No vote is wasted

by Chris Bertram on April 14, 2005

Over at John Band’s site they’re all doing Chris Lightfoot’s Who Should You Vote For? (in the coming UK general election) test. Annoyingly, I came out Lib Dem on this though I fully intend to grit my teeth and vote Labour anyway. But for the purposes of this post I’m going to go all meta and discuss what we are trying to do in voting and how that affects how we should vote. Here’s something I posted on the philos-l list just before the 1992 general election:

A friend asked me to provide him with an argument against tactical voting and I came up with this – derived very loosely from some of the things Geoff Brennan says in his ‘Politics with Romance’, in Alan Hamlin and Philip Pettit eds The Good Polity (Blackwell 1989).
The only situation in which an individual voter can affect the outcome is one where there is a tie among the other voters. But in a large electorate this is unlikely to be the case. I want to do two things with my vote: express a preference and secure an outcome. But since my chances of the latter are so small, I may as well concentrate my deliberations on the expressive side. If I am a positive identifier with a particular party— and this is more important to me than my negative feelings towards another party—then even if my party is third I should still vote for it (if I vote). By doing so I secure one of my objectives (the expressive one) but run only a vanishingly small risk of incurring the cost of bringing about a worse outcome than if I had voted tactically. The rational voter should therefore vote for the party she prefers unless it is more important to you expressively to declare your hostility to the party you loathe most – in which case vote for the best placed challenger to that party.

In other words: it is a waste of time and effort to try to bring about a determinate outcome. You’ll almost certainly make no difference. Tactical voting is an attempt to bring about some determinate outcome. But if what is important to you is saying “Blair hooray!” or “Howard boo!” then you can do this perfectly well (voting being only one way of doing it of course). And there’s no merit to the argument that voting for the Lib Dems, Respect, or even the Monster Raving Loony Party is a “wasted vote”. It is no more wasted than any other. So vote for whom you like best, or against whom you hate most, instead of making micro-calculations about effectiveness.

(BTW I realise that this argument deprives me of one lot of nasty things I might say about people who voted for Ralph Nader in either 2000 or 2004, but there are many other nasty things to be said about such people anyway, so I don’t care that much.)



dave heasman 04.14.05 at 4:39 am

“it is a waste of time and effort to try to bring about a determinate outcome. You’ll almost certainly make no difference”

And yet people do. In Brent East there weren’t 8 000 committed convinced Liberal Democrats. They went for a determinate outcome and got it.


Harald Korneliussen 04.14.05 at 4:43 am

In one way you have a point, and indeed I would not vote tactically. It’s a duty ethics thing: what other people do shouldn’t keep you from doing the right thing (voting for the right party).
But I think that to give that answer alone distracts from the important issue that election systems which reward tactical voting is a bad thing. If you in GB used propotional representation like the rest of us instead of the district-winner-takes-all approach, you wouldn’t have this dilemma. Even in single-winner elections, such as a presidental election, there are ways to avoid tactical voting (keywords approval voting and Condorcet’s method).


John Quiggin 04.14.05 at 5:44 am

I think we went over this and refuted it previously. The argument works only if you multiply your small chance of being decisive by an estimate of your private benefit.

On the other hand, as long as you’re even moderately altruistic, there’s a powerful argument in favor of consequentialist voting.

Roughly speaking (we hashed all this out at length last time) the relevant probability in an electorate with N voters is 1/N. The relevant benefit is the public benefit of the outcome. The cost is the private cost to you of voting in a way that doesn’t reflect your first preference (last time it was voting vs abstention).

Let’s assume, for the sake of illustration, that, on average a Labor victory would yield a net benefit of 100 pounds per person in Britain. Cancelling out the factors of N, the expected payoff from your consequentialist vote for Labor, rather than your first preference who is bound to lose is a public benefit of 100 pounds.

Then the relevant issue is whether you’d rather exercise your right to express your first preference or generate a public benefit of 100 pounds (of which your share is sufficiently trivial to be disregarded).


des von bladet 04.14.05 at 5:48 am

The rational voter should therefore vote for the party she prefers unless it is more important to you expressively to declare your hostility to the party you loathe most – in which case vote for the best placed challenger to that party.

If that’s an argument against tactical voting, I’d be curious to see the arguments for it…

This such linked ideometer declares me, to my great unsurprise, to be a natural Lib-Dem voter, which on policy issues is quite correct. It neglects, however (having no facility for divining it) my utter and implacable contempt for the party, as well as my disdain for approximately all the ideologies I have so far seen claim heritage from the Liberal tradition.


