Alternative alternative voting systems, part eight: Bucklin voting

So far in this series of articles, I’ve looked at only single member-constituency systems, including AV+, which alleviates the disproportionality of single-member systems by combining AV with a regional-list element (which is what AMS does for FPTP). My discussions have concluded that the Alternative Vote (AV), which is the only voting reform we’re actually being offered, is the least good of all the possible single-member alternatives across a range of criteria.

I would say that, of all the established voting methods I’ve discussed, Approval Voting and score voting (of which my ARV system is an example) are clearly superior to AV in that they give more real choice and power to voters, and the results more accurately reflect the full range of voters’ sympathies. Of the methods I’ve ‘invented’, I would say Two-Member Proportional Voting (TMPR – a compromise between a multi-member-proportional and single-member-preferential system) and Net Voting (a system that resolves the absence of a majority for any candidate on the basis of candidates’ ‘net popularity’, which is the ratio of voters who like them to those who oppose them) stand out as potentially quite exciting alternatives that could really revitalise English and British democracy without going as far as full proportional systems.

In this post and the next, I’ll be discussing two further established single member-constituency systems that rank alongside Approval Voting and score voting as much more satisfactory reforms than AV: Bucklin voting and run-off elections.

For an explanation of how Bucklin voting works, I’ll just quote direct from the summary in Wikipedia: “Voters are allowed rank preference ballots (first, second, third, etc.). In some variants, equal ranking is allowed at some or all ranks. Some variants have a predetermined number of ranks available (usually 2 or 3), while others have unlimited ranks. First choice votes are first counted. If one candidate has a majority, that candidate wins. Otherwise the second choices are added to the first choices. Again, if a candidate with a majority vote is found, the winner is the candidate with the most votes accumulated. Lower rankings are added as needed. A majority is determined based on the number of valid ballots. Since, after the first round, there may be more votes cast than voters, it is possible for more than one candidate to have majority support.”

The version of Bucklin voting I will be discussing is where you’re allowed unlimited rankings (up to the number of actual candidates) but can’t indicate equal rankings.

The main advantage I think Bucklin voting has over AV is that it eliminates the ridiculous situation whereby the second and subsequent preferences of most voters (i.e. those who’ve given the leading parties their first preferences) are not counted and cannot influence the final result, whereas the result can be determined by a relatively small number of second preferences (i.e. those whose first preference was for a minor party). This anomaly means that the winning ‘majority’ under AV can actually be smaller than a latent majority for another party comprising first-preference votes for that party plus the non-counted second preferences. For example, if a Lib Dem candidate was in third place behind Labour and the Conservatives once the votes for all the other parties had been transferred, the Lib Dems cannot win, even though they might have the highest total of first and second preferences combined – because the second preferences of Labour and Tory voters (most of which might be for the Lib Dem) are not counted.

Bucklin voting overcomes these imbalances in AV because, if there is no majority of first preferences for any party, the second preferences of all voters are added, and so on with third and fourth preferences, etc., if required. In practice, in many constituencies, just adding the first and second preferences would be enough to generate a majority for one or more candidates, so you don’t need to go any further – which makes Bucklin voting much simpler, more straightforward and easier to count as well as being fairer.

So, for the above reasons, I would award Bucklin voting three points out of five against the criterion Does every vote count, and is every vote counted?, compared with two out of five for AV. There still would be a lot of preferences that wouldn’t count for anything in a Bucklin election: after the second or third preference, there would hardly ever be any point in voters listing further preferences as the result would already have been determined, and this could mean that genuinely ‘popular’ parties who gained a large number of, say, third and fourth preferences could end up being passed over by the system. Plus, as a single-member system, Bucklin is not particularly proportional, so a lot of voters’ preferences would not help to determine the final result.

