I knew Steve Graves around the time that he was starting to work on approval voting. And the only actual academic contribution I made of that type was a book review. Graves' official book. But gradually I got involved by some time, around 2005 or before I was working with Steve and some others on multi-winner electoral systems, which have really been quite interesting to me since then, there is one of the reasons for approval voting becoming popular is that it's something called the Handbook on Approval Voting, which was published in 2011. In that, in 2010, in that, I contributed to a chapter called, Approval Voting for a Multi-winner Elections. Since then, I've been a kind of poster boy for approval of a multi-winner. I should say that I think I've probably, I may not be very good at that, but I'm certainly better than I am at this being technical help. We'll show a couple of my own slides in a few minutes. Let me say that when you have a new idea, it is important for that idea to kind of continue to grow and develop. I think that using a approval voting for a multi-winner elections, this is probably one of the big, big ideas for approval voting. It's a general context. If you're having an election at which there are only two candidates, there's not a lot that should be done. If you have an election in which there are many candidates who don't be one-winner, well, that's really what all the article is about now. That's what approval voting was designed for and there are many competitive systems for running such elections. Now, multiple winners adds a whole new dimension or maybe many different dimensions. It's not, it's not obvious exactly what the problems are, it's not exactly, it's, there are certainly examples of people who just went ahead and used a multi-winner, used approval voting and multi-winner elections without thinking about it very hard. They ran into, as Steve described, the clothing problem, tyranny of the tour. And some of this is still going on. But I think gradually it will come to be seen as a problem. I hope it will, because I think that it doesn't help the approval voting in such a broad way, which it is if it's a multi-winner election and just counting the pros. There are, in fact, in a situation that is somewhat more subtle than you might expect. And I would kind of illustrate this using one of my illustrations is somebody is running a committee, or somebody is running committees to the forum conference. If you're talking about the program committee or the conference, then you're perhaps trying to select the best possible papers and it might be a good idea to count just approval votes in that way, because you would maybe get the very best papers in the field. For another, for a contrasting example, consider the local arrangements committee that is trying to decide on venues for the banquet. There is an important thing, since it's no reason to need more than one meal, the important thing is to get wheels on the menu that wouldn't appeal to as many individuals as possible. So in other words, you want diversity. And the way that I describe this is that the criteria, the first criteria is individual support. Each candidate gets into the winning section, be well supported by the voters in comparison to other candidates. But the second criteria is group support. The winning subset, considered as a group, should be brought to be supported by the voters in comparison to their substance. And my argument is that most of the, most times when approval voting or any kind of voting when an election is conducted, there's some kind of balance between these two objectives that's this desired. And I think it's, in fact, to be expected, there'll be lots of different ways to conduct multi-matter elections using little balance and others to achieve these different, these two, the right balance of these objectives. Now I recently did a study of, it was kind of an example of election in which, sorry, in which a committee of three people was to be elected by some method. And the first thing that I did was elaborate on the set of balances that were, this typically occurs because, because you can't have individual elections. You must have, you must elect the multiple votes or set of practical reasons. It can be done easily, especially in the internet these days in counties. But you can see my view is that approval balance are in a kind of central position. They're both ordinal and cardinal. And there are some smaller kinds, single-vote transferable voting, S&T is really around them. So of all of the kinds of ballots that are regularly used in elections, the only one that is kind of in a different family from approval is cumulative. So I think this is a picture that says something about the approval balance. And maybe why it is, we're studying it, you understand? As I said, I did an experiment in which I assumed a bunch of utilities or candidates. I assumed that the utility of a particular subset was the sum of the utilities of the candidates and all of that's broad assumption. But then I tried all of that. I also assumed the standard strategy for approval voting that is people vote for all of the candidates whose utility is above average. And I tried all of the methods that I could come up with for electing candidates. This is, I created, it's a specific example. These are all counting methods for approval balance. This is to elect a subset of three candidates. As you can see, there are, there were only five candidates to begin with, so there are 10 possible subsets. And I got eight of those subsets turned out to be the winner or tied for winner on at least one of the procedures. So this was not a, it was not an election that was specifically chosen to be competitive, but it was. So by the point further of this, showing you all of these were methods of counting balance, approval balance. And there were lots of ties. But also there are many, there are many different methods and they gave many different results. I think I, okay. I think that's, the end of the story is that there's lots more to do with Baltimore elections. As I say, I think ideas should be developed and put into new areas. This is more approval voting. This is important. Okay, thank you, Mark. Our next speaker is Retruals. I think we have a video of his talk. He's one of the most growing proponents of approval voting and did some very interesting work on his properties in operations research. So he's got a mathematical social scientist in this regard. And as far as I know, he was the first to propose the name of approval voting. This is Robert Weber. He is retired from block Western University. He's our next speaker. Aloha, I'm Bob Weber. I'd like to take a few minutes to look back at my early involvement with approval voting. It all started in the fall of 1970 when I was a graduate student at Cornell. Two liberal candidates faced a single conservative in the race to fill Bobby Kennedy's US Senate seat. The liberals ended up splitting over 60% of the vote and the conservative won with only minority support. The next day, thinking back over the result, I found myself wishing that I could have voted for both liberals. And then I thought, well, why not? I presented the idea to several colleagues, explaining it as allowing voters to vote for all the candidates of which they approved. The name approval voting stuck. One advantage of approval voting was that it could be immediately implemented. Since the late 1890s, lever machines could be set to allow votes for multiple candidates in a single race. And the then new Votomatic punch card systems were completely compatible with approval voting. To evaluate approval voting, it's necessary to represent