Neil Madden 04.14.05 at 6:10 am

What I found most disturbing about that test, was not that it put me firmly in the LibDem camp, but that it actually had me as being slightly more supportive of UKIP than Labour! Did anyone else find this? I feel dirty…

On a related note, has some interesting diagrams about the forthcoming election. According to that test, I should be voting for Labour… in 1972.


Simstim 04.14.05 at 6:35 am

DvB: but I thought you were a Marxist? Oh, sorry, Marxism rarely *claims* heritage from liberalism…


Chris 04.14.05 at 6:46 am

I’ll think about this, John, but I don’t think the argument (whether sound or not) depends on concentrating on private benefit rather than (an individual’s best estimat of) public benefit. My usage “secure an outcome” was perfectly neutral as to the character of the voter’s aims.


John Quiggin 04.14.05 at 7:17 am

The implicit focus on private benefit is crucial to Brennan’s argument. None of us could plausibly claim a private benefit of, say, a million pounds from an election outcome in the UK. Since our chance of being decisive is well below one in a million, the expected private benefit is well below a pound.

On the other hand, there’s nothing implausible about a public benefit of five or ten billion pounds from a good government over four or five years. So, if we’re willing to put in a pound’s worth of private effort to produce a public benefit of 50 pounds, we have a public benefit motive thats at least 100 times as powerful as the private benefit motive.


Harry 04.14.05 at 7:57 am

Chris, I can’t think of anything else nasty to say about the Nader voters, esp in 2000, than that they placed expressive interest over the instrumental goals. And not all of them did that. So I think you have deprived yourself of what I see as the only sensible criticism of them. But I’m willing to hear what the other nasty things are…
(full disclosure: I’m completely in favour of anti-Tory tactical voting, but would prefer to vote LibDem over Labour for expressive/bloody nose purposes).


JR 04.14.05 at 8:17 am

The “expressive” value of your vote is illusory. Unless you are joined by many other voters, your expression goes unremarked. You would do better to stand on the corner and shout at passers-by if what you’re interested in is self-expression.

And the argument that your one vote is meaningless because it can’t by itself alter the election is a manifestation of total alienation. You have nothing in common with anyone else, you are not motivated by the same things as anyone else, you are not part of any social, civic or political community, so if your one individual vote doesn’t decide the election all by itself you won’t participate. This is an infantile expression of utter arrogance combined with utter helplessness. I am the universe! I am powerless! So I’ll just go into the voting booth and wank off — excuse me, express myself.


Hektor Bim 04.14.05 at 8:18 am

I realize I seem to be making a habit of making off-topic posts, but what exactly do people have against the Liberal Democrats?

I mean, they’ve got a long history of fighting the Whigs and were eclipsed by Labor for entirely rational reasons, but now that Labor is a pro-authoritarian, pro-market, pro-preventative war (ie Pro-Pearl Harbor) party, why not vote Liberal Democrat?

A lot of people here seem to despise them, and I’d like to understand why. I’m not a UK citizen, so I’m obviously an outsider, and may be missing many subtle things about their platform that people in the UK pick up on. What do people have against the Lib Dems?


Chris 04.14.05 at 8:21 am

there’s nothing implausible about a public benefit of five or ten billion pounds from a good government over four or five years.

I don’t know about that John. Or rather, since we’re dealing with expected benefits, and what a government will actually do is pretty uncertain (hands up those who predicted Blair-Iraq?), and even when they act with the best of intentions they frequently screw up etc etc, then I think we should guess that the expected difference of the benefit brought by party A over that brought by party B will be rather small.

Having suitably reduced even the expected _public_ benefit, I can also point out that the key probability isn’t that my vote will make a difference in Brent East or wherever, but that my vote will turn out to be decisive in who forms a govermnment. Expected public benefit discounted by the probability of making that difference looks rather small to me ….


Harry, maybe I’ll concede re Nader 2000, but Nader 2004? Someone who voted expressively for _that_ ? I’d feel able to be nasty about their judgement.


JR 04.14.05 at 8:26 am

PS: And the nasty thing to say about the Nader voters is that they chose to vote for a candidate who had none of the qualifications for president- never held elective office, had no party affiliation, never led a large organization- over a well-qualified candidate who was far and away the most liberal with a chance at the White House in a generation, and by doing so have brought the US to the edge of a one-party theocratic state. This all was knowable in 2000, but the Nader voters were too engaged with their self-righteous navel-gazing to pay attention. They are wankers, pure and simple.


