Alternative alternative voting systems, part two: Approval Voting

I’ve been re-examining one aspect of my critique of the Alternative Vote electoral system of the other week: the extent to which it enables voters to express the full range of their political opinions – one of six criteria against which I’ll be measuring a number of alternative voting systems. In my previous post, I awarded AV only two out of five against this criterion: you can vote both for the candidate / party you actually want to win and tactically for the candidate with a chance of winning that you least dislike; but, I concluded, there’s often not much point expressing a preference for any other parties.

However, it occurred to me that, rather than limiting yourself to just two candidates, you might as well list all the candidates you support to some degree or another ahead of your tactical vote, as doing so won’t affect your tactical choice’s chance of winning in most cases. That’s because, assuming your tactical vote is for one of the three main parties, and that none of those parties obtains a majority of the votes as defined in the AV system until the very last stage (when all three parties are still in the race), then it will be only at this stage that your tactical vote may both be needed and come into play, i.e. if your more preferred party finishes in third place and your votes are transferred to your tactical choice. But if a party you don’t want to win has already obtained over 50% of the vote before that stage, then your tactical vote would not have made any difference if it had come into play earlier: the winning party would have got its majority regardless of your tactical vote and that of all other like-minded voters. That’s just mathematical logic, which I won’t bore my reader by going into in any more detail.

But that in a way is my point: a) it’s difficult for ordinary voters to work out how they should rank their preferences under AV in such a way as to help bring about the result they want, if indeed this is at all possible; and b) beyond indicating your actual first preference and your tactical vote, is there any point listing all the other parties in between, as they don’t have a chance of winning anyway? Well, there might be a point in doing so if every single vote and every single preference was counted and recorded in some way: if the reported election results included a break-down of how many first, second, third and subsequent preferences every candidate obtained, in addition to itemising the result at each stage during the AV counting process, together with the final result. If all the preferences for all of the candidates were published in this way, then indicating a preference for multiple parties, rather than only your first choice and your tactical vote, would be a means to communicate to the parties the strength and depth of support they each enjoyed – thereby better fulfilling the criterion of enabling voters to express the full range of their opinions and send a message to the politicians.

Recording the results in this way would be likely to bring out the fact that the Liberal Democrats were the main second preference of voters – both in many individual constituencies and across the UK as a whole – while being only the third-largest first preference. This could boost the Lib Dems’ credibility, in that they could argue that they enjoyed a broad base of support and represented the consensus view; while, at the same time, they could use this data as further corroboration of their arguments in favour of full PR, in that a system like STV (which the Lib Dems favour) would be likely to convert this underlying support into substantially more seats – and a more proportional share of the seats – than the Lib Dems will probably obtain under AV.

A result of this sort would also illustrate a well known problem with preferential voting systems such as AV, which is that the party that most people are prepared to rank as at least their second favourite still obtains only a mediocre third-highest share of the seats. I’ve been alerted to the fact that this is known as the ‘Condorcet criterion’: the Condorcet winner of an election is the candidate who, when compared with every other candidate, is preferred by more voters. AV often fails to bring out the Condorcet winner (although FPTP always fails to do so). For example, if all the preferences for all of the parties were counted and recorded, it would not be uncommon for the winner under AV to actually obtain fewer votes overall (of any degree of preference) than one of the other parties. That’s because the second preferences of the two leading parties (e.g. Labour and Conservative) left standing at the end of the AV process are not counted; but those preferences are likely to be for the third party (e.g. the Lib Dems): the Lib Dems are in this instance the Condorcet winner because, for both Labour and Tory voters, they represent a more preferable alternative than the Tories or Labour respectively.

Discrepancies of this sort would potentially undermine people’s confidence in the AV system. But information about the full set of voters’ preferences ought to be in the public domain. I contacted the Electoral Reform Society to ask them if, in AV counts, this information is published as a general rule. The answer they gave was that the information should be retained and be available to the public; but it won’t necessarily be automatically published in the way I suggest (a simple list of the total number of every preference indicated for every candidate): it would presumably be a case that individuals would have to request access to the full set of results from the Returning Officer.

