A conversation with the game theorist and Professor of

Politics at New York University.

Steven Brams: Steven Brams and I’m a Professor of Politics at New York University.

Question: What is game theory?

Steven Brams: Sure. Game theory is a strategic theory in which there are generally two or more players, so-called, or actors. And the outcome of their game depends on the choices of all the players. So, it’s an interdependent decision situation. And the mathematical theory was developed going back to the 1920’s, but primarily in a book by John Von Neumann, the great mathematician, and Oskar Morgenstern, an economist, who were both at Princeton, called "Theory of Games and Economic Behavior."  This book was published in 1944, and that really started the subject of “game theory.” And it’s been applied in numerous areas. I am a political scientist, so it’s been applied to the study of voting and elections to international politics. It’s probably most prominent in economics; most of economics is now written in “game theory” terms, especially micro-economics, but macro-economics, international economics as well. It’s been applied to biology, evolutionary biology, the evolution of species, their conflicts.

For example, in my work I’ve applied it to text, including the Bible. I’ve looked at the Hebrew Bible and the 20 stories of conflict and intrigue that I thought were most game-like, and starting with Adam and Eve and going through most of the famous stories, and some not so famous. I tried to show with game trees and payoff matrixes that the biblical characters were by and large rational, God included. I made applications in political science and I’ve also done applications to sports; the selection of draft players for example, in the professional sports league. So, those are some examples.

Question: What’s an example of biblical characters acting rationally according to game theory?

Steven Brams: Take the story of Samson and Delilah. In this story, Delilah, a Philistine, tries to get the secret of Samson’s strength; and makes three attempts. Delilah is a woman that Samson loves, he very much dislikes being harassed all the time for the secret of his strength, but he refuses in the first two attempts that Delilah has. Finally he succumbs and he tells the secret of his strength and then bad things happen afterwards. Though, Samson gets his revenge in the end. And I think the interesting question you can ask about this story is; how could somebody like Samson be so stupid as to ignore several warnings?

And my answer is that if you look at Samson’s previous career, he lusted after almost every woman he ever met. Every beautiful woman anyway, and Delilah was the latest. So, you can explain his behavior as rational in terms of this interest in women, allowing him to think that he was taking a risk maybe in telling the secret of his strength, his long hair which, of course, was cut off. But it might not be disastrous. 

In the end, it was disastrous. Samson was mutilated, he was treated with derision, but he got his revenge. He was placed between two pillars, his hair had grown back at that time, and he collapsed this big stadium, killing thousands of Philistines.

So, in games, bad things can happen. One can explain this in terms of the rationality of the player’s actions. And I define rationality simply to mean that you make better – you can rank alternatives and you chose the best alternative. But in the game, it’s more complicated because you have to choose the best alternative in light of what the other players may chose and that affects the outcome. But it doesn’t depend on your goals. Whatever your goals, if you do the best to achieve them, I argue you’re being rational. So if somebody desires to commit suicide, and maybe somebody who is in great pain and succeeds in doing so, I consider that behavior rational because this was the goal of the person.

Most of us don’t have the goal of committing suicide. Most of us have other goals; winning in a contest and the like, getting as much profit as we can from an enterprise. But whatever the goals, if you chose the most effective means to achieve them, you’re being rational. That’s, I think, the best way of thinking of rationality. It’s not that the goals are reasonable; it’s that the means to achieve the goals are effective.

Question: Do you study real-world elections or theoretical models of elections?

Steven Brams: It’s some of both. We try to construct theoretical models that represent real life situations, but like any model, they simplify the situation and we try to derive consequences of our assumptions. It’s a mathematical model so we deduce what our assumptions indicate. We prove theorems, as they are called. But we also ask about the applicability of these theorems, these consequences in real life cases. So, one gets one’s inspiration usually from observing what happens in the real world, and those are the kinds of things I teach. But I try to make them more coherent, understand them at a more scientific level, by constructing a model. A model might be something like that if you can array the candidates on a left/right continuum, you will vote for the candidate closest to you. Now, that is complicated often by the fact that the person closest to you, the candidate, might be somebody who has little chance of winning. So you might want to alter your choice to vote for a more viable second choice, or third choice.