Harry 04.14.05 at 8:28 am

I am a UK citizen, and a LibDem voter,though I live in the US.I don’t think this is off-topic. There’s a bad reason people don’t like the LibDems and a good reason. Bad: a gut-reaction affiliation to Labour and the scorning of alternatives that goes with that. Lots of people simply haven’t internalised the change in Labour that hektor describes.

Good: the LibDems look pretty opportunistic. their opposition, eg, to tuition fees, cannot possibly be a principled stance, but is a sop to middle class voters they seek to win from the Tories, and left voters they seek to win from Labour. The Tories and New Labour have bad policies responding to the crises in public sevrices, but the LibDems give the impression that they don’t think there are crises. In particular local elections particular LibDems have behaved less than honorably. (er… its not as if Labour and the Tories haven’t, too, but I’m just pointing it out).

I suppose the last thing is that lots of people think that once Blair goes everything will be alright with Labour (alright, here, meaning something like ‘Labour will revert to being a not very well thought out rightish social democrat party’), so it is just a matter of waiting things out. I think that’s probably wrong, but only probably.


Chris 04.14.05 at 8:32 am

jr, your comment (9) above seems rather confused. The post wasn’t about _whether_ you should vote. Indeed, I think that all the considerations you mention are worthy ones. Rather it was about what you should do when you are voting: should you aim to bring about a particular result or express your view of which party best respresent the public interest (or something like that)? The claim was that since voting is an ineffective means to bring about a particular result, it makes more sense to do the latter.


KM 04.14.05 at 8:35 am


Last time you raised the “1/N” estimate, I queried it, and didn’t get a response (the post had probably dropped off the bottom of your radar).

I don’t see what natural model you are using to get 1/N. Most of the models I think of give exponentially decaying probabilities. For example, a model where each candidate is preferred by a random proportion chosen uniformly on [0,1] (2 candidates only) gives exponentially decaying chance of you affecting the outcome.


Harry 04.14.05 at 8:35 am

jr’s point can’t be made given Chris’s limitation. Chris, in 2004 Nader voters voted expressively for an anti-war candidate, one who had not held a major news event (the Democrat and Republican Party Conventions) in which he had told the world that he was a vile warmonger. If I’d been campaigning expressively I’d have gone for that, myself, despite being pissed off with Nader for being Nader and for running. I didn’t: I went with one of the warmongers. But that is because I never allow expressive interests to guide my voting or campaigning behaviour.

Incidentally, it was notable how many genuine Democrats, having recruited people like me on ‘being responsible’ grounds, then praised Kerry (expressively) when he made a big deal about stem cell research, which was, as far as I could see, pure expressivism, and may well have cost himthe election.


Chris 04.14.05 at 8:51 am

Worries about hypocrisy aside, why should the same imperatives apply to campaigning and voting? The consequentialist case on campaigning looks much stronger.


Harry 04.14.05 at 9:44 am

Yes, I agree with that. I think the case for treating them the same must be something to do with, not hypocrisy, but cognitive (or emotional) dissonance; its just too hard for people to campaign effectively for someone they won’t vote for, or, correlatively, too hard for them not to vote for someone they have campaigned for effectively. Is this something Brennan, or Brennan and Lomasky, talk about?


lemuel pitkin 04.14.05 at 11:44 am

The fatal flaw in this analysis is that it consdiers voting simply as an individual choice. But the whole point of voting is that it is not an individual act. one votes as a member of an organization, union, ethnicity, ideology — all of which, considered collectively, certainly can affect the outcome.

Consider two groups, one votes expressively as Chirs recommends, the other votes strategically based on its colelctive self-interest. Which group will be better served by the election results? And so, which way is rational?


lemuel pitkin 04.14.05 at 12:11 pm

Put it another way: democracy is not aboutaggregating individual preferences, it is about constituting collective preferences. Which is not at all the same thing.


JR 04.14.05 at 12:16 pm

In voting “expressively,” there are two possibilities:

(1) you are voting for a candidate who is so marginal that the total votes that candidate gets will make no difference to the outcome. In that case, no one will hear you. Your notion that you are expressing yourself is infantile.

(2) you are voting for a candidate who has the ability to draw a significant number of votes. In this case, your “expressive” vote is not individual expression but collective expression. You vote for Nader in the hope — not that he will win — but that you will “send a message.”