Maybe one of the reasons why the information would not automatically be published in the format I’m suggesting is precisely that it would show up AV’s flaws: that it engineers ‘majorities’ that don’t necessarily take account of the full range of voters’ opinions and feelings. There is, however, a voting system that intentionally records the votes of every voter for every candidate they’ve voted for: Approval Voting. In essence, what this system consists of is a sort of multi-candidate First Past the Post: instead of marking a cross beside the name of just one candidate (as in regular FPTP), you can mark a cross for any number of candidates that you support to some degree. The candidates are not ranked as they are in AV: each vote for each candidate carries the same weight and is counted. The winner is simply the candidate obtaining the largest number of votes, whether an overall majority or not.

I think this system possesses some advantages compared with AV, which I’ll explore by grading Approval Voting using the same six criteria I used to assess the relative merits of FPTP and AV last week.

The first of those criteria is: Does every vote count / is every vote counted? Here, I would give Approval Voting a score of three out of five, compared with only two for AV. The fact that every vote for every candidate is counted is precisely the hallmark of Approval Voting: it allows voters to express some degree of support – ‘approval’ – for multiple candidates without imposing on them the burden of ‘ranking’ them in ways that are often compromised either by tactical considerations, confused thinking about the impact of ranking on the end result, or even just the arbitrary nature of imposing an order of preference on candidates or parties, which is not something that all voters will be entirely clear about in their minds. In any case, as I’ve argued elsewhere, the AV system treats each preference as potentially equal: in other words, the Lib Dem candidate could in fact be your fourth preference; but if your first three preferences are eliminated, your fourth-preference vote for the Lib Dem is added to that candidate’s total and is handled by the system as if it were no different from that candidate’s first-preference votes.

You could argue that Approval Voting also does this: that it treats all votes as equal, even if voters in fact have different degrees of support for each candidate. But this fact obliges voters to deliberate carefully about their choices: if you vote for any of the candidates that have a chance of winning, then you need to really weigh that choice carefully and decide whether you would be truly content to see that candidate winning before you mark a cross beside their name. By contrast, AV performs a sort of sleight of hand that could leave some voters feeling cheated. For example, voters could mistakenly believe they needed to rank all of the candidates (some versions of preferential voting actually require this) or would feel conscientiously obliged to rank as many candidates as they felt able to; and that could have the consequence that, say, their fifth-preference vote was added to the total of the eventual winner: the system has treated their reluctant, luke-warm support as equivalent to enthusiastic support, and thereby helped bring about a result that the voter didn’t want. By contrast, under Approval Voting, if you don’t like a candidate or party much, you just don’t vote for them in any form: simple.

And Approval Voting always brings out the Condorcet winner, so long as voters are sincere in their voting (i.e. they vote in accordance with their true feelings and opinions). In other words, the candidate that most voters support to some degree or another always wins: all of the votes that candidate obtains are counted and contribute to the end result. This is an improvement over FPTP, to which I also awarded a score of three against this criterion. However, there are other systems in which all votes are not only all counted but actually count more towards generating the final result – whereas under Approval Voting, as another variety of FPTP, there are still many so-called ‘wasted votes’ that never influence the result.

Does this mean that Approval Voting would deliver a more proportional result overall (the second of my criteria), which in practical terms in England might mean it favoured the Lib Dems more than AV or FPTP? Well, Approval Voting is not a proportional system either, in that it is still possible to produce a wildly disproportional parliamentary majority for one party if that party wins narrowly in a large number of seats. Nevertheless, Approval Voting does favour the consensus party to a greater extent than AV, in that – unlike AV – every vote for that party is counted. So, based on voting patterns at the last election, the Lib Dems would undoubtedly have won more seats if the election had been conducted using Approval Voting rather than FPTP, as they would have won many three-way or Lib Dem-Tory marginals. But as Approval Voting is not inherently proportional, I’ll award it only two points out of five against this criterion: the same total I gave to AV.