On proportionality, my second criterion, I would still award Bucklin three out of five, because it’s clearly better than AV, which scores two. It’s better because it provides a more accurate reflection of the range of preferences of all voters. In particular, in England, the Lib Dems would probably have performed much more strongly in 2010 if the election had been held using Bucklin voting compared with AV, which would barely have improved their performance over FPTP. (According to the Electoral Calculus, the Lib Dems would have won 88 seats under AV based on their vote share in 2010, compared with 57 under FPTP. Using Bucklin, I’m sure their seats tally would have been considerably higher.) This under-performance under AV is for the reason I outlined above: the Lib Dems were the leading second preference of most voters in 2010, but under AV, in many seats, the vast majority of those second preferences would not have been counted. In Bucklin, they are. Have the Lib Dems been misled by the advocates of AV (such as those in the Electoral Reform Society or the Labour Party) into thinking AV is the best compromise for them between FPTP and STV, whereas Bucklin voting would be much fairer and more favourable to them, if they’d had but the wit to look into it?

As for my third criterion, Does the system foster accountability?, I would say Bucklin voting performs at least as well as AV, if not better. So I’m awarding it three out of five. Under Bucklin, winning parties definitely need to solicit the support of voters for other parties because they need their second preferences to be sure of winning. This means, though, that Bucklin would encourage a drift to the centre of the political spectrum as the leading parties competed for support from each other’s voter base.

The same advantage or disadvantage, depending on your point of view, has been adduced for AV: parties need to court each other’s voters. But I would say that, in AV, this actually means that parties have to broaden their appeal in both directions: towards the centre and towards the more extreme fringes of the political spectrum. This is because, in the AV process, the first votes to be redistributed to the larger parties are those of supporters of minor parties such as UKIP, the BNP and the Greens. Therefore, Labour and the Lib Dems will have to appeal to Green voters as well each other’s supporters; and the Tories will have to appeal to UKIP supporters as well as Lib Dem voters. Hence, AV could bring about more polarisation between left and right wing while at the same time leading to more voter disappointment, because the parties will alter their policies and messages to appeal to the broadest church but will not be able to deliver in a way that satisfies many who’ve supported them.

Bucklin, by contrast, encourages genuine competition for the centre ground, which could bring about more consensus politics. Another way of viewing that, though, is that broadly held opinions that are not shared by the party-political establishment – such as support for leaving the EU or creating an English parliament – would not get a look in as the parties made cosy coalition deals involving policies that had not been supported by a majority or even offered to the electorate. Hence, while Bucklin would make politicians more accountable to voters from across the three main parties, it could allow them to ignore popular demands that they do not want to hear.

On the fourth criterion, Does the voting system allow voters to express the full range of their political and personal preferences, and send a message to politicians?, I would award Bucklin no more than two out five: the same as AV. This is for the reason set out above that, after two or three rounds, there’s no point listing any further preferences. Sure, on the first preference, voters can indicate what, in my article on the 3CV system, I described as their emotional or conviction vote: the party they feel most sympathy for but often would not vote for under FPTP because they can’t win or for other ‘prudential’ reasons. But then, in the second preference, voters will often feel constrained to vote for whichever of the parties that can actually win that they feel able to support to some degree. After that, listing any further preferences would largely be academic. Indeed, you would not want to indicate a preference for any party that might stand a chance of defeating your top-two in a third round of voting.

My fifth criterion is: Does the system mitigate [or perhaps ‘obviate’ would be better] tactical voting? Here, I think Bucklin does slightly better than AV, which is prone to a legion of pernicious tactical-voting conundrums, as my previous two posts have argued (see here and here). So I’d give it three out of five. Under Bucklin, there’s no need to vote tactically with respect to your first preference, because, however you vote, if a party you don’t like wins over 50% of the votes, you could have done nothing to prevent it. Your second preference, however, could well be a tactical choice: voting for your ‘second-best’ choice to defeat the party you don’t want to win. But then again, as a second-preference vote, this is technically your ‘second-favourite’ anyway. By contrast, in AV, owing to the complicated logic of trying to ensure that the right two candidates get into the final run-off, you could often feel forced to put down your tactical vote as your ‘first preference’; for instance, in one of the scenarios I’ve described where Tory voters might feel obliged to vote Lib Dem first, rather than Conservative, in order to defeat the Labour candidate.