A good example of this was the 2000 U.S. Presidential election in which Ralph Nader was a third-party candidate. He ended up getting less than 3% of the popular vote; he won no states, so he got no electoral votes. And Nader supporters, generally on the far left, were torn. Should they vote for Nader, who had no chance of winning, or should they switch to a second choice? For many of the Nader supporters, that would have been a Democrat, Al Gore. And in some cases they were torn. And one consequence of being torn is you don’t vote at all. You can’t make up your mind. But some switched, and some did not switch. Of course the major consequence was that enough stuck with Nader so that he, by all accounts, affected the election outcome. In particular, in Florida, Bush in the end got about – he beat Gore by about 500 votes. But there were 97,000 Nader supporters in Florida, and if most of them had gone for Gore as a second choice, then Gore would have won by tens of thousands of votes instead of losing by about 500. That would have changed the outcome in the country as a whole and we would have had a different President. So that’s a good example of a so-called “spoiler,” somebody who can’t win, who changes the election outcome.

So those are the kinds of situations that we study, and I think these models are very helpful in understanding them.

Question: How can your models help voters make the most rational decision in a given election?

Steven Brams: Well I think, what I just suggested about the 2000 election is the example. If you feel that the consequences of electing Bush, let’s say you’re a Democrat, far left leaning, are sufficiently problematic and you are a Nader supporter, then you might well switch. That would be the rational choice. But if you think neither candidate was very good, as Nader argued, they were both cut of the same cloth, then you would not switch and your vote would be more of a protest vote.

So rationality will move voters in different directions depending on what their preference is, their goals. If you want to just protest, or do you want to affect an election outcome, or try to affect an election outcome?

Question: What is approval voting, and how is it currently used?

Steven Brams: Approval voting is a voting system for multi-candidate races. Races with more then two candidates, which are typical in, say, Presidential Primaries with five to 10 major candidates starting off in Iowa and New Hampshire. In those kinds of races, approval voting would permit you to vote for, or approve of, as many candidates as you’d like. So, if there were nine candidates in the race, the Democratic primary in New Hampshire in 2008, and you were a liberal Democrat and you had identified three people as liberal in the Democrat party, then you wouldn’t have to make an arbitrary choice in one of the liberals. You could vote for all three and thereby better express your preferences. So, you can do everything you can under the present system, vote for one candidate if you have a clear favorite. But if you don’t have a clear favorite, if you’re relatively indifferent among several candidates, like the liberal democrats, you can vote for all of those. Or, if you despise someone you can vote for everybody else.

So, it gives you great flexibility in being able to express your differences. It’s on a ranking system. Each person that you approve of gets one vote, and the person with the most approval wins the election. And we’ve shown that it would have had major consequences in a race like the 2000 Presidential election. Presumably, many Nader supporters would have also voted for Gore to prevent their worse choice, Bush, from winning. So, they would have cast two approval votes. Some would have bullet voted, we say, voted exclusively for Nader and Gore would have, of course, his exclusive supporters. But it’s quite clear that a sufficient number of Nader supporters would have also approved of Gore such that he almost surely would have won the election in Florida or in the Presidential elections. So, it would have obviously made a difference in that election. And there are many other examples with significant third or fourth party candidates in which the outcome almost surely would have changed.

We can’t surely quite ascertain that it would have changed in the end because when you change the rules, any change in the rules by allowing approval voting, the nature of the campaign would change and we can’t simply extrapolate from the present campaign. But I think there’s good enough information in the 2000 election to say that under approval voting Gore almost surely would have won.

So, besides giving the voter more flexible options, it tends to elect the strongest candidate overall. Not the strongest minority candidate. And we have examples where significant candidates on the left or the right, have beat out a centrist candidate, a centrist is hit from both sides so to speak by the left and right candidates in a three-candidate race, and comes in third, let’s say. So, even if there’s a run off, which is something proposed as a solution and used as a solution to try to find the strongest candidate, the runoff would put the left candidate against the right when it’s pretty clear the centrist candidate in a pair wise contest against the left candidate would beat the left candidate, a pair wise contest against the right candidate would beat the right candidate. So could beat each of his competitors in a compare wise contest. We actually have a name for that candidate in these multi-candidate races. He’s a Condorset candidate, after the Marquise de Condorset in the late 18th century France, who proposed this kind of candidate and showed that one always doesn’t find such a candidate. It almost surely would elect Condorset candidates winners in these multi-candidates contests. So, generally in the United States, the contest comes down to two major candidates in a general election, even an election like the 2000 election. But in party primaries, when you get 5 to 10 major candidates, it’s often the case that the Condorset winner gets cut out. The field is crowded, the centrist is squeezed, the strong left candidate or the strong right candidate wins.

