Podcast 2012–10–06: Interview with Nobel Laureate Dr. Kenneth Arrow

Dr. Arrow, Stanford professor emeritus and Nobel Laureate talks about voting methods and his Nobel-Prize-winning impossibility theorem.

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Dr. Kenneth Arrow: Dr. Arrow is professor emeritus at Stanford University in the economics department. His work has included social choice theory, risk bearing, medical economics, general equilibrium analysis, inventory theory, and the economics of information and innovation. His most notable work concerns his impossibility theorem for which he was awarded the Nobel Prize.

Aaron Hamlin: Executive Director of The Center for Election Science



CES: Welcome to The Center for Election Science podcast. The Center for Election Science is a nonpartisan, nonprofit dedicated to informing the public about voting systems. You can find more of our work on the web at electology.org as well as on Facebook and Twitter I’m Aaron Hamlin, co-founder and president of The Center for Election Science.Today we have the honor of talking with Nobel Laureate, Dr. Kenneth Arrow. Dr. Arrow is renowned for the development of his Impossibility Theorem within the area of voting theory. In 1972, his theorem made him the youngest person ever to earn the Nobel Prize in economics. Among his many other achievements, Dr. Arrow was also awarded the National Medal of Science and elected to the National Academy of Sciences. Dr. Arrow currently serves as professor emeritus at Stanford University.We’ll be talking with Dr. Arrow about his Impossibility Theorem’s impact on voting theory as well as the status of voting methods in the United States. Hi. Dr. Arrow?

Dr. Arrow: Yes.

CES: Hi. This is Aaron Hamlin again from The Center for Election Science.

Dr. Arrow: Yes.

CES: How are you doing?

Dr. Arrow: Fine, thank you. And you?

CES: Great, great. I think most listeners will be more familiar with your work from your Impossibility Theorem, which you won the Nobel Prize for in ’72. Would you mind describing the Impossibility Theorem for a general audience in summary?

Dr. Arrow: Yes. Well, one way of looking at it is that we proposed some criteria for what a good system should be: what is it you want from a voting system, and impose some conditions. And then ask: can you have a voting system that guarantees that? Now the situation, of course, is only interesting when there are more than two candidates. If there are two candidates, the one that gets more votes wins would be pretty hard to argue against that method. But if we have more than two candidates, and no one gets a majority, there’s a question of what kind of arrangements you want to make. Who do you choose?Now, there are two questions here. One is: what kind of data do we ask? In other words, we’re interrogating the voters as to their preferences. They have a bunch of candidates and each voter has some kind of preference over the candidates. And in my theorem I’m assuming that the information is a ranking. Each voter can say of any two candidates, I prefer this one to this one. So then we have essentially a ranking. It’s a list saying this is my first choice. This is my second choice. Each voter, in principle, could be asked to give that entire piece of information. In the ordinary Plurality Voting, say as used in electing Congressmen, we generally only ask for the first choice. But, in principle, we could ask for more choices. And we do in the Instant Runoff elections.Okay, so in the first place, this is the raw material from which we’re supposed to make a decision. We have a ranking. Each voter has a ranking of all the candidates giving the first choices, second choices, and so forth.

CES: Within your theorem you mentioned that there are certain criteria.

Dr. Arrow: Now the question as to the criteria are, how do you take this information and make it into a choice of candidates, a social decision? One of the principles is that in effect we should be able to get a ranking of all the candidates out of this information. Of course, imagine that you choose a candidate and then somehow that candidate is unavailable. And so you imagine going through the individual information, scrubbing that candidate out, and then saying, “now what do you do”? So presume you get a socially desirable second choice candidate and so forth. Then the other, obviously, if everybody prefers candidate A to candidate B, we certainly want candidate A to be preferred to candidate B. And finally we say that if we strike out a candidate for some reason then only the preferences among the other candidates should count to getting the next candidate. All the information we have of the votes for those who are a candidate, if we decide somehow one candidate is eliminated, then the choice among the remaining candidates should depend only on the voter’s preferences among those candidates.It turns out that if you just impose those conditions and no others, that the only systems that are consistent are either that make choices independent of what people vote (which obviously is absurd), or we have a dictatorship; one person is given the choices. To put it another way, if we assume everybody should count equally, then there is no method of voting which will avoid some possibility of violating the rules.

