Episode 20: Voting Systems / March 12, 2021

With Dr Adam Rieger

Hosted by Kate Moody Alice Caunt

Edited by Signe Emilie Eriksen

Posted in Political Philosophy Main feed Logic

In this episode Katie and Alice chat to Dr Adam Rieger about voting systems, problems with them, and the impact of different methods on election outcomes.

In this episode co-hosts Alice and Katie delve into the complex nature of voting systems with senior lecturer in Philosophy at the University of Glasgow, Dr. Adam Rieger. The episode focuses on first past the post, preference voting, and the alternative voting method – with Adam helping us to untangle some of the key criticisms of each.


00:00 - Starting Off With ‘First Past the Post’

04:52 - Would Collecting More Information From Voters Improve Things?/Alternative Vote

07:48 - Do Votings Systems Benefit One Party More Than Another?/Alternative Vote (Continued)

12:16 - The Condorcet Paradox

15:56 - Can We Rule Out Using Undemocratic Processes?

18:22 - What Do You Think Is The Best Voting Method?

20:48 - Tactical Voting: The Elephant In The Room

23:57 - USA: Electoral College


Dr. Adam Rieger: People were saying — so people, I think Brexit — I think I read somewhere that, you know (again, it’s enough to make you weep, really), but, you know, the morning after the referendum result, you know, people were googling ‘what is the EU?’

Katie Moody & Alice Caunt: [in unison laughing]



AC: Hi and welcome back to another episode of Thoughts. I’m Alice Caunt

KM: And I’m Katie Moody.

AC: On this episode, we’ll be talking about voting systems with Dr. Adam Rieger, senior lecturer of University of Glasgow. Here’s some thoughts on voting systems.

[music swells]

KM: Today, we’re talking about voting systems and so should we start off with 'first past the post,’ since that’s probably the one that most people are familiar with.

AR: Sure, and I mean sometimes the way people talk about ‘first past the post’… um, it’s got a kind of iconic status and some people talk in a way so, you know, ‘what else could there be? So it’s uh — it’s sort of unnatural to have anything else.’ So maybe the first thing is just to explain what’s wrong with ‘first past the post’ and maybe I should make it clear this is not in the context of, um, electing a parliament particularly, so it’s — it’s, um… I mean there are separate problems to do with electing a parliament, but even in the simpler problem of just how to elect a single individual, or more generally a single option out of a number of options — it might be, you know, which restaurant to go to in a group of friends or something — but you’ve got a number of options and you have to choose one and ‘first past the post,’ which of course is the way that we elect MPs to Westminster, um, is basically you just ask all the voters to vote for their favourite candidate and the one with the most votes wins. And as I say you… it’s very natural and you might almost think ‘well, you know, how could there be anything else?’ Um, if you ask, say, not very imaginative conservative MPs perhaps somewhere in Surrey who’s come top of the pole with 40% of the vote, uh maybe the Lib Dem has come second with 35, and Labour has come third with 25 in that constituency — keep it in England because it’s, you know, there are fewer parties so it’s simpler — so it’s 40, 35, 25 with the Tory in the lead, and if you say to the conservative, you know, do you think you should win the election , they’ll probably look at you and say ‘well, of course I should win the election! I mean, how… how else could it be done? I mean, who are you proposing should win instead of me? I’ve got the most votes.’ Right, but it’s not as simple as that and all you’ve got to do really is keep the numbers the same and re-label the options and then people will start to think ‘well, hang on a moment, it’s not so quick.’