voter preferences, predict voter behavior, and compare predicted election results with predictions made for other voting systems. Voter preferences clearly should be represented cardinally via the utilities a voter would derive from the election of any one of the candidates. This allows voters to feel more strongly about the results of some elections than about others. And it helps to clarify why a voter might sometimes cast one approval vote and at other times more than one. Voters will ultimately decide how to vote on the basis of their preferences and how they expect others to vote. I chose to begin with pollless elections. A relevant example would be the election of an officer of a professional organization. Later, I'll return to a consideration of polls. But for now, I'll begin by assuming that every candidate is considered by the voters to be equally likely to be in close contention with any of the other candidates. Comparing approval voting with plurality rule, borders rule, or any other weighted voting system, it turns out that a voter will prefer to assign weights to the candidates in order to maximize the weighted sum of differences between individual candidate utilities and the average utility to the voter across all candidates. For approval voting, this translates to an intuitively pleasing rule. Vote for precisely those candidates who seem to you to be better than average. I ultimately chose to imagine societies where the voters have randomly generated preferences and wherein a voter doesn't know which of the many different roles defined by preferences he will be playing when the election takes place. In this case, he'd prefer the use of a system which maximizes expected utility of the elected candidate across all the different roles he might hold. Even in the two candidate case, that socially best candidate might lose the election if a majority of the voters have opposing weak preferences. I evaluated the expected result of the election on an efficiency scale, starting at the bottom with pure random selection of a candidate and peaking at the top with the unobtainable ideal of always electing the candidate of maximal aggregate utility across all voters. How far up in that range the actual expected utility to a voter of the elected candidate under a particular voting system was what I called the efficiency of that system. When there are only two candidates, the efficiency of any voting system is about 81%. This is the price we pay for not being able to measure a voter's overall intensity of preference. Under the plurality rule, efficiency drops as the number of candidates increases. Indeed, it drops asymptotically to 0%. On the other hand, Borda's rule performs well. Its efficiency increases as the number of candidates increases and rises asymptotically to 100%. What of approval voting? It beats Borda's rule slightly in the three candidate case. For four or more candidates, only simulation estimates are available. However, it appears rather disappointingly that approval voting's efficiency lies somewhere between that of plurality rule and of Borda's rule. In both the three and four candidate cases, the best systems I've been able to find are hybrids combining approval-like and Borda-like features. In summary, in a pollless environment, there seems to be little reason to consider approval voting as a leading alternative to Borda's rule or various hybrid rules. The conclusion is straightforward. If there is a reason to advocate the use of approval voting over other voting systems, that reason must be found in the way that pre-election polls of the electorate's voting intentions can influence voter behavior. For example, under approval voting, even in the face of polls, voters never have an incentive to assign voting weights to the candidates in an order different from their true preferences. Under plurality voting or Borda's rule, a non-monotonic assignment of weights is at times a voter's best strategy. Back around 1987, I gave a lunchtime seminar about approval voting at Northwestern. At the end, I illustrated the challenge of dealing with polls by using the 1970 US Senate race in New York as an example. Imagine that approval voting were in use and that polls predicted that most of the liberal voters would double vote for both liberal candidates, leaving the conservative candidate solidly in third place. Then supporters of each of the liberal candidates would have an incentive to not double vote in order to help vault their favored candidate to victory. If enough liberal voters do this, the conservative candidate might actually win, completely invalidating the poll's predictions. As soon as I was done, Roger Meyerson came up and noted that a new poll reporting the change in predicted outcome would likely lead to the liberal candidate supporters switching back to double voting. This would again invalidate the predictions now of the new poll. He expressed his feeling that there should be some type of equilibrium, wherein the polls could be correct. Not surprisingly, Roger was right. Indeed, the new equilibrium analysis, taking polls into account, revealed several ways in which approval voting is definitively superior to other voting systems, such as plurality or board is rule. I'll leave further discussion of this to Roger. Yeah, but further on to say thank you for organizing this. One of the things about plurality voting is that if you have as naturally occurs a distribution of preferences where a lot of voters, the bulk of the voters in the electorate have preferences that are in some, we'll call it centrist region, but then we can imagine that an important election, like a presidential election, that would have been presidential primaries, for example, that would attract a lot of candidates, that candidates would choose centrist positions, which is where most people are, but having a system that forces voters to split the vote that creates a cost to having too many candidates who look similar because the voters who like them, if they aren't coordinated and have to split the vote, that the result is going to be that occasionally the election is going to be won by an extremist who gets all of one wing and the people cluster in the center of the public opinion, just cancel each other out, just split the vote, and occasionally you're going to get extremists winning the highest office in the land that's happened in the last election, and wouldn't have happened if I believe there had been a approval vote. My paper with Bob, wherever that he did the other, you know, one of the things, so that teaches us that we voters understand that you can't split the vote, you have to figure out which centrist you vote for, and that means you have to get coordinated, which means you need leadership, coordinating leadership before the election, and I think the point of our paper was, well, democracy is supposed to have a choice in your leader, so if an electoral system, a democratic electoral system doesn't work without coordinating leadership before the election, then there's something wrong, and that was really the point of our paper. We used an assumption that shortly after the paper was published to the technical difficulties with it turned up, and I spent a lot of time studying Poisson voter, the problem was to figure out when what possible races do voters take seriously as conditional on my vote making a difference, what's the most likely, what are the most likely races that I should be worrying, that I should be thinking about, and what Weber and I were trying to argue, and I think a paper that all of whose political points I think are valid today, and whose methodology, I'm sorry to say, is embarrassingly