Is it conceivable that Approval Voting could enable the Lib Dems to actually win a general election because the system makes no distinction between ‘first-preference’ votes (of which the Lib Dems would obtain the third-highest total) and second preferences, of which the Lib Dems would obtain the greatest number? I think this eventuality is extremely unlikely because, in most areas, there is a party that clearly enjoys the strongest degree of support: the Conservatives in the south of England, and Labour throughout most of the Midlands and Northern England, for instance. Approval Voting wouldn’t allow the Lib Dems to trump this, because where support for one party is particularly strong, many voters would continue to vote for that party alone; and indeed, Lib Dem supporters might also vote for that party’s candidate in addition to voting Lib Dem. So Approval Voting is likely to alter the result only in marginals, which it would be more likely to swing the way of the Lib Dems.

Third criterion: Does the system foster accountability? Approval Voting shares the relative strength of AV and FPTP in this area, as it’s based on single-member constituencies where an MP is directly accountable to their constituents. However, I would argue that Approval Voting is more effective at fostering accountability than AV or FPTP, in that winning candidates have to appeal to a broad base of voters, even more so than under AV: the candidates need to earn the support not only of their party’s core voters but of voters for other parties. While there is no requirement for the winning candidate to procure the approval of more than 50% of voters, there would be a strong moral obligation to cross that threshold: if in theory each and every candidate can obtain the support of 100% of voters, then to fail to gain merely 50% would be seen as pretty unimpressive. Besides which, the ‘majority’ the winning candidate has to obtain under AV can be inauthentic in some cases. For instance, if a sizeable proportion – e.g. 20% – of the electorate does not express any preference for the two candidates remaining in the race after all other candidates have been eliminated under AV, then the ‘majority’ obtained by the winner is only a majority of 80% of voters, not 100% of voters.

At a national level, as Approval Voting is not proportional, it can contribute to the erosion of accountability that comes from governments having huge, unrepresentative majorities. However, if each candidate has to win the support not only of their loyal voters but of voters of all shades of political opinion, this would, I think, change the political culture quite radically in that the party of government could not depend on the support of only 35% to 40% of voters in order to get re-elected: it would have to reflect the consensus view to a greater extent. For similar reasons, fewer seats would be ‘safe’ than under FPTP and AV, meaning MPs would have to work harder to retain their constituents’ support. For these reasons, I’m awarding Approval Voting four out of five for accountability, compared with only three for AV and FPTP.

With respect to my fourth criterion – does the system allow voters to express the full range of their views and send a message to politicians? – I would rate Approval Voting more highly than AV. That might seem paradoxical, in that you can rank your votes under AV, whereas Approval Voting gives equal weight to all your choices. However, as I was arguing above, the ranking in AV is highly compromised, in that, where it’s not actually artificial (i.e. the voter is just imposing a more or less random order of preference that doesn’t really reflect the way they think), it can be skewed by tactical considerations (my next criterion, see below) or by a mistaken understanding of how the system works.

AV uses voters’ preferences in a merely functional way – as a guide to reassigning votes to other candidates if voters’ higher-preference candidates are eliminated – but does not weight those preferences in the count in such a way as to treat higher preferences as being worth more than lower preferences. However, many voters might think that their first preferences would be given more weight than their lower preferences, which would then fulfil the present criterion very effectively: it would enable voters to express the degree of support they have for each party very clearly. Even if AV does not enable degrees of support to influence the end result in this way – other than using voters’ avowed first or higher preferences to determine the result as much as possible – this deficiency could be remedied at least in part by reporting the election results in the way I suggested at the start of this article: listing all of the preferences indicated for each of the candidates. Then, at least, voters could use their vote to send a message to the politicians.

For example, many people were surprised at how badly the BNP performed at the last election, despite the fact that concerns about immigration were very high on the list of priorities of Labour’s traditional working-class supporters. That’s an effect of FPTP: those voters continued to loyally vote Labour because they wanted to ensure the Tories didn’t get in. If the election had been conducted using AV, the result might not have been very different: even if some Labour voters had decided to indicate BNP as their second preference, those votes would not have been counted, as only their first preferences would have been used to determine the result – although more voters might have voted BNP first preference and Labour second. Reporting the results in such a way as to show the subsequent preferences of first-preference Labour voters would remedy this to some extent, in that it would encourage more Labour voters to list more preferences (including for the BNP), even though those preferences wouldn’t influence the result: they would at least send a message.