So let me give you an example from recent history (and the great thing about this, uh, this bit of, of theory is that real life keeps coming up with nice illustrative examples) so here’s a recent example: um, about, I suppose,  a couple of years ago there was a sort of impasse with with Brexit and there was a serious suggestion that we should have a three-way referendum to, uh, get out of the impasse, with the options as perhaps, uh, ‘remain,’ uh, ‘leave with a deal,’ so they say leave with Theresa May’s deal as it then was, and ‘leave with no deal.’ Um… and supposing you held such a referendum and ‘remain’ comes top with 40%, uh ‘deal’ comes second with 35%, and ‘no deal’ comes third with 25%, and you say to the same Tory MP — let’s suppose they’re an ardent Brexiteer — you say, ‘well okay so just by exactly the same logic as ‘you’re the winner in your constituency,’ presumably you now agree that ‘remain’ ought to win and that’s the end of Brexit?’ And they’ll probably say at that point ‘now hang on a moment, that’s not fair,’ and the numbers are the same, all you’ve done is re-label it, so, um, I mean the moral of this, right, it’s, well (a) even it’s not as simple as, as you might think and (b) that the reason ‘first past the post’ is not the end of the story, it’s actually because — and what’s gone wrong in this case is that ‘remain’ has won with 40%, but you’ve got 60% voting for leave options, and so in some sense you might think ‘well, the winning option ought to be a leave option’ and that might be too quick as well, but anyways it’s — it’s the ‘divided opposition’ problem, right, that if you’ve got, um, one option representing, uh, one super option, if you’d like, and then you’ve got the other super options split into a number of possibilities then you can get, um, what looks like it might be the wrong option, um, coming top because the opposition to it is just split too many ways.

KM: So it seems like maybe the way around this is that we want to collect more information about voters’ preferences, is that right?

AR: Yes, okay so the obvious, uh, and as you say, in a way, it’s a separate point, I think, against ‘first past the post’ that it’s… it’s quite crude in terms of, um, what information it collects from the voters, so it only collects the information as to who — to what the first choice is of each voter, so you don’t know anything about, um, the second and… and perhaps lower preferences of the voters, if they can’t have what they most want.

So yeah, I mean, the obvious way to improve on it is to collect people’s preferences and ask them not just to put an ‘x’ in a box, but to— to rank the candidates or the options, so to put a ‘one’ by their favourite one, a ‘two’ by their next favourite one, and so on. And a lot of people seem to think that that’s the main alternative to ‘first past the post’ and once you’ve decided to do rankings, that’s the end of the argument; you just do rankings rather than the ‘first past the post.’ But it’s not so simple.

What people who favour rankings often have in mind is a system called the ‘alternative vote’ (it’s often called ‘instant run-off voting’ in the US), it’s called the ‘alternative vote’ in the UK. It’s the system about which there was a referendum, uh, in the UK in 2011, which you were probably too young to remember much of, but it was… it was a very depressing experience for those of us in voting theory for various reasons. I mean, one is that ‘first past the post’ won, uh the other — another is that the other option was ‘alternative vote’ which is not great either, and the third reason is that the level of debate was enough to make one want to weep.

But anyway, the way ‘alternative vote’ works is that you count the first preferences and you then, uh… if — if someone’s got more than 50% then great; they’ve won. If not then you eliminate the candidate with the fewest number of first preferences, you transfer the votes of all the voters who voted for the losing, uh you know, the bottom candidate, you transfer all those votes to, uh, the second choices of those voters and then you, uh, do it again, you… you see if anybody’s got more than 50% yet, and if they have then hooray, and if they haven’t then you see who’s now in the bottom position and transfer their votes and so on. Um, and then you go on until you’re going to come down in the end to two candidates, if you haven’t got one earlier, and then the one with the more votes wins.

So that is certainly better than ‘first past the post.’ Uh, say in the ‘remain/deal/no deal’ situation, if all the dealers and no dealers are definitely brexiteers and they’ll transfer to each other, if they can’t have the ‘leave’ option they prefer, then it will make one of the ‘leave’ options win, and so on and so it’s definitely an improvement on ‘first past the post,’ at least as a system for electing a single winner. I mean it may be actually even worse than ‘first past the post’ for a parliament, but let’s not talk about parliaments at the moment, but it’s for — for single winners, it’s a — it’s a better system, but it’s not perfect, I think, anyway.

