SPEAKER 1: This is a production of Cornell University.
SPEAKER 2: I'd like to welcome you to the third in this Messenger Lecture Series on measuring, electing, and ranking. Let me remind you that there's a web page. It's basically the math department web page. If you follow the link for events, you'll find a page relevant to this series. It'll will have a list of references for each lecture. And we'll soon have the slides of the lectures if you want to look at them.
Eventually, the lectures will be available on streaming video through some university website. And they also will be turning up in various libraries on DVD. So if you feel the need to go rewatch one or watch one you hadn't seen, they'll be available.
So without much further ado, I'd like to introduce once again our speaker, Michel Balinski from Ecole Polytechnique in Paris who will tell us today about how to eliminate gerrymandering. OK, thank you. Michel.
MICHEL BALINSKI: Thank you. And thank you for persevering and being here for a third time, those of you who've managed that much.
Well, I'll just remind you then that this is the last of these three lectures. And all of them somehow, there's a certain motivation about trying to get something-- sorry. I'd better begin again.
So again, I will repeat what I said. For those of you who have persevered, I thank you for being here. In some sense, all of these lectures have something to do with equity in representation or in electing. So there's a very strong motivation to fight some of the rather bad consequences of the mechanisms that are now being used to elect and to represent people in this and other countries.
So I'm going to start talking about the effects of gerrymandering. And here is the original gerrymander. Let's see, there used to be-- oh, I guess there's no pointer for once that I thought of using it. Is it here?
SPEAKER 2: It's in the box.
MICHEL BALINSKI: Oh, I see. Sorry. Thank you.
Here's Marblehead, so Boston is somewhere down below. And I guess you all know the story. This is the cartoon that caused this to be called the gerrymander. It'd due to an ex-vice President of the United States, at the time, Governor Jerry.
And what is political gerrymandering? This is from Black's Law Dictionary as quoted by Justice Antonin Scalia in the recent decision. It is the practice of dividing a geographical area into electoral districts, often of highly irregular shape, to give one political party an unfair advantage by diluting the opposition's voting strength.
So what are the realities? Well, I'll have a better map in a moment. But I think you all know where this is. You see Ithaca is up there. And that is your congressional district. And it's quite a nice example.
Here's another of the same map. And one sees it a little bit more clearly. So again, Ithaca is right there. I don't quite know why, because I don't know the political situation here. But you can see, for example, the 20th is something that snakes around like this. And this is really gerrymandering in practice.
But there's an odd similarity here, because look at this district, your district 22. And look at the original one. I was absolutely struck when I noticed this. It's almost the same thing.
Pennsylvania is a very serious case, because there's been a very important Supreme Court decision that hangs on the Pennsylvania case. Here is the 12th district. I will also show you the 18th. And there are others.
Now, I think this one was referred to as the upside down Chinese dragon. I don't know. There was another one called the supine seahorse. I'm not sure that it's this one. I couldn't really identify it. But here are the kinds of districts one has. That's a reality.
Now, what is the effect of this? And here is a table of what's going on in the US House of Representatives from a point of view of who is elected in the elections of 2002, '04, and '06. So in the first line, you see the incumbent candidates. 2006 is somewhat better than the other years in the sense that there's some sort of change. But still, the changes are really quite minute. But 2002 and 2004 are absolutely amazing, because when you look at the number of incumbent canned candidates, essentially all of them are re-elected.
Incumbent candidates who lose to outsiders, why this extra description? It's because sometimes you have two incumbents against each other because of a redistricting. So that is something you have to take care of. And then when you look at, across the nation, the margins by which people are elected, it's also extremely striking.
So this elected candidates ahead by at least 20% of the votes, that means I take the winning candidate. I look at the next candidate. And I look what is the difference in the total percentages. I'm just doing a subtraction, OK? What's the difference between them? And at least 20%. Of course, if you're thinking of just two, that means at least a 60% to 40% win, which is an absolutely mammoth win.
So most people are elected that way. When you go to 16%, it's, of course, still more. And to look at the other end, which are the close elections. Close elections then, less than 6% difference. That is, if they're 53%-47%, which incidentally, in France, 53%-47%, that was the last presidential election. That's considered a big win.
Here, look, 24 races out of 435, 10 in 2004, 39, a little bit better, but still minute, in 2006. So this business of gerrymandering is quite ecumenical. Both parties do it. Sometimes both parties do it together.