If your goal is to “send a message,” you are conceding that voting is a collective effort, not an individualistic one. Once you concede this, you must recognize that your individual vote is not necessary or sufficient for the sending of the message; your individual vote will not change the percentage of votes that the sure-loser candidate receives. Your individual vote is precisely as ineffective a means of self-expression as it is as a means of bringing about a desired result.


theCoach 04.14.05 at 1:04 pm

There is a disconnect, or impedence mismatch in the theory and the actual voting. You mean this in the sense that there is no other action than pulling the lever in the booth. This implicit discounts any signaling, or campaigning that you have done previously, and it discounts any argumentation regarding the point, making this a little awkward.
Furthermore, in considering this argumentation you should be determine whether or not this general line of thought is more amicable to groups that favor candidate X or candidate Y.
In the real world elections are a part of a campaign and there are relevant actions outside of the narrow action of casting a ballot.


anon 04.14.05 at 1:16 pm

Am I mistaken in believing that in Britain one votes for Parliamentary candidates of a given party, and if that party wins, it chooses a (known in advance) Prime Minister? If this is so, it seems inappropriate to compare a choice made in a British election with the Nader choice in the U.S.

The British choice is more analogous to voting for a Green Congressional candidate. In the U.S. Presidential case, the system has many characteristics which make the choice binary by state. Thus voting for Nader really is a vote for the most “non-Nader” of the two major party candidates in your state. Unless the major party candidate closest to your own views is certain to win in your state, it really is innumerate to vote for a Nader-type candidate.


saurabh 04.14.05 at 2:47 pm

What I find impressive is that you were on a discussion mailing list back in 1992. Hardcore!


saurabh 04.14.05 at 3:01 pm

By the way, harald, for once we Americans get to turn the tables on you and your exclusionist rhetoric! Don’t marginalize us by saying “the rest of us use proportional representation”. We here in America are way too backwards for that. Hell, no one here even KNOWS there’s other ways to vote.

Anyway, there are ways to mitigate tactical voting even in single-winner systems. I’d be content just to see something like approval voting put in place here, forget about proportional representation.


John Quiggin 04.14.05 at 3:11 pm

Chris, if you make the difference smaller than ten billion pounds over four years, that’s an upper bound of a pound a week per person. If the perceived difference is that small, it’s unlikely that your expressive motive can be very large. The recommended course of action is to go to the football instead (or stay home and watch it on TV), and exercise your expressive motive there


rachel b 04.14.05 at 4:08 pm

Thanks for pointing out the complete irrationality of talk of some votes but not others being ‘wasted’ — this has driven me up the wall for years. In any case it’s always seemed to me that it’s not just a matter of enjoyable self-expression to vote for the candidate you think is best; this is in fact your duty as a citizen. It’s what voting is *for*, and this is why quietly selling your vote (the rational action, surely, on most consequentialist theories given any plausible set of assumptions) is wrong. The likely consequences of any individual vote are nil, and the fact that this doesn’t and shouldn’t stop those who vote just shows that it makes no sense to adopt a consequentialist framework in this context. If you’re involved in a campaign, or part of a movement in such a way that voting really does become a coordinated collective action, then that may be a different ball game.


Michael Otsuka 04.15.05 at 7:39 am

I believe there’s an extensive, sophisticated social science literature on the expected utility of voting in elections which has made some progress beyond the speculations posted above. Could anyone who’s up-to-speed post a reference to an accessible summary to save us the trouble of trying to reinvent the wheel?


saurabh 04.15.05 at 9:59 am

The wikipedia voting systems pages are pretty good.


Chris Lightfoot 04.15.05 at 12:36 pm

(!) Sorry, I hadn’t spotted this post earlier. I did not write this test — it was done by some people at ThoughtPlay. I did spend a couple of minutes doing some optimisations on the server setup, and I did make some comments about the questions, but I didn’t have any influence on how the test works. I’d be grateful if you could correct this in the post at the top….


Chris Lightfoot 04.15.05 at 12:37 pm

Oh, and I should also point you all at something I did write:


KCinDC 04.15.05 at 3:59 pm

Rachel B, surely it’s highly unlikely that the candidate I think is best will be one of the people actually on the ballot, so if everyone followed your interpretation of their duty as a citizen, almost everyone would cast a write-in vote, and the candidate with the most votes would be lucky to get even 1 percent. It doesn’t sound like a great way to pick a president (or fill any office). I don’t feel that I’m shirking my duty when I take likelihood of winning into account when voting.


Benno 04.17.05 at 5:21 am

Dude, stop fretting and get the condorcet method, or at the very least compulsory preferential voting.

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