AC: I think it’s interesting how issues arise when perhaps parties don’t get the result that they want, and so then they try to manipulate the voting system to get the result that would benefit them, so do you suggest that voting systems benefit one party more than another?

AR: Well, it’s a perpetual problem with trying to do anything about reforming voting systems that we, you know, we can only do that through the political system, and of course, the way politicians look at these problems — I mean, the first question they ask is ‘am I going to lose my seat if we change the system?’

[KM chuckles]

And the second question they ask is ‘how is my party going to do if we change the system?’ And you can see, I mean, historical examples of this, that Labour in the 80s and 90s — Labour lost four elections in a row, I guess the first one in 79, but in that era they lost four elections in a row. And as they lost more and more elections, they became more and more interested in electoral reform, because — I mean, one reason that Thatcher was so successful was because the… the broadly left vote was split between Labour and, originally, the ‘Alliance’ as it was and then it became the Liberal Democrats. So Labour became very interest in electoral reform and then of course Blair won this absolutely stinking majority in 1997. Um, so having come to power with a commitment to look seriously at electoral reform, it kind of faded away a bit, and of course, you know, it just sort of disappeared.

It’s very hard to change the constitution without some kind of cross-party agreement, and, um… that’s a perpetual problem, I think, with the practicalities of getting any electoral reform. So talk first of all about the ‘alternative vote,’ because, I say, that people talk sometimes as though that’s, you know, that’s what’s in the frame: it’s either ‘first past the post’ or the ‘alternative vote.’ And that’s how it was the debate seen in 2011. But that’s really not how it seems to people who work in this area.

Essentially, the trouble with the ‘alternative vote’ is — remember what happens is you… the candidates get eliminated round by round; you start with the one with the fewest number of first preferences and then you repeat, um, having done the transfers. But that means, to stay in the game, you’ve got to get some first preferences, and the problem with it is there can be candidates who are basically acceptable to a lot of the electorate, but don’t do very well on first preferences, and those candidates will tend to be eliminated early on, under the ‘alternative vote.’

So you can imagine, for example — I mean, if you change numbers in my original example a little bit, so it says 40 Tory, 35 Labour, and 25 Lib Dem, so the centrist candidate is… is last. That does get eliminated under the alternative vote, um, because they got the smallest number of first preference votes, but you can make a strong case that they ought to win the constituency because — well let’s say that, you know, that their the second choice of both the conservatives and the labour voters, so if they’re… if they’re nobody’s last choice, and everybody’s either first or second choice, you can make a strong case that they ought to win. So, um, another way of putting this is that there’s — there’s a thing called ‘the Condorcet criteria,’ named after the Marquis of Condorcet, who was a sort of, uh, aristocrat who studied this, um, this sort of thing around the time of the French Revolution. But anyways, what is the Condorcet Criterion? It says that you imagine sort of head-to-head contest between the candidates, so imagine a, um, temporarily ignore the Lib Dem and pit Conservative against Labour and then you temporality ignore the Conservative and pit Lib Dem against Labour and so on. So you get these… these sort of head-to-head contests, and it — the Condorcet Criterion says that if there’s a candidate that wins all of those head-to-head contests (it wins them against all the other options), then that candidate ought to win the election.

And um the alternative vote does not obey the Condorcet Criterion, but for the reason I said that that somebody who’s a Condorcet winner — it might be the Lib Dem in my example as a Condorcet winner — they’re preferred to every other candidate by a majority of the electorate and… um… nevertheless, they’re going to be eliminated in the A.V. system because they haven’t got enough first preferences. I mean, it’s already — it’s not entirely clear — I mean, there are people who think A.V. is better and you shouldn’t elect somebody with, uh, not very many first preferences, but I think most theorists think that, on the contrary, that somebody who’s a Condorcet winner has a pretty strong case, uh, to be the winner in these circumstances.

KM: I was reading a little bit about this and I came across the Condorcet Paradox, em, and could you tell us a little bit about that?