And I think the other thing is to note the number of candidates who are elected without opposition. Let me again define that. It means without opposition of either Democrat or a Republican. So I'm not counting some very small party that is presenting a candidate. Often there are a few that get 2%, 3%, 4% of the vote. They really don't make very much of a difference.
That is why I maintain that it is entirely possible for a majority party in the House to be elected by a minority of the voters, because if you live in such a district-- it doesn't matter. Say you're a Democrat and you live in a district where the Democrats win by at least 20%. What's the point of voting? And if you're a Republican there, what's the point of voting? Same thing. So it's all perfectly symmetric.
So a lot of people don't vote. And in particular, of course, when there's no opposition, then what you don't need to bother to vote. Therefore, the total vote that is actually recorded may have very little to do with what people really want. They are faced with the situation, they either vote, don't vote, express themselves as they can. But often, they cannot even express themselves at all. And so this is another pernicious effect of gerrymandering.
So in total, it is said about 400 seats in the House of Representatives are considered safe. And let me give you a few more examples. For example, in the 2002 congressional elections, together, the Democratic vote exceeded the Republican by 35,000 in Michigan, but Republicans elected nine representatives and the Democrats only six. In Maryland, this thing was somewhat the difference. It took more than twice as many votes to elect a Republican than it did a Democrat, on average.
In Connecticut-- and I do this because we're going to look at this example in more detail. The Democratic vote in 2004 exceeded the Republican by 156,000, yet Democrats elected two, the Republicans three. This got reversed in 2006. Now there, too many Democrats were elected and too few Republicans, given the total vote of the state.
Massachusetts, everybody's a Democrat. But more serious, in these three years, six, five, and seven of these candidates were elected without any opposition whatsoever.
In California, well, that's particularly striking, I think. Every one of the 53 congressional districts have returned a candidate of the same party, of course, it's usually the same person, in these last three elections. And respectively, 50, 51, and 49 were elected by margins of at least 20%. So to change anything in California, it really takes one hell of a lot.
That's an error. 2002 to 2004 is what it should read. In the change from 2002 to 2004, 45 states returned exactly the same party representative in every district. Four states shifted in one seat, and only one state changed significantly. That was Texas. It gave Republicans six more. Why? Because Texas, like every other state, had redistricted for the 2002 election. But Karl Rove, Tom Delay, and company encouraged them, I guess as you all know, to redistrict again using the advanced gerrymandering technology.
This was, in the end, turned down by the Supreme Court. But it was too late to change anything for the course of the 2004 election. And this worked extremely well. In 2002, there were 17 Democrats and 15 Republicans, and in 2004, 11 Democrats and 21 Republicans.
However, every one of Texas's 32 districts had a census population of exactly 650,619 or 650,620. It was a perfect, from the numbers, reapportionment. How did they do this? Well, I'm going to take Pennsylvania as the example, because it is what came up to the Supreme Court.
Democrats rewrote the book when they did George. And we would be stupid not to reciprocate. The Pennsylvania redistricting will make Georgia look like a picnic, said the chairman of the National Republican Congressional Committee. Obviously, in Georgia, Democrats had done the same sort of thing.
Pennsylvania's governor was Republican. The party controlled both House and Senate. And I note again, this is perfectly ecumenical. And they used the new computer technology to create the distracting plans.
And it's very interesting. You can read the account of this and the court decisions where witnesses have come to say exactly how the process went. Well, a bunch of people stood around the screen. And there was a technician who would redefine-- they'd start with a definition of, it turns out in Pennsylvania, 19 districts, start with some first approximation of 19 districts, and then start-- get equal populations in each district.
And with each click of the mouse here, you'll get a host of data, numbers of inhabitants, past votes, presidential, congressional, local, breakdowns by ethnicity, religion, income, sex, color, age, religion, everything. I guess I said religion, as advertised, I'll give you the reference in a moment, by the place that sells the software, over 600 demographic variables.
Districts favoring Republicans in red, those Democrats in blue. Elephants located where the incumbents live if they're Republicans, otherwise they're donkeys for the Democrats. And they are clicking the mouse and pushing one census tract from one district to another, because the smallest atom in this procedure is the census tract. The census tract is the smallest area that the census considers from the point of view of where they count. And I'll give you a notion of what the numbers are a second, at least in Pennsylvania.
The reference is Caliper Corporation's Maptitude for Redistricting, which could be bought for as little as $6,000. Pennsylvania, by the 2000 census, had 12 million some-odd inhabitants, 19 congressional districts representing a drop of two, 67 counties, 9,000 voting districts, and 322,000 census tracts. So an average of 38 persons per tract.