One other tactical ploy under Bucklin voting could be so-called bullet voting: where supporters of one of the parties in contention to win the seat would not offer any subsequent preferences in order not to harm the prospects of their candidate (e.g. Tory voters not listing a second preference for the Lib Dem candidate in case that helped the Lib Dem to win on second preferences). However, I don’t think there’s anything objectionable about this, and it’s not really tactical voting in the ‘pure’ sense: you could just say it’s voters listing only one choice because they want only one party and no other to win. This could, in any case, equally back-fire on such voters in that, by not voting Lib Dem as their second preference, Tory voters could indirectly help the Labour candidate to win. So voters’ behaviour in this respect is more likely to be shaped by the dynamics in each individual seat rather than being a systemic failing of Bucklin voting.

Finally, How easy is the system for voters to understand, trust and use effectively? Well, much easier than AV, for sure! In fact, I’d say it’s pretty simple and easy to understand: if there’s no majority winner on first preferences, then the second preferences are added (and subsequent preferences if need be) until one is found. It’s much more transparent and obviously fair than AV, as all preferences of all voters are treated equally. Plus it’s easier for voters to work with the system to try and get a result they want, as it’s much easier to predict what the impact of different voting strategies will be: ‘if I put party A ahead of party B as my second preference, will I get my desired result?’ So I’ll give Bucklin four out of five here.

So how does Bucklin shape up in comparison with the other systems I’ve discussed in this series? See the table below for comparison:

Criterion FPTP AV AppV ARV TMPR AV+ NetV 3CV Bucklin
Does every vote count?

3

2

3

4

4

3

4

3

3

Is the system proportional?

1

2

2

3

3

3

3

3

3

Does the system foster accountability?

3

3

4

4

4

4

4

4

3

Does the system let voters express their views?

1

2

3

4

4

3

4

3

2

Does the system mitigate tactical voting?

1

2

2

3

4

2

3

3

3

How user-friendly is the system?

3

2

4

3

3

3

3

3

4

Total scored out of a maximum of 30

12

13

18

21

22

18

21

19

18

So Bucklin performs as well as Approval Voting but less strongly than the score-voting ARV system – but, obviously, much more strongly than AV. Why hasn’t it been considered?

Next time, run-off elections.

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9 Responses

  1. “eliminates the ridiculous situation whereby the second and subsequent preferences of most voters (i.e. those who’ve given the leading parties their first preferences) are not counted and cannot influence the final result”
    There are very good reasons why AV doesn’t do what you think it ought to do. In fact, Bucklin is the ridiculous system, since subsequent preferences can defeat higher preferences. It was ruled unconstitutional in the US for this reason. It also fails Condorcet Loser, which is pretty bad.
    AV is objectively superior to all other ordinal single winner methods. As for Range, etc they are for the birds. Ain’t gonna happen.

    • Thanks, Rod. Yes, in the Bucklin system, subsequent preferences can defeat higher preferences (later-no-harm criterion) – but most voters would be aware of this danger and wouldn’t award subsequent preferences to any candidate if they thought that would lead to their first-preference candidate being defeated, unless this was for the tactical reason of ensuring a third candidate was defeated. In any case, if they did indicate a second preference that defeated their first preference, one would be justified in arguing that, overall, the winning candidate had appealed to more voters and that, therefore, voters would be more satisfied with the result. That’s not the case with AV, where there can be a latent majority of first, second and subsequent preferences for one candidate that is greater than the ‘winning’ majority or plurality.

      Yes, you’re right that Bucklin fails Condorcet Loser (a candidate can win who would lose a pair-wise contest with every other candidate). But this is akin to where a football team is to all intents and purposes relegated but still has a ‘mathematical possibility’ of being saved: it’s so unlikely that this would happen in the British context that this objection is pretty much irrelevant. Can you really envisage a situation where a candidate from one of England’s three main parties won a Bucklin election (which usually implies winning a majority) and was capable of losing a pair-wise contest with every single other candidate, including, say, the Green, BNP and English Democrat candidates? Come on!