AR: Okay, yeah so you might think if we — given what we’ve got, you might think, well, you know… if you agree with what I’ve said up till now, the direction I’ve been heading in, you might say, ‘okay so that’s a better system: elect the Condorcet winner’ (so like the Lib Dem in my example). The trouble is, it turns out, that there need not be a Condorcet winner; you can have what are called ‘preference cycles.’ Um… and what does that mean? That means you can have a majority preferring Candidate A to Candidate B, you can have a majority preferring Candidate B to Candidate C, um, and yet a majority prefers Candidate C to Candidate A. Okay, so it kind of goes around in a circle. It’s like 'scissors paper stone,’ right; A beats B, B beats C, and C beats A. So there’s no Condorcet winner. Um, and this is one — this was actually discovered by Condorcet — it’s been discovered various times, independently, over the history of this industry. Um… yeah so, so that I mean — this is an example of a general phenomenon that, uh, if you try and — what we’re doing is actually aggregating preferences. We’re trying to sort of combine a number of preferences into a single preference; they don’t combine well.

Um… so the kind of standard theory in this area is, you know, pick a Condorcet winner if there is one. So if there is a Condorcet winner, there can only be one, then that persons’s won the election (great) and if there isn’t a Condorcet winner, you have a tiebreaker. So you pick, um, the nearest miss to a Condorcet winner, right? So somebody who’s almost a Condorcet winner but not quite. There are different ways of defining what that means, um, and there’s a lot of argument about how to do the tiebreaker and so on. But nevertheless, um… you — but there are — there’s, for example, a theorem that was proved by a guy called Hervé Moulin, who’s a French economist, who’s actually now at the University of Glasgow and, um, in the business school, and he proved that any Condorcet method, um, has what’s called the ‘no show’ paradox, which means that it’s sometimes — when you’ve got at least four candidates, it’s got the ‘no show’ paradox, which means that you can sometimes benefit your preferred candidate by not bothering to vote. Right so your candidate’s actually made worse off by you showing up and voting for them, so, uh, you can’t have a Condorcet System that doesn’t have that property. I mean, it’s horrible, absolutely horrible, um…

So basically the — there’s a kind of pessimism in the literature, uh, about all these ranked methods. Um, you can even find books  — you can find people saying quite exaggerated things like, in my view, that democracy is impossible um, that, um it’s all hopeless, that the most you can hope for is that, you know, you’ve got the right to throw out a government if it’s really awful, but you shouldn’t… you shouldn’t in any sense try and, um, think that the winner of an election is supposed to be chosen in some scientific way from the preferences of the population. Um… but that’s — that’s in my view too pessimistic, but the way that people get to this pessimism is by, um, taking note of these theorems; that the very bad way in which, un, preferences aggregate — they don’t aggregate in a well-behaved way.

AC: A question that I had for you, Adam, is: should we completely rule out undemocratic processes as a way of achieving social preference?

AR: Well, I guess you can ask two slightly different questions: I mean one is, you know, what’s so great about democracy? And I think, you know, it needs to be asked, I think, you know, and all right and answered and the political scientists have, uh, have answers, but I mean that there is, uh — there’s like this one, Jason Brennan, who’s an American philosopher (I think primarily), who’s written a book, I think it’s called ‘Against Democracy,’ or something like that, sort of reviving very old ideas that go back to Plato that maybe, you know, you shouldn’t just let them, the masses, decide; you should have experts of some sort.