CES: When you’re saying that no ranking method is able to fulfill these rules, it seems like a lot of people; they become highly pessimistic and they think: “well, let’s just forget about improvement.” So, when people have that reaction, what kind of response do you take?

Dr. Arrow: I think the answer is you have to ask, in effect, which ones get closest to this combination? And we have to then begin to look at what actual votes are. The real we do it is to apply some rule and to take elections and apply different methods and see what violates these conditions as little as possible. Remember all we’re saying is there could be a set of. We’re not saying you’re always getting a violation of these rules. We’re just saying there can be preferences of individuals which will cause one rule or the other to be violated. It may be the preferences of individuals which cause violations to occur very infrequently.See, let me give you an example. Supposing, we imagine that just really one basic issue and many possible policies, but there’s only one basic issue. You know, for example how much you should spend on education. And so the only question is the dollar amount. In those cases, it’s very likely (but I won’t go into technicalities) that there’s one position which would get a majority against all others. And that’s because we’re restricting, we’re assuming that if a person has a most preferred (an individual voter that is) has a most preferred level of education expenditure, he would prefer things closer to that than things further away. So if I think we should spend $5,000 a student, I’d rather spend $5,100 than $5,200. And I’d rather spend $4,900 than $4,800. So we’re assuming that the preferences of the voters are known in advance to have a certain structure. Then it would follow in that particular case that there is going to be one level which will get a majority against all other levels. And therefore most voters would regard that as a pretty satisfactory outcome.

CES: So it seems like one of the points that you’re stressing within the theorem is that even though none of the ranking methods can fulfill the criteria, that’s really not speaking to the degree that they fail nor the frequency they fail-even if at some point it’s possible for them to fail.

Dr. Arrow: That’s correct. Yes. Now there’s another possible way of thinking about it, which is not included in my theorem. But we have some idea how strongly people feel. In other words, you might do something like saying each voter does not just give a ranking. But says, this is good. And this is not good. Or this is very good. And this is bad. So I have three or four classes. You have two classes is what you call Approval Voting. Just say some measures are satisfactory, and some aren’t. This gives more structure. And, in effect, say I approve and you approve, we sort of should count equally. So this gives more information than simply what I have asked for. This changes the nature of voting. We don’t just rank the candidates. We say something like they’re good or bad or something. This again, this method does not necessarily avoid paradoxes. But it seems empirically to minimize their importance.

CES: Now, you mention that your theorem applies to preferential systems or ranking systems.

Dr. Arrow: Yes

CES: But the system that you’re just referring to, Approval Voting, falls within a class called cardinal systems. So not within ranking systems.

Dr. Arrow: And as I said, that in effect implies more information.

CES: So what do you think about Approval Voting as a voting method as an alternative to Plurality Voting or another preferential system.

Dr. Arrow: I really would like to see it studied in some novel system, maybe an experimental situation. I’d like to see how it works out in practice. In other words, take a variety of situations, a variety of cities, or whatever. And see how this would work out and whether the results really look reasonable. One of the things that come from my theorem is that you really have to take an empirical view of the matter and not rely on a priori thinking. So Approval Voting obviously works well in a number of circumstances. It does, I think, something a little more refined than Approval Voting is probably needed. In other words, two classes are probably not enough to do a good job would be my feeling-if you really had a fragmented electorate.

CES: So if you’re referring to allowing more expressiveness than two levels which is what Approval Voting does, what do you think about something like Score Voting where voter rate candidates along a scale so that they can have more than two levels, say 0–10. So 11 levels in that circumstance, or more.

Dr. Arrow: There’s only one problem that bothers me about that. And that’s something my theorem really doesn’t cover. In my theorem I was assuming people vote sincerely. The trouble with methods where you have three or four classes, I think if people vote sincerely they may well be very satisfactory. The problem is the incentive to misrepresent your vote may be high. In other words, a classic view is that there’s a candidate I really like, but I know is hopeless. I may put him down at the bottom and vote for the next candidate simply because I feel there’s a chance. Now, if you have a very large electorate you might say no individual has much of an incentive to misrepresent. But I’m not sure. You probably need experience rather than theory.

CES: Do you have any particular preferences or ideas as far as how voting methods should be evaluated in the future? Or, do you think there are certain things we should look at in trying to figure out what voting methods we should push?