With Approval Voting, on the other hand, all of these considerations fall away: people can vote for whoever they want to, and all of those votes are counted. So if you’re secure in the belief that none of your votes for alternative candidates will jeopardise the prospects of your ‘first-preference’ candidate, you can go ahead and vote for them, thereby indicating that you support other policy agendas to some extent, in addition to those represented by your traditional party. The effectiveness of the Approval Voting poll in sending these messages would be enhanced still further if the results were recorded in such a way as to show, for instance, which other parties Labour voters had voted for. That could actually be easily done by, for instance, counting the vote by logging each voter’s multiple choices in an Excel spreadsheet. This could of course also be done to log the various preferences of voters in an AV ballot.

To return to the point of departure of the present article, though, how would Approval Voting have altered the way I voted at the last election? I indicated previously that, under AV, I would have voted UKIP first preference and Lib Dem second, the Lib Dem being the only candidate with a chance of defeating the incumbent Tory. Now, there were two other candidates for whom I might have liked to express some degree of support: the Green and Christian People’s Alliance candidates. Let’s say, for example, that under AV I’d decided to vote: UKIP 1, CPA 2, Green 3 and Lib Dem 4. UKIP actually finished fourth in the real election. So assuming that after the elimination of the CPA, independent and Green candidates in the AV counting process, the Tory had still not obtained a majority, my vote for UKIP would have been re-cycled to the Lib Dem: my second and third choices would have been ignored altogether, and the system would have recorded that I was one of x thousand whose votes were transferred from UKIP to the Lib Dems. So I might as well have just stuck to my decision to vote UKIP 1 and Lib Dem 2.

By contrast, if all of the preferences were reported, my votes for the CPA and Greens would be included within the total of second and third preferences obtained by those parties. But as I said above, the results are not necessarily going to be reported in this way. Under Approval Voting, none of this is an issue: I could have just voted for all four parties, secure in the knowledge that the only vote that stood a chance of influencing the result was the one for the Lib Dem candidate; but also knowing that my votes for the other parties would be counted and would help send a message to the politicians. Accordingly, I’m going to award three points out of five to Approval Voting against this criterion, versus two for AV. There are some other electoral systems that perform better than Approval Voting in this respect, which I’ll discuss in subsequent posts. Hence, I haven’t given it a four or five.

How about my fifth criterion: does the system mitigate the need to vote tactically? It is commonly said of AV that it eliminates the need to vote tactically, but this is not in fact true. The pressure to vote tactically derives from single-member constituencies, meaning there can be only one winner. Hence, people feel forced to vote for only one candidate on the left or right who has a chance of winning, e.g. UKIP supporters voting Tory or Lib Dem supporters voting Labour. This factor still prevails under AV, the only difference being that you can specify which candidate is your actual first preference while effectively still voting tactically via your last-preference candidate. Approval Voting is no different in with respect to the need to vote tactically; although I would say that the fact that voters are not forced to rank their preferences takes some of the sting out of the obligation to vote tactically. What I mean is that AV could be even more frustrating than FPTP in that it creates the illusion of being empowered to vote according to your true preferences; but in fact, what you mark as your ‘last preference’ becomes your effective vote: the only one that ultimately counts towards the end result. So the last preference effectively becomes the only preference and the tactical vote.

Under Approval Voting, there would be a greater sense of openness and freedom, and a feeling that you owned your choices rather than being directed by the system to specify and rank those choices. If you decide to include a tactical vote among those choices, that is in a sense your choice. The meaning of doing so is slightly different: you’re indicating that you would be content for that particular candidate to win, and you haven’t been forced to pretend they are your ultimate and only effective choice, just one among several. But as the need to vote tactically is still present under Approval Voting, I’d give it a two for this criterion: the same score as AV.