off, which is why I doubt it's on anybody's reading list now, even though I think there are things that have not been said as well since. Electoral systems that require coordinating leadership, like plurality voting, are in the interests of those people who are in a position to be leaders, the party leaders, media people control the media, and therefore they have a vested interest and their interests are adverse to the rest of the voting population, because the elections are then less competitive. I think, Steve, I learned today that Steve Rebs first tried to get approval voting adopted in New Hampshire presidential primaries, I think presidential primaries are exactly where most could benefit in the United States, as I say, unfortunately New Hampshire might be the worst place because New Hampshire, well, it would be best if you could have gotten adopted because it's so conspicuous in the New Hampshire election. On the other hand, one of the interests, it should be, theoretically, it should be an easier sell in Illinois than in New Hampshire because the later primaries, typically the races become down to the two guys who are the front runners in the previous rounds, and the third ranked guy would say, oh, the approval voting one, that's where my hope is I'm gonna go campaign there, and because they're not gonna be afraid of splitting the vote by also adding a vote for me, and his spending more time in that state will then, of course, bring the others into that state, and they'll all make promises to the special interests of that state, and so that state should want to adopt approval voting, and I would, but of course, if everybody adopts it, we'll have better presidential primaries, but I'm just saying there's a first adopter advantage for any state except New Hampshire. But I think there was a history, you were arguing with Don Sorry, and he was attacking, let me say what I think was the essence of the matter. We have, there is no strategy-proof method of social choice. People have to respond to their environment, people will respond to their environment of alternative preferences, and the true test, we're gonna ask a political system, we're gonna advocate a new electoral system to the first political system to adopt it, first polity to adopt it. You have to road test it theoretically, among other things, and it is exactly how do voters respond to the competitive environment given voters' desires, and how candidates won't even more importantly respond. Don Sorry typically used the fact that he was assuming sincere voting, and with rank order systems, there's a unique rank order, with strict preferences, there's a unique vote, whereas an approval voting is an ambiguity. How many of your top people do you vote for? And so he could get all kinds of results where he'd say, if there are any paradoxes that are perverse, I can make them an approval voting, while he was manipulating adversely the decisions by the voters of how many people to vote for, and that is of the essence of that, how would they decide, and how will the candidates decide? I guess I'd like to say that the things that I was trying to do, in 1993 I had two papers, one, effectiveness, you can't read that, effectiveness of electoral systems for reducing government corruption in games and economic behavior, and the other paper, no not that paper, where is it, it was also mentioned in 1993, that was mentioned back in 1993, incentives that number five, number two, and number five I wanna talk about, the incentives to cultivate favored minorities under alternative electoral systems. This number two, I think I revisited last, and I think best in this bipolar, multi-candid elections with corruption, I think, with electorate that kind of split on it, the biggest issue to them that splits them is a yes, no issue, I use the term bipolar right now on all kinds of psychiatry, spam, mail, but other than that, I think that's the paper that replaces the GDP-93. What do I wanna say in brief? I think the incentives to cultivate favored minorities starts with the Cox threshold, the Cox threshold of diversity. If you're looking at the bipolar case where there's people who split on a yes and no, and you ask for, you've got given K candidates, I think Cox asked the question I ever find in this paper, what's the largest sought queue fraction of a, we'll call it a minority, such that there exists an equilibrium where all the K candidates choose to, choose to go with the one minus queue called majority block. And under the assumption that once they choose to be on the left side, let's say queue is the leftist minority and one minus queue is the right, what's the largest queue on the left? Such that everybody will go on the right, what the assumption is that in there actually voting, the voters will treat all the leftist candidates, all the rightist candidates symmetrically. The answer with plurality voting is the Drupal quota. Once you have one over K plus one candidate, once queue is larger than one over K plus one, a serious wind-motivated candidate wants to go over there, and if he's wind-motivated, it means he has a chance of winning, which means that in a single winner election, it's going to be a good problem. With negative voting, with pure negative voting, you've got a possibility of a majority, of a strict majority being neglected. You can't even get it. So there could be too much clustering or too little clustering, and approval voting is neutral with respect to that. The corruption side was saying, supposing you've got people on two camps, but they differ in their corruption level, and the voters all care. They like some like the leftist, some like the rightist better, and, but everybody hates corruption, and corruption is known. It's like when the candidate files his candidacy papers, he says, I'm the leftist or rightist, he does that, because he's committed to the leftist position or the rightist position, and here's how much I'll steal from the national treasury for my personal, like I'm bidding on my salary, and everybody would like zero, the minimal corruption. The question is, can you guarantee that in equilibrium, a guy who has zero corruption was the minimal corruption on the majoritarian side will win the election? And the answer is yes under approval voting, and no under almost any of the story rule. This kind of system, the single transferable vote also works pretty well. So what we're trying to do is disentangle the left versus right and the incentive for candidates to reduce the corruption. Where the single transferable vote fails is what I went further with in the consent of the public minorities was I considered where the campaign strategy that each candidate has to do is he decides on a district, he's got an average of $1 per voter if he wins the election, and what he can do is he can send a distribution offer some voters more than a dollar and some voters less, nobody less than zero, let's say taxes are fixed. So he's got to give away money, and now the only question is does he try to appeal to everybody equally, give more to some, less to others? The answer is you do want to give more to some and less to others under any electoral system. But how unequal? Do you want to cultivate a favorite minority? So this is the incentive of candidates to divide us in different ways, and the idea would be basically choose the distribution in the model, every candidate, every voter that goes to each of the candidates little, he logs on to the candidate's electoral side and puts the types in, the voter types in his voter ID number, gets a randomly generated promise out of the distribution, and then of course he votes for the candidate who promised him the