Dr. Arrow: Well, I’m a little inclined to think that score systems where you categorize in maybe three or four classes probably (in spite of what I said about manipulation) is probably the best. And that is to look at the outcomes and see if everybody says, “well, that seems intuitively a reasonable outcome given the inputs.” And some of these studies have been made. In France, [Michel] Balinski has done some studies of this kind which seem to give some support to these scoring methods. And he showed the result. If you look at the votes you kinda say, it’s a little hard to define to answer criteria. Because that’s what I was trying to do theoretically. But if you look at the outcomes that you may try to reproduce elections in the United States. Of course, we don’t have the ranking data, or any scoring data, or anything like that. But sometimes you can imaginatively reconstruct them. You know, people have argued that Lincoln never would have been elected in 1860 if we had some system like that because he was in some sense an extreme candidate.

CES: Now, in the US we use Plurality Voting, which is: you look at a slate of candidates. You pick one. And the candidate with the most votes wins. Now what are your thoughts about the US using this voting method as opposed to something else? Do you think that this is just good enough? Or where do you think this puts us as using Plurality Voting in the US?

Dr. Arrow: It always depends on the fact that there are several different positions, more than two possibilities. There have certainly been clear cases where the Plurality Voting gave the wrong result, where an extremist candidate won who clearly was not the one that people would have preferred. In other words, there’s another one who would have gotten a majority. That happened, and has happened several times in senatorial or gubernatorial elections. And certainly when you come to local elections where party lines matter less, you can get absurd results.And for example in the Bay Area, we do have, there’s been a movement for the so called Instant Runoff elections which are in effect a kind of ballot which uses all the information. Where voters really rank the candidates and if nobody gets a majority you eliminate. And of course it saves the cost of a second election. Whenever people complain about the results, that it turns out that clearly the winner would’ve gotten a majority against let’s say the person that got the plurality. Otherwise, you usually do it by eliminating the lowest ranking candidate and redistributing the ballots. So it’s clear the person you’ve elected clearly would have gotten more votes in a two-candidate race against the person who got the plurality vote. So in those cases, it seems perfectly reasonable to say that the winner is the right person and not the plurality vote. I think Plurality Voting lead to very unsatisfactory solutions in a number of cases.Now, there is a problem which certainly in my social choice theorem didn’t address and a lot of discussions don’t address about elections which is the long-run implications of an electoral system on parties. Partly, if you have a Plurality system, you’re kind of driven to a two-party system. If a party splits, both factions lose because they’re less likely to get a plurality. So there’s some pressure to create two-party systems. Now some people have argued that two-party systems are a good idea. And others say no. It stifles innovation. It stifles real contest. New ideas are suppressed in a two-party system. I’m inclined to the latter view that if there really are a number of political positions, it’s better they be raised explicitly. But I will say that some people have argued that two-party systems have more stability, countries with proportional representation have a lot of parties and that’s a problem. That’s a dynamic question which is pretty hard to assess from a formal point of view like mine. So I just raise this question about the long-run effects. But I’m a little inclined to feel that it’s better to have the difference of opinion explicitly represented by parties-if going away from a Plurality system leads to a multi-party system, that’s actually a good thing. But I say different opinions could be different on that point.

CES: A lot of the electoral systems in the US rely on winner-take-all, which sort of directly bars out proportional voting methods. And within the winner-take-all systems that we use, we tend to use (again) Plurality Voting. Which, within Plurality Voting, as you mentioned before, we frequently can’t vote for our honest favorite where we feel that our vote’s gonna be thrown away.

Dr. Arrow: Yes

CES: And that candidate’s not electable. Now, do you think possibly that having alternative methods implemented that allow voters to always choose their honest favorite without repercussions that that might help to encourage alternative candidates to enter the field?

Dr. Arrow: Yes. I think definitely. I think there’s no question about that. The Plurality system chokes off free entry. In other words, in the economic world we’re accustomed to the virtues of free entry. We don’t want a small number of corporations to be dominate. We favor the idea of new firms entering in order to compete to bring in new ideas, to bring in new products. Well, the same way in the political field. We should be encouraging free entry, I think, in order to have new political ideas come in. And they may flourish. They may fade. That’s what you want, them to be available. So I’m inclined that the Plurality system will choke off by encouraging, the two-party system will choke off new entry. So I’m really inclined to feel that we don’t want Plurality as a voting system. It’s likely to be very stifling.