And the legislative committee cracked, packed, and kidnapped. So let me tell you what those terms mean. Cracked means you crack, in this case, it would be Democrats, you try to push them apart so that they become minorities wherever they are. Packing them is to do the contrary, push them all together so they get whopping majorities so many or thereabouts are not needed and so, quote, unquote, wasted. And kidnapping is the practice of putting two incumbents in the same district so that one of them has to go. So they did this to several Democrats, especially abetted by the fact that they were dropping from 21 to 19.
Now, in 2000, there were 10 Democrats, two running unopposed, and 11 Republicans, two unopposed were elected. 2002, the numbers changed to seven, only one Democrat ran unopposed, and 12. So this worked quite well. Four of the Republicans ran unopposed.
The Democrats filed suit, claiming essentially two things. The big claim was, this is a blatant political gerrymander. A very minor secondary claim was, look, there's a disparity of 19. That's not the best possible.
The federal court's decision was this. Relying essentially on Davis v Bandemer, which says, in obviously very summary fashion, that in order to prove that there has been blatant political manipulation, you have to prove two things, that it was intentional and secondly, that there is an actual discriminatory effect against an identifiable political group. And it's got to be proven. But of course, it can't be proven, because it's done before the election, this plus lots of other points.
They relied on that. And they said, no, according to following precedent of Davis v Bandemer, we cannot give you reason on the first point. Although, everybody basically admitted, yes, of course it was a political gerrymander.
Some of the defense here was that it is none of the court's business to look at this, and cutting up something with political objectives is totally legitimate. That was one of the arguments that was quite strongly used by the defense.
Well, what did the court do? They accepted the plaintiff's claim. They rejected their claim of gerrymandering. They accepted the claim that 19 is avoidable. So a few more clicks of the mouse gave districts of perfectly equal population, but of course, with upside down Chinese dragons and supine seahorses. And in particular, 21 counties and 81 municipalities were fractured into smaller pieces.
Now, there's another phenomenon going on here, because this is done at the federal level. But there's also a local level. So there are state senators, state legislatures. Each of them have districts. All of this is done independently. So if you're going to put all of these grids down together, I don't know how a voter knows where he lives, to somehow to try to identify what's going on, in some sense, from the point of view of electing all of these people.
So this finally went to the Supreme Court. And their decision was announced on April 28, 2004. It's Vieth v Jubelirer. First, no one disputes blatant political gerrymandering. But Justice Antonin Scalia announced the judgment, joined by only three other Justices, concluding, although this was the decision, 18 years of essentially pointless allegation have persuaded us that Bandemer is incapable of principled application. We would therefore overrule that case and decline to adjudicate these political gerrymandering claims. The judgment of the district court is affirmed. So the court, though not by majority, has ruled that it will no longer consider such cases.
Now, what's gone on here? Well, in the end, there's exactly one criterion that the court has been able to agree on, and that is equality. This is an old point made in 1969 in Patrick v Chrysler. The nearly as practicable standard requires-- this is the ruling-- that the state make a good faith effort to achieve precise mathematical equality. Unless population variances among congressional districts are shown to have resulted despite such effort, the state must justify each variance, no matter how small.
In fact, I've read all of the decisions beginning in the '60s in the Supreme Court. There is an incredible amount of contradiction and confusion in all of the opinions and counter-opinions and all the rest. There's a complete misunderstanding of what's going on. And there's a complete confusion and mess that has been left. And in the end, although Scalia's decision, in many ways, was written in an extremely arrogant fashion, I believe his decision is perfectly right. There are no criteria. And that is the big problem.
Justice Harlan, and somebody I quoted in the abstract for the talk, was really prescient in 1969 and in a 1969 dissenting opinion when he said, "the rule of absolute equality is perfectly compatible with gerrymandering of the worst sort."
And I'll stop for a second. Incidentally, obviously, the census count itself has quite a bit of errors. So to go below 19 is just perfectly idiotic. 19 is way under the accuracy of what the census can get. So even when you take that into consideration, but somehow the law wouldn't except that.
"A computer may ground grind out district lines which can totally frustrate the popular will. The legislature must do more than satisfy one man, one vote. It must create a structure which will in fact, as well as theory, be responsive to the sentiments of the community. Even more than in the past, district lines are likely to be drawn to maximize the political advantage of the party temporarily dominant in public affairs." So there's the charge. And here is a possible answer.