most money, or in the electoral system he gives more votes and more to vote, he ranked them under approval voting, it's complicated, what does he do? The answer was under single transferable vote, which worked well against corruption, it still created the results of multiple equilibrium, including equilibrium where the most important race was avoiding being the first guy cut out in the single transferable vote with a single winner where they're gonna cut out the person who has the least first preferences and transfer their votes to the next. And so there could be, there were equilibrium with great inequality and equilibrium with less inequality, whereas approval voting encouraged candidates, it was complicated, but encouraged candidates to give the overwhelming majority of voters a little more than one and finance that by omitting a small minority. So the incentives to create favored minorities was much lower in this model under approval voting than anything else, I'll stop there. Okay, got you. Okay, so our next speaker is Jack Nagel from University of Pennsylvania. Go ahead. Let's see. My remarks are about approval voting strengths and weaknesses, principally in comparison with the AIR single transferable vote system, which I prefer to call instead of an option on IRB. I subtitle my remarks, Reflections and a Friendly Apostate, and the reason for that will become clear because a lot of talk will be about my experience of approval voting and emphasizing the experience of actual uses of approval voting, because I think we learn tremendously more from experience theory can go a long way, but the assumptions are our theories may or may not correspond with the behavior of voters and what's all this sign language about? I'll see you here in the camera. Oh, no, no, you're fine, you're fine, you're fine. Well, now you're not fine, okay? I'll do it that way, okay, sorry. It was fine before, sorry, sorry. Okay, we learn a great deal from experience. Actual voters can think of all sorts of ways to behave that we might not even anticipate in the best of our theories. I first learned about approval voting from Steve in the probably late 1970s, and I quickly became an enthusiastic convert. I started advocating it everywhere I could from Atlantic City to New Zealand. I had no takers in those two places, but I was instrumental in three actual uses of approval voting, two of them fulfilled expectations. These were, first, a sprawl vote in December 1983 among eight candidates for the Democratic presidential nomination. This was taken with five members of the Democratic State Central Committee in Pennsylvania. The other Steve has mentioned the first years of approval voting for the presidency of the IEEE, which at that time had about 350,000 members, tens of thousands of them actually voted 60,000 in 1970. In those two multi-candidate contests, many voters approved two or more candidates. As a result, also grants received substantial votes rather than suffering from wasted votes fall off, but the winners emerged with support from a substantial majority of voters. So approval voting has accomplished all that we hope to have done. Both of those experiences were written out in paper. Steve and I go off on about the IEEE. The third experience did not turn out so well. Ironically, this was my own department of political science department at Penn. In the early 1980s, I ensured a committee to revise our department of bylaws and I got approval voting written into elected chair with the help of a colleague Henry Tooney and Bill Crystal, who's since gone on to fame and fortune elsewhere. A few years later, we had a serious multi-candidate contest that Dean had authorized an external search for a new chair. We had five strong candidates, any one of them would have been a great help to our department. There was no guarantee that whoever won would accept the Dean's offer. So our vote was advisory to the Dean. It seemed clearly in our interest to approve as many as possible. And the rule says that all those who got approved on a majority of ballots could be appointed by Dean. The situation seemed ideal for casting multiple approval ballots. I did, I voted for four of them. The vote was by secret ballot only counted the results without a root shock. A substantial faction, a minority of the department had fuller voted for only one candidate, the same candidate. And as a result, that candidate was the only one who emerged with a majority of the rules. You can imagine that the Cabales collusion did a lot of damage to Colletial Trust in Goodwill. So besides being curious, I was also puzzled what had happened, why had Google voting failed in this situation but not in others. So I enlisted mathematician Sam Merrill to help me with this and we came up with an explanation that was published in the APSR in 1987. And Sam and I argued is that Google voting strategically is more problematic if you use it in a two-stage procedure, the character it was that we're basically nominating to the Dean, or if you used it with ballot threshold requirements such as majority requirements. So we decided that approval voting could still be recommended if you just had approval plurality for a single winner in a single stage procedure and would read this side please. Nevertheless, that experience, let's say, was three warning flags in the back of my mind. First, that insincere bullet voting can be a real problem with the approval ballot. Secondly, strategic voting is more likely if the product of concerted behavior among groups as opposed to the atomized decisions of isolated individuals. And third, the threat or actuality of strategic voting can have a powerful emotional impact with the threat of group solidarity. It's not just a matter for bloodless rational calculations about the third outcomes. Now, those concerns came to the forefront in my mind some time later when I occurred to me who I would argue that the original US presidential election system was strongly analogous to approval voting system used in the first four US presidential elections. And I wrote that up in a journal in politics paper in 2007 about what I call The Bird 11. Now, getting to the comparison with instant runoff voting, I had done work in New Zealand on the adoption there of mixed member proportional. And as a result of that, I came to the attention of the group that's now called Fair Vote and its leader, Rob Richie, and established a friendly relation, formal and informal, that's continued for 25 years. Fair Vote was interested in New Zealand mainly as an example of how reform could be accomplished in a single vote plurality system. Their preferred solution is to hear single-term survival vote system with multiple winners. But that's a proportional representation system for single-winner elections. They had the analogous or the minimal case of hair of the instant runoff vote. With a lot of persistence and savvy, Fair Vote and its allies have achieved considerable success with the instant runoff voting. It's been adopted in a number of cities in California and Minnesota and most recently for all elections in the state of Maine, although that was subject to a poor challenge and there was an implementation into doubt. So as practical reforms, approval, plurality, and IRB are competitors. As a friend of both Steve and Rob, I was kind of caught in the middle. In several situations where adoption or repeal of IRB was under attack or from advocates of approval voting, I intervened to defend IRB and then in a Minnesota court case, Steve and I submitted assidations on our subsides. My site prevailed. Now, what I'd like to do, although I think my time is running short, is to make a quick comparison