CES: The idea of being able to vote for your honest favorite-in the social choice world, we call that the favorite betrayal criterion, the idea that you can choose your honest favorite without fear of repercussions along your other preferences.

Dr. Arrow: So if your [first preference] doesn’t do well, your second choice counts. You haven’t been penalized for having an eccentric first choice.

CES: In, for instance, some ranking methods. For instance, one that has gotten more reform (Instant Runoff Voting) fails the favorite betrayal criterion in that if you choose your honest favorite, that may help to elect someone that you really don’t like.

Dr. Arrow: Yeah

CES: Whereas, if you had voted for a compromise, then you might get your compromise candidate to win. But you’re not ranking your favorite as your first preference.

Dr. Arrow: And then, therefore, you don’t know. For example, one thing you learn from an election, let’s say if you have someone you think of as an outlier. But you vote anyway because you’re not wasting your vote. Because your second choice will count. Then one thing you learn is how strongly how many other people feel the same way. And the same way in a market, you want a specialized product. You may find that a lot of other people want it. You may, you don’t know how many other people want it. But you try to get it. And then you may find that there are enough other people to encourage other people to supply it. The same thing applies in economics. Elections are a way of revealing to each voter how many other voters feel the same way, or how few. If it’s very few, you get discouraged. And that’s exactly what you want.

CES: You mentioned Approval Voting earlier as well. And one of the interesting things I think about Approval Voting is that it actually is one of the few voting methods that passes the favorite betrayal criterion in which a voter can always choose their favorite candidate-no matter what-in every circumstance. And given that Approval Voting allows voters to always choose their favorite and thus give a more representative support for candidates that have some kind of favor towards them, do you think that characteristic within Approval Voting would help third party or just alternative candidates in general?

Dr. Arrow: I haven’t thought about that issue. On the whole, it’s right. But still, I may find myself with a candidate I really want, but I think he may not be very popular; and a candidate that I’m middling about but I really don’t want; and a candidate I really hate. I think I may well find myself approving the middling candidate and giving him an unrepresentative support to him. So I think Approval Voting is a little too coarse. I think if you had three or four candidates the incentives for this would be much less if you had three or four classes. There would be a tendency to approve candidates you don’t think very well of just to avoid somebody you think is a real catastrophe.

CES: Within that sort of strategy, first off, you’re looking at an Approval Voting election. If there’s someone you really like, it doesn’t matter what their viability is.

Dr. Arrow: Oh, you want, that’s quite true. You will vote for first choice candidate whether or not you think he’ll win. But I’m saying you may find yourself for a candidate, a middling candidate, a candidate you don’t think very well of, really. And you really don’t like to avoid a catastrophe. Well, maybe that’s a good thing. You can argue that back and forth. You see what I mean? There may be an excessive preference for the kind of middling candidate.

CES: So, with that, are you thinking of a kind of situation as in 2000 where say someone on the Left likes Nader. But there’s also Gore and Bush running. So, if that were an Approval Voting election, they would, say if they were really on the Left, they’d vote for Nader. But if they were sort of middling, as you referred to it, on Gore, they would vote for Gore as a way to hedge their bets against Bush.

Dr. Arrow: Well, yeah, that’s right. Let’s say if you’re really a Naderite, which you might well vote for Gore against Bush. Well, it depends on your attitude. [laughing] If you think Gore is only mildly worse than Nader, then that’s okay. But you see what I mean? I really strongly prefer Nader and also approve Gore and therefore Gore will appear on an equal basis. And I really haven’t thought this through too carefully. I’d have to think more about it.

CES: Now, what do you think in general about the progress and direction of social choice theory? Do you think that it’s been moving in a good direction, that there’s been development on this front?

Dr. Arrow: Well, I think what has been really interesting is the application to a specialized situation. I think, for example, there’s been a lot of literature that has not come to a strong conclusion, but on preferences about the future. Say climate change or something like that, policies which involve time. And, of course, the problem with decisions being made not by everybody involved, but only by those alive today. And the question of appropriate criteria, which is still being debated, I must say. A lot of various progress has been made. A lot of criteria have been discussed in the literature on how to make decisions when the consequences are in the future, any kind of long run investment policy. Climate change would be a very good example where we’re talking about really long futures. So the decisions are made not by everybody because the future people that are affected are not yet here to vote. And this creates an interesting variation in social choice theory. But I’m afraid the conclusions, the people are still coming from quite disparate points of view on that subject.