And it’s a disaster, in my opinion, for the country. It happened in 1964 when the Republicans nominated Barry Goldwater, an extreme right-wing candidate. He lost disastrously to Lyndon Johnson that year in the general election. It happened to the Democrats in 1972. They nominated George McGovern, a far left candidate, who lost massively to Richard Nixon that year. And that’s not good for democracy because the election is essentially decided when one party nominates an extremist against the centrist of the other. And I think if approval voting were used, especially in primaries, it would tend to surface the strongest candidate in the party and make the contests much more competitive with two centrists running against each other rather than extremists, who usually gets beaten in these kinds of contests.

So I think not only does it help the individual, it helps the social choice, the candidate elected making him or her a much more plausible candidate than a **** of extremists like Goldwater in ’64, and McGovern in ’72.

Question: Would this system encourage strategic voting as opposed to voting one’s conscience?

Steven Brams: No, I actually think the opposite. I think when you can approve of more than one candidate, you are less likely to vote strategically. If you mean by strategic voting, ignoring a first choice because he, a Nader, is our of the running and voting for a second choice or a third choice to prevent your worst choice from winning, under approval voting you could have your cake and eat it too. You can vote sincerely for the candidate who can’t win, the Nader, and you can cast a second approval vote, or strategic vote for the candidate who can, Gore in the 2000 election. So, I think it actually minimized the strategic voting. 

The two arguments that have been made against approval voting; first, that it would tend to elect the lowest common denominator, the centrist candidate who tries to be everything to everybody. But I think the candidate who is the lowest common denominator is generally going to be unappealing to most voters. You try to be everything to everybody; you’re not going to be acceptable to very many people. A good example of a candidate who would win under approval voting would be Ronald Reagan. Ronald Reagan won in landslides in 1980, and 1984. He was a right-oriented candidate, but he was appealing to a substantial majority in each election. Nobody ever accused Reagan of being weak or pusillanimous; he had strong convictions, and he would have won not only in approval voting, but virtually any other system.

So, I think that’s the kind of candidate who is generally appealing, maybe right of center or left of center, who’s going to win. It’s not always going to elect the candidate – inoffensive, bland, who has nothing to say. So, I think that’s my argument that it wouldn’t have that affect. 

The other argument sometimes made against approval voting is that it would undermine the two-party system. Well, first of all, I think there is nothing sacrosanct about the two-party system in the United States. Most western democracies have multi-party systems and in my opinion they’re just as democratic, if not more so, than the United States. So, I would argue that if the two major parties, Republicans and Democrats were so derelict as to nominate extremists in the same year, there should be room in the center for a centrist to come in and win. And approval voting would tend to promote that.

Ross Perot, for example, in 1992. He was a significant third-party candidate who ran against Bush, the father, and Clinton that year. And he got 19% of the popular vote. Almost an all time high for a third-party candidate. If there had been approval voting, he conceivably might have won because Democrats might also have approved of Perot. He was liberal on social issues, and so might conservatives. He was conservative on financial and economic issues. Now, he was also a little crazy. So, that dispirited many of his supporters in the end. But a more credible centrist candidate, I think, should have that opportunity to win. And right now, our two-party system is pretty much impregnable under plurality voting. You have to vote for one or the other candidate. You’re generally going to ignore the third or fourth party candidate. So, that candidate has no chance.

With approval voting, you can afford to vote for additional candidates and if there is sufficiently strong third or fourth party candidate, I think he or she should win. 

Question: Which present-day democracy offers the fairest system for electing officials?

Steven Brams: Well I think most of the democracies in the world use what we call proportional representation. That parties run, not candidates by and large, and you vote for a political party and the party gets a number of seats in the legislature proportional to the number of votes it got. The problem that critics of this system have is that people don’t have their personal representatives. It’s a party that you vote for, it’s not the individual. And shouldn’t a voter have the opportunity to go to a representative, or his staff, and seek redress from grievances. That’s harder to do if it’s got an impersonal party than if it’s a real person.