of advantages and disadvantages of the two systems. The advantages of approval voting, first of all, is simplicity and implementation. The binary vote, the simple counting, is conducive to existing equipment and the counting does not need to be centralized as IRB does. Secondly, as Steve and others pointed out, approval plurality is monotonic and IRB can be non-monotonic like any multi-stage procedure. Thirdly, with respect to strategic voting, approval should never produce favorite betrayal, which is a big problem with single vote plurality. On the other hand, the disadvantages of approval plurality, it conveys less information about the voter's preferences and less people genuinely are indifferent among sets of candidates. But the big problem is that there's great uncertainty about how many approvals the voter will or should cast. Look at that quickly, schematically in one minute. It can be influenced by valid instructions as a student of mine demonstrated apparently. Secondly, the average utility rule, which is appropriate when voters have no information, is subject to framing effects so it's not independent of irrelevant alternatives. You add a candidate to the bottom and you'll approve a different number. Thirdly, with information, the polling assumption that Steve has advocated, we vote for the preferred front runner plus any trailing candidate to like better than the preferred front runner makes sense and would solve the problem where you have a very asymmetric division of the majority, the native or problem or the Stein-Plenton situation. If voters are instrumentarily rational, rational they should be given the polling assumption. But if you have a non-hubergeant equilibrium where you have three or more candidates who are pretty equally divided, then the problem of the bird dilemma comes up. The two who divide the majority group, each, that group should all cast double balance to votes, but each candidate has an incentive to have some of his or her supporters cut a few so that that candidate will merge as the plural plurality winner. And this is a situation that I argue happened between Burr and Jefferson in 1800 in the Latin to a debacle. Now the reason for this problem is that Pugl plurality violates the later no harm principle by casting a sincere second vote for your true second favorite candidate you can damage your first thing. And that is problematic. IRB is not subject to later no harm, although it does have some of the disadvantages I've pointed out previously. So between imperfect systems as we always have such a choice, there's an argument to be made for both of these systems. What I'd really like to see is more experience with each. We are accumulating quite a lot of experience with IRB, not to mention the century of experiences in Australia. I'm glad that Aaron Hamlin and his colleagues at the Center for Election Studies are getting support for possible more experiments with Pugl. I'd like to see what actually happens in real competitive situations. Sometimes it seems to work, but there's great risk that it may not in some cases. Thank you, Jack. Final speaker is Mahendra, my side and he was the organizer of this session. So, go ahead. All right, well, Mark is getting his slides ready. I want to frame my discussion. So basically, I'm going to be talking, so Meghna's designed about trying to achieve a objective function given that people will be insincere. Can be insincere. So given that's the case, the question is what should our objective function be? So that's a lot of what Mahd talks about. And based on what I'm already arguing, is that we should think of approbability in terms of maximization of consent or consent of the majority, as opposed to think of it in terms of, instead of being majority rule in terms of majority practice, just the usual interpretation of such a choice. Try it while you're talking. Okay, sure. I'll just put it in. If you can, I'll point, if you can. All right, so 40 years of pool voting research. So this is just giving an idea of where we're going. We're starting off with a thesis and a background and four arguments and supplementary slides, if y'all want to talk about more stuff. So, first, there's two interpretations of majority rule in the literature. One is majority preference, the other is consent of the majority. So in the majority preference interpretation, the voters ask, which do I prefer in the proposal or the status quo? And this generalized multiple alternatives is represented by Congress say amendments. The second interpretation is consent of the majority. And the voter asked in this situation, given that they're confronted with a proposal, yes, you know, do I consent to the proposal? And when generalized multiple alternatives, this is represented by Google voting. So this is a whole in the democratic theory literature, because while democratic theories would often use both interpretations, they rarely distinguish between the two interpretations. So if you look at the literature, and I have it in other slides that I'm not gonna go over, but they're the supplementary slides, there are several democratic theories who use the language of consent of the majority. These are people who like John Lawton, John Johnson or so, John Rawls said, take listen to Congress say. So my goal here is to demonstrate that to generalize majority rule to multiple alternatives, consent of the majority and approval voting are better generalizations than majority preference in Congress say methods. So despite there being strands of majority in the sense of the literature, you know, existing in a lot of economical works, it's usually interpreted as majority rule as majority preference in the social choice literature. And this allows the paradox, primarily Congress say's paradox, which is that, you know, a voting system either violates transitivity or independent relevant alternatives if it tries to adhere to majority preference. That's roughly what it is. And this creates a big problem in terms of normatively generalizing majority rule to multiple alternatives, which is the big case that William H. Recker made, that basically, because you're gonna always have cycles or possibility of cycles, you can't, you know, majority rule and voting is meaningless. And so ultimately, democracy has can't be based on some popular consent or will of the people or general will, that's based on some sort of liberal consent. Now I'm not denying the liberal perception, but I'm saying that like, you know, well, it can have me, votes can have me. So there are the various defenders of majority rule. These are on two alternatives, these are like Robert Dell, who gives four major arguments. Christian, who lists more recently, gives three major arguments for majority rule on small changes. But both agree that all the arguments have difficulty generalizing to multiple alternatives. So these are roughly the four arguments. Mace theorem, which is given by both Dal and List. Great Taylor theorem, both given by Dal and List. Maximization, self-determination, which is given by Dal and Loan. And then conversation theory theorem, given by both. So what I wanna show is that an aerobian version of approval voting generalizes each of the four arguments better than any other aerobian voting system. Now one reason I have to define in terms of aerobian terms is so I can make the claim that it's better than any other aerobian voting system. So what is an aerobian voting system? Basically, each voter submits a rank ordering of alternatives, and the output gets a rank ordering of alternatives. So we need to also define a majority aggregation procedure to define an aerobian version. So basically, it's, you