So the argument I put forth goes as follows. Clearly, by tradition and by law, a member of the US house of representatives represents the people of a district. In fact, he or she represents what? The people of her or his district, the people of her or his political party, and the people of her or his state. Often, of course, you get representatives of a state, Republican and Democrat, voting together for matters having to do with the state. There's a very strong state identification as well as political.
Incidentally, in the Congresses of 2002 and 2004, everybody was either a Republican or a Democrat, except for one candidate, Bernie Sanders who is from Vermont, who always voted with the Democrats but ran as an independent. He's since been elected to the Senate. So really, he's quite an outlier. So really, everybody did represent one or another party.
So from this perspective, as we've already seen by the examples, a lot of electors are very, very badly represented. So here's the new proposal, I'll just say, that I make. Voters should cast ballots in single-member districts as usual. However, when voting, a vote for a candidate is a vote for the candidate but also a vote for the candidate's party.
Then two rules will decide who is elected. First determined is how many representatives will each party receive. And that is to be determined on the basis of the party's total vote in the state. Using Jefferson's method, that I can give reasons for later, but that's not the essential point. But the essential point is then that you vote. When your vote goes up for a candidate, it goes for his party. And the party is going to get seats on the basis of its total vote in the state.
So it's going to be proportional representation statewide. But at the same time, there will be one candidate per district. So the candidates elected, exactly one in each district and the requisite number of each party, are determined by a certain procedure which I will now describe. And I'm going to do it via the example of Connecticut.
Here are the 2004 results in the congressional election. As you see, there are five districts, five candidates, five representatives. And in red are the people who won because they had the most votes in their districts. So the Democrats elected two, the Republicans three. But as you can see, the total Democratic vote was 779,000 to only 622,000 for the Republicans. So according to the method of Jefferson and good sense here, the Democrats should have had three and the Republicans two.
So the question then becomes, which three Democrats and which two Republicans? Well, so now I will give you two approaches to explaining who should be elected. If the candidates with the most votes in each district, I'll call them the district winners, give each party the number they deserve, the requisite number, then that is the solution. Connecticut, this was not the case.
Well, why wasn't it the case? Somehow the vote is unbalanced. In Connecticut, the Democrats' vote did not count as much as they should have. So the parties' votes should be adjusted. But in effect, this is a symmetric problem.
For example, take the Democrats. We know they're going to get three. And we know the Republicans are going to get two. Therefore, the two Republicans are competing among the five for who will be the ones that win, and the same thing for the Democrats. Therefore, we can adjust votes. But if we do, we should stick to relative votes.
So what we want to do is the following. We're going to adjust the Democratic or the Republican votes in a relative way. That is, we'll multiply by a constant all votes of the Republicans or all of the Democrats or both, thereby maintaining their relative position. So this is purely a rescaling.
So again, here are the actual votes. And in bold are the winners. And what are we going to need to do? Well, there are only two Democrats. So what we're going to do is increase all of these votes proportionally until they get exactly three. And this happens when you multiply by this factor, 1.09. And you get these numbers.
So this list, of numbers, of course, is exactly proportional to that one. So relatively, everybody's the same. And now here, notice that this candidate's adjusted vote is just one higher than the Republican's, therefore this candidate wins. And now we have in red, this candidate , that one, that one, that one, and that one are the elected ones. And this is what this method would do. It would say, these three are elected.
Ah, yes, but you can say, why do I do this by the rows or by the parties. Maybe I should do this instead the other way around, by the columns or by the districts. That is, I could now take a orthogonal point of view, a dual point of view, if you wish. If the requisite number of candidates with the most votes in each party, the party winners, give each district one representative, that is the solution.
So in this case, it doesn't work out. The two with the most votes among the Republicans are those two. And the three among the Democrats are these three. But that gives two to this district. So that's too much. And of course, that means it has two seats, it has none. So either we have to increase these or decrease those. And in the example, I've chosen to decrease those in the second.
And so we start decreasing until we come just under this total. And at this point, when we come down to that, then the two with the most votes in this line are those two. And the three with the most votes among the Democrats are the three in red. And they are the elected ones. Notice, they are exactly the same ones as before. And that is a theorem. The solution is always the same. You can do it one way or the other, it doesn't matter.