Anyway this, I mean, if you look at, you know, what’s happened in some places recently, with when they are allowed to vote for the general population, you might think, you know, there’s something in this, but obviously it’s highly controversial to say the least. I mean, the way you put it was as a way of social choice — I mean, I guess, I mean I suppose, you know, if you think that democracy leads to bad results, I suppose you’d be saying ‘actually people don’t know what’s good for them,’ right? I mean it would be like letting the children decide on their bedtime, right; that’s kind of the idea, I guess. But I guess the aim would still be, you know, to benefit society as a whole. Um… I guess you might also just be a dictator that was quite happy to run things, you know, for yourself and your family or something, but, you know, maybe people are not expert enough. I mean, it’s not — I think it’s one of your — it’s not mad, right? I mean, you know, maybe it’s rather hard to know… um… people were saying so… people — I I think Brexit — I think I read somewhere that, you know (again, it’s enough to make you weep, really), but, you know, the morning after the referendum result, you know, people were googling ‘what is the EU?’ [a chuckle] Voting to leave, you know, they were voting to fight, they were going to find out what they’d voted for. And the people were saying, you know, ‘I don’t know enough about the EU and, you know, what it does for us, you know, to know which way to vote.

Um… on the other hand, you know, I mean… who does know enough and how much do you need to know to make a really good judgement in these circumstances? It’s… and I guess most people would say it’s, you know, the expert argument is overridden by the danger that some, uh… that you know if you did restrict the franchise to an elite group, then they might run things in their own interests. Um… so I suppose democracy is some kind of check on that, but, um… I think these are good questions, certainly.

KM: So it’s not sounding great, in terms of the systems that we’ve discussed for far, um, so do you have any of your own ideas about the best voting methods, or any methods that you think are particularly promising?

AR: Yes [chuckles] so my own interest, I mean, I — I think this pessimism is not really justified. Preferences are completely dominant in the literature, but I think really for bad reasons. There are — the system that I call ‘range voting,’ where rather than just say, you know, ‘number one number two number three,’ you give candidates scores out of ten, let’s say. It’s informationally more rich, so one reason for going from an ‘x’ in the box to preferences is because you get more information that way, and you can push that further and say, ‘well, if I get scores, I’ve got not just a ranking, but I’ve got a sort of strength of preference.’ So all preference systems — in a way this is the problem: all preference systems, they’re not sensitive to strength of preference. So I can prefer A to B to C but that might be because I think A is a tiny bit better than B and both those are miles better than C, and I really hate C, or it might be because I think A is fantastic and I think B and C are both absolutely awful, but B is just a tiny bit less awful than C, right? And both those give the same orderings (suppose ABC in each case), um, but with different strengths. And if you have a scoring system, you can express that, because you can rank them, say, you know, 10-9-1 in the first case and 10-2-1 in the second case — something like that.

Um, and it turns out there’s a thing called ‘range voting,’ where you just get each voter to score the candidates out of 10, let’s say, and then the candidate with the highest average wins, and it turns out that those things do not have the same sort of pathologies in terms of cycles and you know you are — if A beats B, and B beats C, you will never get A beating — you don’t get C beating A in this sort of case, because they’re just numbers; numbers behave well, okay, they’re just averages. So that’s the way I would hope to go is some kind of range voting.

And in my own interests, I mean, that — you can do other things with the numbers and that’s what I’m interested in myself; that once you’ve got these numbers, you can interpret them in different ways and you can do different things with them and I’ve invented a weird system that, um, doesn’t take the average but does something else with the numbers and then I’ve tried to argue that that’s superior.

KM: It stills seems though like the issue of tactical voting would come up.

[AC concurs]

AR: Yeah.

AC: This feels particularly susceptible to manipulating it so you can always get…

AR: Yeah… good. Yes, now that, that looks — the first thing to say is — I mean, tactical voting is a big elephant in the room; I think I mentioned it hardly at all. It’s a problem. There’s a theorem that says that any… basically any preference system satisfying certain weak criteria is susceptible to it. Um… there’s one quite nice system actually that isn’t — which I just mentioned in passing which is to — it sounds mad, it’s actually quite a good system, which is: vote as now ‘first past the post,’ put an ‘x’ in the box, and then rather than count the number of votes, uh, pick out a ballot paper at random from the ballot box, and whoever that voter’s voted for is the winner.