know, there's a more technical version. Basically, if more voters prefer X over Y, they prefer Y over X, then X should be associated around the above Y, subversive, and then of course an equal number prefer X over Y, and for Y over X, and then X and Y should be associated around the above. Okay, so basically, aerobian approval voting is, you know, each voter, they partition the set of alternatives into two parts, right? They're different between any two alternatives they consent to, they're indifferent between any two alternatives they don't consent to, but they prefer any alternative they consent to over any alternative they don't consent to. So this turns, you know, approvals into a aerobian preference order that has at most two levels of preferences, and that just application of majority aggregation procedure to that set of aerobian preference orders is basically, you know, aerobian approval voting. So what I show is that aerobian approval voting generalizes these four arguments better than any other aerobian voting system. So first, let's start with May spam. So May and May famously, Kenneth May famously argued that majority rule on two alternatives with ownership domain could be uniquely characterized by four conditions, decisive and limited neutrality of positive responses. What I do in the generalization is so to show that among the aerobian approval voting system is the unique aerobian voting system with the least restrictive domain which satisfies May's four conditions and independent relevant alternatives or IAA. So this is really interesting in this relationship to aerosphere, right? So, let me come over here. So basically, if you look at the conditions of aerosphere which are here on the right and the conditions of our theorem on the left, except for decisiveness in an ownership domain, basically our conditions imply aeros conditions. So you take the strongest versions of aeros conditions like for example, anonymity implies non-dictation, neutrality, assuming that the voting system doesn't always output a time, implies non-dictation, so, you can go to the next slide. So what we can do is we can restate the result in an aeromeic way, which the mantra is basically, what we've done is we said, we could ask the question, what is the aerobian voting system with the least restricted domain which satisfies decisiveness and the strengthened versions of the remaining aerosphere and its conditions? And basically the answer to that is aerobian approval voting. So then there's the rate-tailor theorem, right? And basically what it says is, under certain background conditions, majority rule maximizes the overall utility of voters when there are two alternatives. And what we show is okay, this is just a special case of a multiple alternatives generalization of the rate-tailor theorem. And that's basically characterized by aerobian approval voting. So, now you can potentially criticize the rate-tailor theorem saying, well, it uses non-traditional utility because under a traditional utility theory, at least one voted for X over Y and at least one voted for Y over X, then you can't really say which alternative maximizes the overall utility of all voters, right? So, another prism is that it doesn't use a notion of utility that has basis in economics or psychology literature. So we could use another notion of utility, not that it's non-traditional, but it's a Herbert Simon's satisfies account, right? Which basically, each voter has a utility threshold and if an alternative is above that threshold, that they consent to it or satisfy by it and it's below that threshold, they don't consent to it and they're not satisfied by it. And then it should be pretty clear that when voters are sincere, aerobian approval voting chooses the alternative which maximizes the number of voters that are satisfied. And I think that's a better utility argument than the rate-tailor theorem. But we can still generalize it with the rate-tailor theorem. Then we move on to the next argument, which is the idea that approval voting maximizes self-determination. So, the way to think of it in this case is think of each alternative as a potential contract, right? It's a potential multilateral contract. And each voter, when they're sincere, they consent to exactly those alternatives to which they consent to, and they don't consent to those which they don't consent to, then clearly, approval voting would choose the alternative that maximizes the number of voters who get an alternative to which they consent to, that the contract was the opposite. So, it maximizes the consent to that. And then, the final argument is counter-sites-jury theorem. So, under appropriate background conditions, majority rule and two alternatives tracks truth. Now, what our generalization does is that we show that aerobian approval voting is the unique aerobian voting system with the least restrictive domain for which there exists background conditions such that it's at its counter-sites-jury theorem, it's decisive, it's neutral, and it uses majority aggregation of every pair of alternatives. So, you know, counter-state methods can't do that because they have to maintain transitivity, they have to violate the events around an alternative so they can't maintain majority of the preference on all of the pairs, but, but aerobian approval voting can't do that, it can ensure that you always use majority aggregation of every pair of alternatives. So, what we've demonstrated is that aerobian approval voting generalizes for a majority of multiple alternatives. It suggests that majority consent is a better interpretation of majority rule than majority preference, and additionally it suggests that approval voting is a better generalization of majority rule than the counter-state methods. So, with all that said, I think what I think I'm trying to demonstrate here is that we should think of approval voting as a better and more for multiple alternatives than the counter-state methods in terms of representing majority rule. The question should be, we've developed several methods for trying to track counter-state winners, and I think there should be more mechanisms of design and research on, and empirical research to understand how to achieve sincere approval winners. Okay, thank you. So, we've got those speakers. And now it's time for discussion. First of all, I want to ask many of the speakers of anything to add in light of the other speakers. Yes, Jack. Not an addendum to my remarks, that some of you may have heard before, but one of the really unfortunate things that happened over the last couple of decades is that we had two, of course there were more, but two in the arena reforms, trying to solve the same problems with single vote plurality, and sometimes the supporters of one became enemies of the other because they wanted their own system to prevail. And most likely what happens then is we work to the status quo and we get no reform at all, and no experience within the systems. So, I really have argued strongly and continue to argue that each, we need more experience with both the alternative vote IRB and with the plural voting, but they shouldn't try to tear each other down. They shouldn't try to block the adoption where one group has a foothold on the ground, let them do it and see what happens, and not try to get the repeal or to revert to the status quo so that someday, far in the future, your favor might prevail. Now, in some situations, and this is sort of what happened with the IRB, probably a group may say, we want to know what would be the best reform here, and you can lay up pros and cons of each one and let them choose it up, but that's different than kind of coming in and trying