And if you use both multipliers, that is at the same time, we use the factor we used for increasing this, and we use the factor decreasing that, then the numbers in the Republican line are the two highest. And the three in the Democratic line are the three highest. And within each district, it is the bigger number. So we get all the properties here at once.
So what is this saying then? It's saying a number of things. First of all, and this comes back to this property of coherence that I talked about in the first lecture, for every pair of candidates of whom one is elected, the elected candidate has a majority of the justified votes. The justified votes mean those that have been transformed. So we're allowed to do anything with the votes. We can multiply by any factor in a row or by any factor in a column. In some basic sense, that does not change anything, because all it's doing is rescaling.
And the reason we can do this is because the total for the Democrats is fixed. The total for the Republicans is fixed. And of course, one is fixed for each district.
Now, notice that if you take, in this table, any pair of candidates, say, this one and either one in this row, say this one and that one, take an elected one and a non-elected one, always, the one who is elected has more votes than the other. And there is no other solution unless if wish a degeneracy, a tie. But that is extremely rare. And ties are, of course, unavoidable.
So this method, I call it fair majority voting, is coherent with the idea that it is a majority decision for every contested pair, given that we accept the idea that rescaling is a fair thing to do. And the theorem is, such rescalings can always be found, and for any number of parties and districts. They always yield the identical set of elected candidates. And no other set of feasible candidates-- feasible meaning they add up right, add up right, that is one per district, the requisite number for each party. No other set of feasible candidates is coherent with a majority decision for every contested pair.
Now, effects. First of all, for the most part, political gerrymandering is eliminated in the sense that a vote for a party counts wherever it is cast. Districts, for that reason, don't need to be exactly equal. Of course, it's already silly from the statistical point of view, from just this notion of accuracy. But there is a sense of maintaining traditional boundaries, which are either traditional because they're boundaries of counties or because there are rivers or mountains or whatever else may that may be involved.
You can practice something. I don't know. There's a thing called minority-majority districts which have been allowed by the Supreme Court in order to give ethnic minorities the possibility of electing a candidate. It has been allowed to create districts where a minority ethnic group is able to become a majority in that district. Well, you could still do this. But you would not have the political impact that it now has. And now it has important impact. It's a very effective way of putting a lot of Democrats into one single district.
Almost surely, a minority would not be able to elect a majority in the House, simply because it's inconceivable, in my opinion, that a major party would not present a candidate in every single district. And secondly, everybody would realize that their vote counts, so that even if they're not going to be electing their own representative, they can participate in electing somebody from the party they wish to adhere to in their state.
So an argument that this notion of a mirror of the US electorate which has always been a word that is used-- was used by James Madison and many others as what was wanting the House of Representatives could be realized. I already said, no candidates would run unopposed. And finally, there is one federal law that concerns congressional elections which stands today which says that representatives must-- they cannot be statewide. They must represent a particular district. And so that would not require any change in the law, if you wish, it would obey it.
Now, there's also the incentive structure. Notice that this scheme allows two things that go on together. In some sense, there are two basic strains in political theory having to do with representation. One is so-called proportional representation, where the notion is people vote for parties. And parties get seats in proportion to their total votes. For example, this is practice nationwide in Israel. And the other, of course, is representation by single member districts. And then let the cards fall where they may from the point of view of the total party representation.
And here then, both things are being mixed together. Realize one at the same time--
Now, in the traditional proportional representation things, usually it's a list, it's a fixed list. And therefore, those who are very high on the list have very strong motivations, but usually, if it's a big party, almost certain of being elected. That's why many politicians like them if they're important ones. On the other hand, people who are very low on these lists have almost no chance at all of being elected. And therefore, their motivations are not very strong.
With this scheme, everybody has a very strong motivation to get as many votes as he can. You want as many for your party so that your party has as many seats as possible. But of course, you also have a motivation to get as many for yourself, because you'll be competing against the others in your own party.
There is of course the drawback that, relative to actual votes, an elected candidate may have fewer votes than an opponent in the same district. And of course, this is what would happen. Here are the actual votes in Connecticut. And obviously in this case, this would be the elected candidate. And yet the other had 13,000 more votes. But you can't have everything. So one has to make a choice.
Now, I remember talking about a year or two ago to a political scientist at NYU who said, oh, this is all very interesting. But the electorate would never accept anything like this. So you might as well forget it. And it's very satisfying to be able to say that the evidence shows quite the contrary, because the scheme has been adopted in a more general form which I will describe in a second, in Zurich. And here it goes by the name of biproportionality.