Finally, is the system easy for users to understand, trust and use to their advantage? Here, I would say that Approval Voting is superior to both FPTP and AV: it’s much easier to understand and operate for voters than AV – as well as easier to count on election night – in that it’s a basic extension of FPTP requiring no complex ranking and multiple counts. You vote for all the candidates you like instead of just one as under FPTP. Simple. And it’s easier for voters to have a sense of how their choices could influence the result than under AV: you can just indicate your personal preference alongside your tactical vote without making prudential – and often erroneous – calculations about whether you should rank the tactical vote ahead of your real favourite, and whether including other candidates in your list of preferences might impair the chances of your tactical choice.

Indeed, more people would vote both according to their real preferences and tactically under Approval Voting because they would be confident that neither vote would damage the other. Not that they would necessarily damage each other under AV; but because AV forces you ultimately to choose between a personal and a tactical choice, some voters will choose one and not the other. So I’d give Approval Voting four points out of five for this criterion, compared with two for AV and three for FPTP: it’s both easier to understand than AV and more empowering than FPTP.

So let’s summarise the relative standings of FPTP, AV and Approval Voting by adding the scores I’ve just awarded to Approval Voting to my comparative table of voting systems:

Criterion FPTP AV AppV
Does every vote count?




Is the system proportional?




Does the system foster accountability?




Does the system let voters express their views?




Does the system mitigate tactical voting?




How user-friendly is the system?




Total scored out of a maximum of 30




Approval Voting beats or ties with FPTP and AV on every criterion: it counts every vote, and every vote counts, more than AV; it’s not proportional but is not less so than AV; it fosters greater accountability, in that politicians are forced to seek the support of a greater cross-section of voters, to a greater degree than AV; it frees voters up to express the full range of their views; it is still prone to tactical voting, but no more so than AV; and it’s easier for voters to understand and use to their advantage than AV and FPTP.

In my next post, I’ll be comparing the relative merits of these systems and one of my own invention: the Popular Vote (PV).


14 Responses

  1. This analysis is hilarious. Approval voting has done no such thing where it’s been tried. You completely overlook the key fact that with approval voting, you can only cast equally weighted votes for anyone you prefer — and so you have overwhelming incentive to vote for only one candidate unless you have very precise poll results.

    See: Saari, D.G. and Van Newenhizen, J. (2004) “Is approval voting an ‘unmitigated evil?’

    • JB, can you be a bit more specific, please? What specifically is ‘hilarious’ about my analysis? What do Saari and Newenhizen argue, other than what I can gauge by a quick web search, which doesn’t give you access to their full article? I agree that if you strongly prefer only one candidate, you’re going to vote for that candidate alone. So what’s the problem? Others won’t strongly prefer only one candidate and will be happy voting for several so long as by doing so they’re not prejudicing the chances of the candidate that is their strongest preference.

      E.g. in the case I gave, if the last election had been held using AppV, I’d have voted for three other candidates in addition to the Liberal Democrat, knowing that doing so wouldn’t prejudice the Lib Dem’s chance of winning. The Lib Dem was the candidate with any chance of winning that I supported; my strongest preference was for UKIP – so Approval Voting would have allowed me to express both priorities. Maybe you’re worried that the poll result doesn’t accurately reflect the full range of voters’ preferences. Maybe so; but nor does the Alternative Vote.

    • JB,

      That is completely wrong. The clear tactic with Approval Voting is to vote for the same candidate you’d support ordinarily, plus everyone you like better.

      For example, if you preferred Independent but voted for Democrat, then with Approval Voting you’d obviously want to vote for both of them (plus anyone else you prefer to Democrat).

      You have it precisely backwards, as it’s IRV that degrades to our ordinary plurality voting system.

  2. Bravo. I’m glad to hear approval voting is getting a better look.

    Will you also be considering score voting (AKA range voting) at any point? (Just like approval, only with more than two levels (approve/disapprove.))

    I wonder if you might also be interested in the work of Dr. Warren Smith, who instead of taking your qualitative approach went with a more quantitative method using a computer simulation. Results summarized here:

    And to JB: I would also like to know what places you’re talking about. Also, I have a refutation of your “Bullet Vote” fallacy written here:

    • Thanks, Dale. In the next post, when I can get round to it, I’ll be looking at a range-voting method that I’ve devised myself, called the ‘Popular Vote’. I’ve discussed this before here.