CES: What do you think about the lack of improvement on voting methods over, say, the last 50 years? Or do you think that the voting methods in practice have improved over the last 50 years?

Dr. Arrow: Well, in The United States, the only real change I know has been Instant Runoff, which is usually applied to municipal elections. I see no real improvement. There’s another aspect which comes out of the two-party system, which the primary, a funny kind of two-stage election. And people certainly have complained. But the upshot has been a polarization that people have simply engaged in the primaries are generally more extreme than the population at large. I’ve never seen a good theoretical analysis of that, of how you apply social choice theory to that two-stage case. In California, they just made an extremely radical alteration of this process by having the open primary. It’s a very funny solution. But the problem was getting really acute. And I think this deserves a sounder theoretical discussion than I think it has received so far.In other countries there’s been some very interesting attempts to, say, in legislatures we haven’t discussed legislatures, proportional representation plays very little role in The United States, but they do play a role in a number of countries. And the question of whether single-member districts are appropriate or not. The Germans, for example, have some kind of compromise between single-member and broader districts. In Israel, you have nothing, you have only a national election. You have no local districts at all. And that’s because of the idea that in addition to other ideological differences, locality matters. The question is does the congressman represent his district and the interests of his district? And as I said there’s quite a variety of systems the democratic world. The implications need to be examined.

CES: Do you think that there are any factors within the US that perhaps are preventing better voting methods from being utilized and implemented?

Dr. Arrow: Well [laughing] You consider that the biggest single anomaly in the system is the Electoral College. And though it gets talked about from time to time, there seems to be no serious move to change it. One feels that the situation at most levels of extremely conservative. It’s not changing at all. It’s only in municipal elections that I’ve seen significant alterations.

CES: Do you think that the Electoral College would make a significant difference given that if we went to a popular vote we would still be using Plurality Voting?

Dr. Arrow: Oh, we know that there’s been several elections (not many), but there’s been several elections where the Plurality vote was different from the electoral vote. There, we actually have data, like 2000. So we know it makes a difference. I think I’d prefer something other than Plurality Voting. But certainly the Electoral College only adds. It doesn’t subtract. It only adds to the problem. Actually, there’s a lot of strange consequences. For example, in campaigning and power, states that are doubtful have more power than states that are clearly one party or another. There’s no reason for that to matter, to play a role. A vote in California has less and less significance. That means policies are changed.

CES: Do you think that there are any particular research areas that you would like to see developed in the future within social choice theory?

Dr. Arrow: I think one of them is the question of more information. And scoring methods are a way of getting more information. But I think, even as it is, the theory has gotten so far out of the practice. Things that are obviously anomalies persist. But I would encourage, of course. I think the biggest topic right now is the question of time as I alluded to before, preferences extending into the future and how they’re taken care of by the present generation. I think that’s probably the biggest area where profitable research will occur.

CES: If you could, just sort of dictatorially, change something about the way that we do voting in the US, something that would make the biggest impact in your mind, what do you think you would do?

Dr. Arrow: The first thing that I’d certainly do is go to a system where people ranked all the candidates, or as many as they wish, and not just two. And that these data are used in some form or another to choose the candidate, say by eliminating the lowest, or some method of that kind. I’d be interested in experimenting with the idea of categorization and creating interpersonal comparisons by that. And those are the things that I would argue for, and certainly the abolition of the Electoral College. It goes without saying.

CES: Dr. Arrow, it’s been a pleasure talking with you.

Dr. Arrow: Thank you. I’ve enjoyed this conversation very much.

CES: Great. Thank you.


CES: This podcast was brought to you by The Center for Election Science. You can find a transcript of this podcast and more of our work at our website, electology.org. If you enjoyed this podcast, you can support us by donating on our webpage and by sharing our work on Facebook and Twitter. You can also follow us at facebook.com/electology and on Twitter under @ElectionScience. Until next time, thanks for listening.


The music in this podcast, “ Parametaphoriquement,” is generously provided by gmz under a Creative Commons license, as is this podcast.

Originally published at https://www.electionscience.org on October 6, 2012.



Executive director at The Center for Election Science. Attorney. Utility maximization enthusiast. Lover of effective altruism. Other work at: aaronhamlin.com

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Aaron Hamlin

Executive director at The Center for Election Science. Attorney. Utility maximization enthusiast. Lover of effective altruism. Other work at: aaronhamlin.com