And incidentally, there's been a site established by the person who sold Zurich on this, Friedrich Pukelsheim. He has a site whereby he's got his software on. And if you want to run any biproportional solutions, he's got all kinds of things that you can use. And anybody can take it off the web.
And the Zurich story is the following. Following the February 2002 Zurich City Parliament, a citizen, let's call him-- I don't know what his name is. Mr. Schmidt? I was going to say Mr. Smith, but it didn't sound quite right. Filed suit in Swiss Federal court, claiming that his constitutional rights were violated, because his vote never counted at all.
Now, as you'll see, I think he was quite right. What was going on? Well, the method at that time that was used was the following. Each city district-- so we'll talk about Zurich City Parliament. This has also been adopted by the Zurich Cantonal government. So it's being used and it's being used in two elections at this moment.
Each city district is apportioned a number of representatives on the basis of its total population. Then each political party presents lists of candidates in each district. And the seats of each district are allocated among the competing party lists by the method of Jefferson. That's the old method.
Now, Mr. Schmidt was the resident of a district with only three representatives. He regularly casts his vote for a party that never received enough votes to receive a seat to elect a candidate. So therefore it's quite true. His vote never made any difference anywhere. And the court gave him reason.
So the Department of the Interior had to find an acceptable method. And they googled this. You would have also, presumably. And found biproportional apportionment, which is a general form of the scheme I just described. And I will describe it to you in terms of the first election that was held in Zurich. These are the numbers from that election. There is one blank down there, and this party presented no list. So instead of putting a 0, I put a blank. So here are the actual votes.
Since the suit, they had redefined the districts so that they would not be such large disparities in the number of seats held in each district. So before, you had districts with two or three and then big ones. But here, these new districts are no longer the old whatever they call them in Switzerland, arrondisements, that they had. But they put certain together in order to make these numbers not too different.
So these numbers, as you see, add up to 125. And so the scheme was this. First of all, add up these votes. I haven't bothered giving you the sums here. I'll just give the results. Add up the votes. Then determine, by whatever method of apportionment as we discussed a couple of days ago, how many seats each party should get. I think they used Jefferson's method. And here are the results.
So now this is exactly the same kind of setup as before, except that before, first of all, there were only two, if you wish, in one sense. But here we have a bigger matrix. Here are the number of seats due to each row. Here are the number of seats due to each column. And of course here, these numbers are no longer just ones, they're any integer.
And so now what we need to decide is, how many seats do I ascribe to each of these lists. They've got to add up. And the idea is this, we're going to simply rescale for the same reasons as before, because that maintains relative position. And rescaling doesn't change anything for the party, because what they're going to receive is fixed, same for every district. So if I multiply things within the votes, it's not going to change anything relative.
And so the statement is this. Multipliers can always be found to rescale the rows or the votes in districts and/or the columns or the votes for parties, so that rounding the results to the nearest integers yields an apportionment that gives to each district and each party the seats it deserves. And in this case, here are the numbers. Now, I show them. These are the actual numbers.
So what is the statement? We can find multipliers so that we get these rescaled numbers. And then what are we going to do? Well, we're going to round each one to the closest integer. So we'll round that to four. We'll round that to two, three, two, one, and so on. And we get these results. They don't really need to be looked at. I will point out the interesting aspects in one moment.
Here are the interesting aspects. Now, I've just taken out several lines, the fifth district, the eighth district, and the ninth district, to show that of course, we can have the same phenomenon that we had with Connecticut where the person elected had fewer votes than his opponent. For example, if you look here, these are the actual votes. And these are the number of seats they got.
So here we have 1,642, and they get two seats. And here you have a much lower total vote, but they get three. But the party, of course, has gotten the number it's supposed to get, and the same thing for the row. And here's another example, two for 631, and only one for 661. So that's the downside.
It's already been used twice in elections. And nobody has objected. They seem to be very happy with the results. In fact, two other cantons are now saying they wish to adopt the method. And there is some discussion of adopting it for the entire country.
SPEAKER 3: Is Mr. Schmidt happy?
MICHEL BALINSKI: I haven't spoken with him. But I know nothing about Mr. Schmidt, to be honest with you. All I know is that it is one citizen who did this. So presumably, he is happy. I hope so.