to tear down a convenient reform. Any other speakers want to say anything? Yes, I'd like to extend your, I think, both, an advocate for either reform has given an audience to try to mention the other reform as well as a general rule. They're both toward the consideration for sure. I just wanted, on Mark, I wasn't clear what proportional, what multi-winner they'd be considering. What I thought about this, it seemed to me, one, I don't know if this was on your list, it was just the generalization of Dahant PR to approval voting, which would be, is that on your list, that Dahant PR? Yeah, it's not under that name. Okay, yeah, what do you call it? This is where the first, you're gonna allocate K seats, sorry, gonna allocate M seats, M is the number of seats. You're gonna allocate M of district magnitude seats. The first seat goes to the guy who was the most approval votes. Then, to allocate the second seat, you discount the, you divide the, any vote which included the winner of the first only counts as half a vote. And the general rule is, if we're allocating a seat, it's the part way through the list, any vote that has already proved of S winners so far counts divided by one over S plus one is the value of that approval vote in electing the next guy. And this would generalize the Dahant rule for, if everybody's single voted. In fact, if everybody voted for a single party list, if everybody voted for Democrats and Republicans that either voted for a public list or a straight Democrat list, then this would allocate according to the Democrat and public by Dahant. Okay, that's called sequential proportional SBA by list. Sequential proportional, that's right. And another, because it's a, it's a sequential version of proportional approval vote. Yeah. You're gonna go through an entire full set by a subset by a subset by another one which is on the list. We think that sequential proportional is a lot like Jefferson, yeah. Differentation. Tiffson is Dahant. Yeah, okay, so then the other one is Webster. With Webster instead of fractions, one, one-half, one-third, one-quarter, he is one, one-third, one-fifth. So that's another one that's on the list. I see, so he reduced the Webster votes. Both sequentially and sequentially. I just mentioned that there are some attempts to combine what are the foundations of each system, the foundation of ranking systems and the foundation of approval systems. And I've written a paper with Rem City, that's just last name, 9% of it, yeah, called a preference approval voting. So you ask the voters to do two things. You ask them to indicate a preference order as you do with any of the ranking systems. But you also ask them to draw the line between those acceptable and those not acceptable. And we have rules to determine which takes priority under what circumstance. And it seems to, because each system is, each way of giving information, ranking versus approval, is giving different kinds of information, it's a good question I think to ask, how might this be combined if you want to ask voters to inform on both criteria, preference, and where they draw the line? Anything else that can speak of that? Just a comment about my ideas. They have some appeal to me because I think there really are situations where what we're looking for is something like consent. I've, in retirement, done a lot of work with the legal women voters, which is the most effective reform organization in the US, and they have a quicker tradition. So they make decisions by consensus. The consensus does not mean unanimity and the quicker style consensus is, would only say this is unacceptable to me if it really is below a threshold negative voting value. Otherwise, it would go along if it seemed like most of them would want it. And that's not a bad system, but the cultural norms of support that being done properly as opposed to somebody, you know, going the way around with a kind of legal or a veto my way or the highway, are delicate and they don't exist everywhere. So the question is how we can find them or how we can foster them. Also in that connection, I mentioned the experiment by Ed Kutch back in the 80s, published in Politico. The valid instruction to make a difference on that. So he did an experiment where one was the most neutral approval valid instruction, both for one or more. And that got fewer, elicited fewer approval multiple votes than the next, which was vote for all those who approve of. And then the third was vote for all that are acceptable to you and that got still more multiple approvals. And so he could frame instructions to make this empirical not theoretical that might list something like that, but then you still need people who are responsive or have the kind of cultural norms to do this in a genuine and sincere way rather than a way to maximize their own veto power. So I like to respond to what Jack said. So I think, well in terms of the manipulation, obviously, you know, basically all the voting systems are suspect to manipulation. So we always have taken account mechanisms aside basically, whenever dealing with voting systems. I'm taking account of the current situation that's going on in the particular voting situation. I think we can figure out a lot of what we need in terms of background institutions from Congress. This Congress, actually I think that's what most of this political writing was about, what kinds of background institutions you need when you're having a majority vote. Because it wasn't just the majority who wanted background institutions that encouraged people being educated, people being independent, thinking people being honest, people being altruistic. And so, and then this would be the, these are background conditions of the jury theorem, that's what makes the jury theorem work. And so what I think we have to do today is focus a lot on, well what kind of background institutions do we need to get people to be able, it's not, you know, we can't guarantee it, but it's better to have certain background institutions to push towards the norms. So then basically these voting systems can work better. But that's true of every voting system. I think that brings in deliberative democracy because in the literature out there that says people benefit from deliberation, and this presumably sets the tone for voting in the end. Well, I might say that that kind of application is not the typical election application, in an election we have a highly competitive situation, especially if one only wants to win. And so those assumptions are gonna fall out, but when you want to approve a set that has that broad acceptability, there are situations where we want to do that, maybe more for policies or for nominating slate of people. And if we can find ways to achieve that, we would think. I think we should open things up. We have a few non-speakers in the audience, so if you have any questions or comments, feel free to make them. I'm not real familiar with this literature, so I apologize for my ignorance on it. On the subject of manipulation of voting systems, plurality voting, what would be the impact on the candidates themselves? As far as gaining the system, in other words, are candidates more likely to lie under plurality voting or approval voting? Is there any research on that subject? Ted, I'm not sure about the lying. Well, to appeal to voters, not revealing their true policy preferences. A big argument for both Google voting and for the right towards instant runoff voting is that it should either opponents and state that they will lose less adversarial campaigning because you would want supporters of some of your rivals to cast an approval vote for you as well as for the rival or cast a second