  3. Voting method performance is measured via Bayesian regret.

    Score Voting and Approval Voting dominate.

    Instant Runoff Voting is pretty terrible.

    End of story.

  4. but Approval and Range and Borda can all violate the principle of Majority Rule, so the chances of them being adopted in a mass democracy are zilch…

    With these systems, the minority can overturn the majority because they “feel more strongly” (or say they do) about their position. “Bayesian Regret” is just a smokescreen for “Revolution!”

  5. RodCrosby,

    In practical terms, the odds that a candidate would be the favorite of a majority, but would fail to win with Score or Approval Voting are virtually nil.

    And alternative methods like IRV are subject to more and more severe pathologies, which are disturbingly common.

    IRV, Borda, and all Condorcet methods violate the Favorite Betrayal Criterion, which basically means that a candidate cannot win if voters don’t BELIEVE he can win, even if they prefer him, so long as a sufficient number of them are tactical. Score/Approval Voting avoid that rather terrible bug.

    And if you want to be really esoteric, it is mathematically PROVEN that a candidate preferred by a majority of voters is not necessarily the “best candidate” according to the electorate, meaning that failure to elect the “majority winner” is not a flaw.

    Bayesian regret is essentially mathematically proven to be the “one right metric” of voting method performance.

  6. RodCrosby,

    To extend on my previous post…

    With Score Voting and Approval Voting, a majority can ALWAYS win if they just give the maximum score to their favorite candidate and a minimum score to everyone else (or with Approval Voting, just “bullet vote” for their favorite candidate).

    But say you have 3 strong candidates, and you feel that X=10, Y=7, and Z=0. Do you really want to risk having Z win because you gave Y a zero? Well, with Score/Approval Voting, you THE VOTER have the choice to decide that for yourself. If voters feel that majority winners should always win, then they can just bullet vote.

    But my bet is, they won’t. They will democratically decide that they think their expected value is more important than guaranteeing victory for a majority candidate. Rather than being told by you, Rod Crosby, that it’s a “flaw” for a majority candidate not to win, they can just decide that for themselves. If they decide that expected value really is more important (i.e. that Bayesian regret really is the right metric), then the result will reflect that. That’s democracy.

    Who are you to tell them they MUST use a voting method that satisfies the Majority Criterion, rather than always having the right to democratically decide?

  7. I recommend you also consider Bucklin voting. In its simplest form, also known as Majority Choice Approval, it’s just Approval with an extra “preferred” category above the level of “approved”. If one candidate has over 50% “preferred”, they win; otherwise, the approval winner wins. It was used in several US cities in the early 20th century – but repealed for technical arguments, without public debate, after it had elected some third-party winners.

    It’s much like approval in practice, but you don’t have to waste energy responding to the know-nothing objection expressed by JB in the first comment (“people
    would just vote for one candidate”).

    Ranking on your criteria, it comes out pretty similar to approval. Using +/- for a negligible improvement/flaw versus approval, I’d give it 3-, 2, 5, 4, 2+, 4-. (That totals out to 20-, almost two points better than approval). It is a hair worse than approval for “counting all the votes”, since mere-approval may not count – but that only happens when there is a clear winner at the higher “preferred” level. It’s a better in terms of accountability, because even a tactical voter has the option of ranking their compromise main-party frontrunner as only “approved”, so the main parties would have to actually earn “preferred” status. It’s clearly better in terms of voter expressiveness. It’s a hair better for mitigating tactical voting, because it doesn’t force a voter to choose between the most expressive vote and the most tactical one, so the naive vote is more likely to be the tactical one than with Approval. And it is a hair worse for user-friendliness – a tiny extra complication, but still no ways to spoil your ballot; this small disadvantage is clearly dominated by the extra expressiveness.

  8. Dear “David” (whoever you are)

    I just found out about your blog here the other day and I’m quite interested in what you have to say and would like to correspond with you via email, except I currently have absolutely no idea how to do so or who you are. You can drop me a note at warren.wds AT

    An example post by Jameson Quinn on the range voting yahoo group about this here blog post, is:

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