And that’s one of the very few systems that… where there’s no incentive to vote tactically. Of course, you know, it might on a bad day produce a really weird parliament but it’s not really likely actually if you’ve got enough seats. Anyway, I mention that in passing.

But, um, there’s a theorem that basically says that… um… apart from ones like that that involve random processes, basically all preference systems, uh, are susceptible to people voting dishonestly in order to manipulate, uh, the winner. And range voting, as you say, and it’s a good point, I mean, it’s — that’s also susceptible to tactical voting is the first thing to say and the second thing to say is, given that all systems more or less are vulnerable to this, the question is then, well, which systems are less vulnerable to it and intensively ones where it’s less obvious what to do. And you might think range voting is bad from this point of view in that it’s rather obvious what to do, so you basically… I think that the thought was, you know, if they think it’s going to be very close between A and B, and they do definitely prefer A to B, um, then there’s an incentive to mark B down artificially. And if you’re  really sure that it’s going to be between A and B, I think that is… that is a temptation undoubtedly.

Um… if there’s another candidate — I mean, the risk is, you know, that maybe some other candidate C, who you really hate, does unexpectedly well, then if you’ve given B and C both zero out of ten, then you haven’t expressed the fact that you greatly prefer B to C, so I think that is a problem and there are various suggestions of what to do about this. So one is, um, something called ‘approval voting.’ It’s kind of a limiting case of range voting, where you have to give every candidate either 10 out of 10 or 0 out of 10, because the suggestion is that’s what people would do anyway. You know, they’ll either give 10 or they’ll give 0, um… because there’s no point being wishy-washy, you may as well decide which ones you think are okay and which ones are not. Um, or equivalently you could — because, you know, basically it’s either one or it might be one or zero, you can just have ordinary ballot papers, you know, put ‘x’ in the box, and just say to people, you can vote for as many candidates as you like. So just, you know, if you want to — if you really want to vote Green but, you know, you don’t hate the SNP, let’s say, you can vote Green and SNP, right, and that’s fine. And then you can just count the number of votes and the one with the most votes wins. That’s not terrible actually.

KM: I think it’s interesting because in the example you’ve given so far, it seems like the voting system you choose has a pretty massive impact on the outcome, ehm, of the votes. And so that sort of makes it clear the real-world importance of picking a good system. And I remember we were talking before, you mentioned the electoral college system in America and how that can lead to some pretty weird outcomes and so could you tell us a little bit more about that?

AR: Yeah sure well of course you’re absolutely right it does really matter. I mean, that’s, you know, you can hardly think of something that is more significant and I mean, the President — the U.S. presidential election, and I mean, that’s obviously enormously important, and you know, we’ve had, um… I think, you know, either the wrong winner or near miss wrong winner on several recent occasions. So in a way I think that — I mean 2016 is perhaps the most famous example, but I think it’s too quick to say ‘Hilary Clinton got more votes than Trump and, therefore, she should have won’ because, as I say, I mean that’s just approaching it with the ‘first past the post’ mentality. And we know there are problems with ‘first past the post.’ There were some minor candidates and there was a libertarian in 2016 who got, I think about 4% (I forget exactly) but fairly significant number of votes, 3% something like that, and there was a green as well, so you have to think, well, you know, if they’d had a, let’s say, if they’d had a, um, AV system or something like that, some system that took account of second preferences for those minor candidates, where would those have gone, and so I — I looked at it once and I think I decided Hillary would just have scraped home, probably, because the problem is that even though she only got more votes than Trump, you’d think that probably a majority of Libertarian votes might have transferred to Trump, rather than to Clinton, so… but on the other hand, the Greens — that’s the other way around — the Greens will probably have gone to Clinton, so I think she’d have scraped home, but you know in a way basically, you know that there’s — there aren’t third parties in the US in the sense that there are in most countries… um… so I think America would be the, you know, the one country where having ‘first past the post’ would be an improvement.


[music swells]


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Transcript written by Adam Nicholson