The theorem then, is this. Such multipliers can always be found for any number of parties and districts. They always yield the identical set of elected candidates. And no other set of feasible candidates, feasible meaning they all add up right, will be coherent with the simple rounding rule for every pair of party district lists. Every pair meaning-- sorry, I'm going to come back here-- that I take any pair. For example, I take this one, third district party B, and take this one sixth, party E. You look at them together. What is the rule by which it's decided? It's the simple rounding rule for the two. And of course, this is the only solution that will do the job.
Well, that's about all I have to say. I would like to just end by two remarks. First, Lou Lehrer underlined this already that the terms of Dr. Messenger's original gift was to provide a course of lectures for the special purpose of raising the moral standard of our political life. Excuse me if I drop the other terms.
And I'd like to add to this a very telling comment that Alexis de Tocqueville wrote to his cousin Gustave du Beaumont in 1851. "How sad it is," he said, "that everywhere on earth, governments are always precisely as roguish as the morals of their subjects permit them to be. Their vices have found but that one limit."
So I hope the students here-- obviously the faculty is beyond this. But I hope the students will take this charge seriously. And I thank you very, very much for this opportunity to talk
SPEAKER 4: One political question and one mathematical question. You commented that in Switzerland, people are pleased with this. But in Switzerland, of course, people are accustomed to voting from party lists. And even though in the US, there's tremendous party loyalty, people like to think they're voting for individuals rather than for parties. So do you see that translating here? And the other mathematical question is, the theorem's properties and the method don't really depend on using Jefferson in the first round.
MICHEL BALINSKI: Of course not, no, no, no.
SPEAKER 4: So you're doing that just to amplify the--
MICHEL BALINSKI: Well, let me answer both. First, look, obviously, I think within the context of the United States, the big problem in my mind is that gerrymandering is here to stay. You can't stop the politicians from using this. So what are you going to do? Are you to do anything? And of course, it may be just as Justice Harlan said. The temptations are there. And they're going to be used.
Now. I honestly didn't feel that this would be very hard to be accepted in the United States. And I tried it out a number of years ago on political scientists and professors of law at the University of Pennsylvania. And I was quite surprised that their reactions were, except for one person, really surprisingly positive as a notion of, here's a way of going about things. Now, how to do this, I don't know.
Second point, there are difficulties in the sense that there is a tradition of saying, well, anybody can become a candidate, so that if you live in a district and you, Bob Bland, want to become a candidate and you get a lot of people to support you, then you could become a candidate and this, that, and the other. And obviously, this scheme totally excludes you, because how are you going to get enough statewide in order to get a seat for your party, so to speak.
But on the other hand, there is this other reality. And of course, I think that the state of representation in the United States, not to speak of France, England, and other places is really pretty bad. And so maybe something has got to be done. And something has got to be changed.
But yes, I'm quite aware that changing anything in the political system is extremely difficult unless somebody sees that it's in his or her self-interest. That's the only way. But unless, as de Tocqueville says, their vices have found just that limit. And I think that's the truth of the matter. So vote them out.
Your second question, yes, Jefferson. There's a good reason for taking Jefferson, because if there are a number of states with only two seats-- if you were to take any other one of the divisor methods, then-- I'll put it in the other way.
If you take Jefferson's method and use it for apportioning two seats, then what will be the result? The party that finishes first will get two seats unless the second party has at least half as many seats as the first. And if it's any other method, then the second party will have to have much more. Yeah, they will. They'll have more seats in order to get one. And so that seems not bad for two.
And when you get to 10 representatives, then you're getting things that are closer to proportional. So it doesn't matter as much. So it seems to be the best scheme from that point of view.
And the second reason is that it does favor the big party. And the fact that it seems to go against each other. But it does tend to favor the big party. And that is a good property in order to have a more stable government, so that there'd be a slight advantage to the big party.
SPEAKER 5: So observed that what happened in Connecticut was that when the Democrats won, they won with, roughly speaking, a margin of 50%, and when the Republicans won, they won with a margin of something like 15% or 20%
MICHEL BALINSKI: Right.
SPEAKER 5: I assume, of course, that this is completely deliberate.
MICHEL BALINSKI: Well, of course.
SPEAKER 5: They definitely arranged that.
MICHEL BALINSKI: Well, look, there are two things, two remarks. One is certainly, there is some deliberate effort. On the other hand, this is always going to happen, because the Democrats are the more popular party. And their electorate tend to be more urban. So you draw blindly, and you're going to have more packing in of Democrats together. So there's always going to be a tendency in this country for Democrats to be disfaored.
On the other hand, as you'll remember in this last election, the Republicans only elected one candidate, and the Democrats had four. So it did sort of swing in the opposite direction.