But I think Germany and a few other countries that use basically the German system do well on both counts. In Germany you vote for parties and they get seats in proportion to the number of votes of the parties, but in addition, you vote for an individual representative in your district. And half the German Parliament, the Bungestag is called, is elected on the basis of your vote for the representative in your district, and half depends upon your vote for the party. And if your party, say the Green Party, which typically gets about 10% of the vote, wins no seats at the local level because it’s one of the major parties that usually wins. The Socialists or the Christian Democrats in the case of Germany, then the Green Party is going to be compensated from the seats at the national level when you vote for party. So, if they got 10% of the vote for the party, but no seats because they won in no districts, then they would get seats from the national vote and the representation would be made up. It would be made proportional because you have that 50% at the national level to play around with. So, I think that’s a kind of near-ideal system for a parliamentary democracy. You have your personal representative, but you have your proportional representation at the national level. And a few other countries have adopted this, in Eastern Europe for example.

Question: What would you recommend doing about the Electoral College?

Steven Brams: Abolishing it, in a word. I think it’s an anachronism. It was designed so that the masses, we’re going back to the 1800’s, actually 1700’s, would not be able to directly influence the outcome of the election. There would be kind of an intermediate body, the Electoral College, that would be elected and perhaps they would in deliberation would make a considered choice and thereby perhaps endorse what regular citizens chose, but perhaps not.

The real problem, however, is not the Electoral College itself, it’s winner take all. So, under the present rules, in all but two states, the winner of a state, even a plurality winner not necessarily the majority winner if there are two candidates, wins all of the electoral votes of that state. So, in a state like California with, I believe now 53 representatives, it’s electoral votes and the number it is representative of is 53 plus the two senatorial electoral votes, so that brings it up to 55, and that’s about 10% of the entire electoral vote. Which means California is very decisive. Well, in a sense, not really because California has recently been a democratic state, like New York. Texas is primarily a Republican state, so these states in effect don’t swing votes. They are almost sure things for one party or the other. But a state like Florida in 2000 or a state like Ohio in 2008, were critical to the election of Bush in both years. These were close elections in each case. So how they go very much determines the outcome and isn’t necessarily the case that these large states that can change the outcome in a close election are representative of the country as a whole. I think not. Moreover, winner take all means that you spend many more resources, even proportionately in these large, well there are various names, but essentially they are a the toss up states. And even small toss up states like New Hampshire now is pretty much a state that has gone either way. And basically ignore the states that are kind of sure things; California, New York, Texas. And I think elections, Presidential elections, would be much more exciting and bring in everybody in all the states if candidates had to seek out support everywhere. Maybe roughly in proportion to the size of the states, but there would be no toss up states that would be decisive, or everybody would be in that sense would be decisive. And what that does is distort campaigns themselves. Candidates spend the bulk of their time in these toss up states ignoring the rest of the country.

The last President to visit all 50 states was Richard Nixon in 1960 in his campaign against John Kennedy. He pledged that he would visit all 50 states and despite injuring himself and sidelining his campaign for 10 days in September of 1960, he kept his pledge. So, he spent basically the last 36 hours of his campaign on planes to Hawaii and Alaska to fulfill his pledge. And then he lost the election by a squeaker. And most people think if he had spent a little more time in Ohio or another key state, he would have won. Well, in 1968, Nixon abandoned that strategy and followed what is called “the Rose Garden strategy,” basically stayed in the White House, and won the election. So, since then, no candidate has visited all 50 states. Whereas, I think if we abolish the Electoral College and votes counted the same everywhere, then we’d see much more national campaigns in all the states.

Question: How can your work on fair division theory be applied to political problems?

Steven Brams: Well we actually did apply one of our procedures to the 1978 Camp David Agreement between Israel and Egypt, which eventuated in a peace treaty in 1979. And there were several major issues dividing Israel and Egypt; the return of the Sinai after the ’73 war, which had been captured in the ’67 war for Israel, was recognitioned, diplomatic recognition by the Egyptians. And there were several other issues. And we assessed how important winning on these issues, getting one’s way, was to Israel was on the one hand and Egypt on the other. And we had given these attributions of importance using the algorithm to determine who would win on what issues. And it pretty much matched the actual agreement which took many months to negotiate; actually many years. And we think it would have been a much more efficient way to use the algorithm to determine who would win on what issues. And it pretty much matched the actual agreement, which took many months to negotiate, actually many years, and we think it would have been a much more efficient way to use this procedure and have countries indicate their interests using the procedure and then the procedure, the algorithm, would say who wins on what issues.