preference for you as well as the first preference for the rival. And there is empirical evidence from some American cities using the IRB system that campaigns have been somewhat less adversarial. They're still competitive, so it's not going to be all combined up, but it might go in that direction. Now, a big problem with Google that I point the burden on the term for is that strategic tension. It's much easier to say, okay, cast your first vote for me and I have no problems with your casting a second preference for somebody else. But when that second vote under approval counts equally with the first vote for me, then you really don't want them, or at least not all of them, to cast that second approval or rival because that might sink your own situation, your own prospects. One of the criticisms of approval voting is that there's no standard to determine the voters where they draw the line between acceptable and non-acceptable. And I'm not particularly bothered by that. I think voters should make up their own minds and some are going to be more discriminating than others, so the discriminating voters might pull a vote and vote only one. Invest discriminating and going to say more acceptable and I think we can have different standards. So this is a path to the strategic element of just giving voters sovereignty. And I think that's a good thing. Is it up? Yes, over here. This is a question with respect to the multi-border form. Say we introduced party competition into that context. What sort of, what would a seat maximizing party tell its voters to do with their ballots? We're using simple counting. Both of them, obviously. We'll vote for all of our guys. What's it called? That's a help. If you're using one of the other counting methods such as proportional, then it should not be as effective to do that, whether it will work or not. Certainly these methods, these different methods of many different voting systems will have different levels of sensitivity. What's the strategy on behalf of the Congress? The method I was describing, which is pure too complicated, too hard to logistically for a large election would function exactly like the normal Dahant PR parties would put up the list and say, oh, for all of us, don't cross over. There would be a way of allowing people they wanted to cross over. I think, by the way, I think the best use of approval voting for party PR elections is the idea of using, say, a standard Dahant PR on the, I'm sorry, the best use of approval voting for the context of multi-seat elections is actually, I think, open list PR. So you're gonna have, let's say, the Dahant system, every voter has to articulate a preference for an individual party. The parties are then gonna get, say, by the Dahant roll seats in rounded proportion to their vote, their share of votes, but then they put out a party list that included enough candidates to take all the seats, which of those people get the votes, and the closed list is the party, the Central Committee has rank ordered them. The most dominant system is a version of plurality voting, which, I think, originated in Brazil, where you name, when you vote for party, you also name one candidate of that party, and that just tears the parties apart, especially in Brazil, where a candidate was allowed to, on his own, the Central Committee didn't say, didn't have a say about the incumbent, could run for re-election on the label of the party elected him. Then once you get the drupe quota, you're guaranteed a seat no matter what your party is doing, and everybody's running for the drupe quota, and it essentially became equivalent to single, non-transferable vote, with all the tearing apart, whereas the approval voting within the party list, where you vote for a party, you can then approve as many people as you want on that party ballot, and then the K seats that are being allocated are being allocated to the top, if the party gets K seats, they go to the people who are approved, but most people, now you've got candidates competing, not to carve out their own constituencies, but to appeal to the mainstream, to the center of the party. That doesn't provide diversity, so you use the cross-party to solve the diversity problem, and then within the party list, you want competition based on competence, honesty, effectiveness for voter constituency work, that would be, approval voting would be, you should have a very strong case for that in that context. I'm sorry, we didn't try to talk about that. Approval voting as the use within the party list for open list PR. Yeah, I'm not sure of any place where it's used. Typically, these countries have one or three approvals, and I would say allowing the voters to approve them is, you're gonna have a limited number, list increase the number, and let them move up to any, you know. If there was model legislation for something very much like that, that was the original vision for proportional representation of this country. And in a few minutes, I'm gonna talk about why that politically not workable. It was called the Freelance System, if you wanna work it out. Okay, Darren, it's very technical. You mentioned before different types of variables that would affect the number of approvals that a voter would put on the ballot. At least some of them were kind of out of control, like the number of candidates may be even pretty different, number of approvals or an average year for voters. But when you go and talk a bit more in terms of a variable center within, or within control systems, instructions, and the vision differences between different types of levels within the variable such as that different type of language. So how much of this is different? And for the different ends of the spectrum, like, can you see that as being good or bad in terms of leaning towards what we might consider an outcome? Well, although Steve's right that a discerning voter or a voter that's very, you know, Steve, one candidate is way better than the other, he shouldn't be able to vote for just one. In general, if a lot of people do that, approval voting is breaking down and it's going back to a single vote plurality. So you want, for the system to work, you have to have a lot of people who go cast multiple votes. In the Cauchy experiment, I think the numbers were with minimal instruction, 1.7 approvals per ballot on average. And within most of the candidates, I think he varied that. So this is one figure. But it went up to two with approve and 2.1. So it's not huge, but it has an effect. And I might have more effected with not just something written on a paper, but something emphasized in social issues of life. I do think that with more knowledge, we, you know, polls were the like, we'll get fewer approvals because the front-runner kind of thing starts to take over. As opposed to voting under completing, we're in swing, we'll probably vote for all those of average utility, which should typically be less than fewer than half of candidates, but more than one in those cases. The biggest thing that I worry about is the strategic thing. And again, the argument that I would make is that we shouldn't think of voters as individual. I mean, sometimes they behave as individuals, but they typically, in competitive situations, behave under the influence of leaders, candidates, parties, interest groups, opinion leaders, and those leaders would damage much more of a game theoretic than a decision-theoretic situation. Projects failingly. And I mean, the risks that leaders, whether overtly or covertly, will encourage people to bullet vote is a real one. I think we're at the end of our session. I thank everybody for coming, especially the speakers, and my group of organizers.