SPEAKER 5: That's the point, of course. If you had a substantial change in the feelings of the electorate, those things that were so carefully designed to give more districts to one are more likely to split.
MICHEL BALINSKI: Yeah. Yes? I'm sorry.
SPEAKER 6: In this final method, you described it more or less on a state by state basis. And I'm wondering, is it obvious that you get the same result if you do it on a state by state basis scaled to a national level. In other words if you do it state by state--
MICHEL BALINSKI: That's a very good point. Obviously, some people say, why don't you just do this nationally and so on and so forth. I don't think it's realistic, because I think that there is a strong-- in the United States, there is such a strong identity with states, that my sense is that, practically speaking, that would never fly.
Incidentally, this is one of the things you see Supreme Court Justices talking about, the horrors of proportional representation. I actually don't think they know what they're talking about when-- some of the things they say. But there's always this attack, as though proportional representation, my god, that's-- no, no, no, no. So you're perfectly right. This could be done nationally.
Second point is, well, no. I think you'd get a somewhat better proportionality to parties-- you'd certainly get a better proportionally to parties if you did it nationally. But if you already would be doing better if you did it by states then what is happening now. So I don't know.
I think this has so much to do with the traditions of the country you're talking about. And in this country, I think going to proportionality countrywide, just forget it. No one would ever consider it. There would be such strong opposition that it just seems to be totally out of the realm of possibility.
And even now, this notion of doing it on a state level is already pretty bad, except perhaps that the abuses of gerrymandering are so strong. And come back to California, where this is ecumenical in California. When we're talking about everybody being elected essentially by margins of 20%, it's Democrats and Republicans. And there is a sense of outrage that's growing over this. So maybe there would be hope of doing something.
But I'm again, I quite ascribe to what Bob said, as he pointed out. Bob Bland, in Zurich, people we used to party lists. Now, they were not used to party lists getting fewer seats when they have more votes. No, certainly not. But they are used to it. So there's maybe more abstraction from the point of view of who the individual candidates are.
SPEAKER 7: Is there an estimate on how many of these districts will turn out such that the minority person becomes the winner? Could it be there's a large number of minority winners?
MICHEL BALINSKI: It's a good question. I don't know what the answer is. I have not tried to answer that question. Excuse me, what would happen? And I'll say, it's not going to be an answer to your question directly, all right? But it comes on the fringes, so to speak.
You take California, I did computations here and there, just taking actual votes as much as I could to see what kinds of things might happen. Now, the Libertarians run candidates in most of California's 53 districts. So they get-- I've forgotten. They had something close to 2% of the vote.
Anyhow, in one of those elections, one year, they would have got either one or two candidates. Then you ask, who are those candidates. Well, it turns out, of course, that the Libertarians, they pick up a small number 53 times. And so it's got to be one of those small numbers who's elected. And so in the face of this candidate, this candidate would be getting 15,000 votes. There was somebody else getting 55,000. And they were defeated. That wouldn't wash.
Now, my sense about that is that there should be, with this, a stipulation which says, a party that does not have at least-- I'm going to pick this out of the air-- 25% of the vote gets no seats. Now, look, this is the truth today. In fact, you have much more than 25% to find yourself at least one seat. But it's not an admitted truth. It's not a constraint. It's open and all the rest of it. But it is a fact. Therefore, putting a 25% cutoff would easily take care of this kind of problem.
One could try to invent the worst possible situation. That should be an easy exercise to just try to see how bad you could make this from the point of view of the question you raised. But I would say that, on the whole, it shouldn't be-- well, I gave you the example of Michigan. And I don't remember exactly what the numbers were, except I think there was a disparity. It was nine for the Republicans and six for the Democrats. And yet the Democrats had a little bit more of the vote.
So we can see it right there that that would mean three candidates. Yeah, if the Democrats had more votes-- so two candidates who had the most vote at least would have to have lost. But presumably, if the votes are more or less spread well throughout the districts, that is that the districts don't differ too much in the total vote, these disparities shouldn't be too bad. But I'm sure you could get some examples which are a bit-- and yet would they very often happen in practice? My sense is no. But I can't give you the specific answer. I don't know.
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Why blatant political gerrymandering is unavoidable in today's system... and what to do about it.
The third in a series of three Messenger Lectures on representing, electing and ranking by Michel Balinski, Professor Emeritus, École Polytechnique, Paris.