And it also can be used in more mundane circumstances, in dividing the marital property in a divorce. Again, you indicate how important it is to get the car, the house, the boat, the children, and so on, and it tells who gets what. And what we’ve found using these procedures is that most disputants can get between two-third and three-quarters of what they want because they want different things.

So, if you use an algorithm that does things fairly, makes the division what we call “envy free” so you don’t envy what the other person got because you got at least as much, it makes it equitable so that you both get the same amount, about 50%, that because the parties want often different things, they both can win. So, we actually call this a win-win solution. But we give more than that, an algorithm for making this division. So that’s some of the work that we’ve done on fair division.

And then we’ve done more theoretical work. This is work primarily with Allen Taylor, the mathematician at Union College. We came up with an algorithm for cutting a cake. Not just dividing separate goods like the house, the car, the boat, and so on. But what if the cake is something divisible, like land. How do you divide the land so that it satisfies these fairness properties and we came up with a cake cutting algorithm that basically generalizes the procedure everybody knows; I cut, you choose. That’s for two people. One person cuts 50/50 in terms of his preferences, and the other person will chose one half or the other. But her preferences are likely to be different from his preferences. So, she’s going to see one piece is worth more than 50%, but he, the cutter, has protected himself by dividing it 50/50. So I think we are all familiar with that. But how do you extend that to three persons, or four persons? So that’s what the algorithm did with the cake cutting algorithm. It’s actually very complicated so we’re not recommending this to be used practically to divide cake. So we came up with other procedures that are more practicable. And NYU, my university, actually patented one of these algorithms. It’s called Adjusted Winner. It’s a point allocation algorithm. So I’m the only political scientist I know with a U.S. Patent, and it’s an unusual patent. I think it was the first patent every issued for a legal dispute resolution procedure. Now, NYU has licensed the patent to a Boston law firm and a company has been formed called Fair Outcomes, Incorporated. It has a portfolio of these algorithms for settling disputes. And it’s in its embryonic stage, so I can’t report much on what’s happened. But I think that it’s a better way to solve disputes than the usual legal proceedings, which can be very costly to the litigants. They end up paying the lawyers most of their fees and it’s also usually quicker to use an algorithm than to litigate or simply negotiate sometimes over weeks, sometimes over months with a party you don’t particularly get along with. So, I’d like to see more of this actually used. And I’ve talked to bar associations and lawyers groups about this, and while some lawyers, of course, see their billable hours going down the drain if an algorithm is used rather than they’re using their great negotiating skills. But others see this as a procedure which would help them. And they could use their hours for more constructive purposes; advising people and to use this algorithm well. It’s a very simple algorithm. And to publicize it, we wrote this book, a popular book called The Win-Win Solution, which has not been translated into six languages. So, it seems to be attractive to people around the world. And we hope the company sells this idea and makes dispute resolution less burdensome and less trying for people.

Question: Will you apply your solution to the cake-cutting problem on your 70th birthday this year?

Steven Brams: Oh, well what I’m – in birthday parties, not necessarily my own, I’m usually the one asked to cut the cake, because I have done these kinds of things. But no, it’s a little too complicated if there are a lot of people. So, I am not recommending that this particular algorithm be used. But the one whereby you allocate points is very simple. It’s applicable to basically two-party disputes; those tend to be the most common. And we get some very nice properties out of it. We get the fact that not only is it envy-free, not only do both parties get the same amount – get more than the other party, but they get the same amount, about 50%. And it’s efficient, which means that there’s nothing better for both of them out there. So it has these kinds of guarantees which I think make the solution very attractive. And we’ve actually tested this in the laboratory and it’s been used in real life in a few cases, and it seems to work very well. So, we hope more people come around to the idea that this is, I think, the way to settle disputes. The alternative it’s actually called alternative dispute resolution, ADR, tends to take a more psychological approach. There’s a famous book called “Getting to Yes,” by Fisher and Ury, that says that if you communicate clearly, if you take into account the other side’s interests, you both can win also. I think the problem is that this is kind of naïve because people have strong incentives to exaggerate or to posture in negotiations. And what algorithms do is prevent that. It’s in your interests to be truthful, otherwise you may hurt yourself. In the absence of algorithms and in the absence of this kind of discipline, given my algorithm, you can give advice that you should be honest and communicate clearly, but that might not be in your best interests. That might not be rational. So, I think we need something more than what I call the “feel-good” approach.