      In reality, Bucklin produces a majority that is much fairer and more transparent than AV, because it’s based on a like-for-like comparison of parties’ performance, e.g. the first and second preferences of all parties, not the first preferences only of parties A and B, and the second and potentially multiple subsequent preferences of voters for parties C to X. Now of course, under Bucklin, a party winning 40% of first preferences but only 20% of second preferences could be trumped by a party winning 30% of first preferences and 31% of second preferences, where in a straight fight between just those two, the first party might win. But AV is prone to the same flaws and is worse because it allows the xth preferences of some voters equal status with the first preferences of others. Besides which, neither system assigns a weighting to preferences – which is what allows the xth preference of some voters to be treated as if it were a first preference – so to criticise Bucklin for allowing a party with more subsequent preferences but fewer first preferences to win is hypocritical if you allow it with AV.

      And in terms of Condorcet, AV (and Bucklin) also fails the Condorcet Winner criterion: always electing the candidate who would beat all others in any pair-wise contest. In fact, AV can elect a candidate who is neither the first choice of most voters, nor the second choice of most voters – which is theoretically possible but unlikely with Bucklin but highly likely with AV; e.g. the case of Labour (second on first preferences) defeating a Tory (first on first preferences) based on (third-placed) Lib Dem second preferences, whereas the Lib Dem wins most second preferences but they are not counted.

      I’d love to see you make an argument for why AV is, as you say, ‘objectively superior to all other ordinal single winner methods’ when it has so many manifest flaws. Plus the fact that Range isn’t going to happen says more about the unwillingness of the political class to put power in the hands of the voters than about Range’s objective merits.

  2. First off, all systems have manifest flaws. So there is no perfect system. AV is objectively better than all others though for several reasons.

    1) It’s clone independent. Very few other system are. Any democratic system in which the presence of similar candidates can hurt or help each other is a joke.
    2) It passes Condorcet Loser and Majority Loser. Any system which can elect the objectively worst candidate is a joke.
    3) It FAILS Condorcet winner. Yes you read that right. It fails, which is a good thing, since unfortunately to pass CW a system must necessarily fail later-no-harm (a joke) and be susceptible to the burying strategy (v.bad). As a result, AV in practice will elect more CWs than Condorcet methods themselves. Strategic voting under Condorcet methods may in fact elect Condorcet Losers!

    To my knowledge there is no other system which possesses all these properties.

    The only downsides with AV are the more ethereal failures such as monotonicity, participation and consistency. I’ve always thought these pretty irrelevant, and not fairly compared with other more obvious failures in other systems.

    e.g. Condorcet Loser failure can be detected conclusively by simply examining the actual ballots in one actual election. Monotonicity failures, on the other hand, are always hypothetical , e.g. “IF x number of voters had ranked A lower, A would have won.” So all AV really fails are conjectures, which to me is of little practical significance.

    • Well, clone-independence is another hypothetical criterion like monotonicity. In practice, you don’t know how the subsequent preferences of voters for candidate A and their clone B would split in AV: you can’t guarantee that they would just be exchanged between each other, apart from in the theoretical case of candidates genuinely being identical.

      Bucklin also passes Majority Loser. Approval and Range Voting don’t, but then they make different assumptions about the meaning of voters’ choices, and voters aren’t obliged to express approval or to give a score to any candidate they don’t want to win, even if they do approve of them to some extent (i.e. in practice, as opposed to hypothetical instances, those systems will also not elect the majority loser – even though they don’t allow a majority loser to be formally determined).

      Perhaps you would care to elaborate in laymen’s terms your points about the Condorcet winner. I think I understand why a Condorcet-compliant system must fail later-no-harm; but you’ve lost me on the other points.

      Re monotonicity and consistency, I agree with you. However, participation is more serious, since it involves people deliberately not voting at all (i.e. as a tactic) in order to improve the chances of their favoured candidate. This is related to the point I make in my post about Lib Dems voting Tory tactically under AV: the system encourages insincerity and produces perverse outcomes. But that’s a criticism that applies to most (all?) single-winner systems. But yes, participation is also essentially a ‘what-if’ criterion.

      More seriously, AV fails majority winner, contrary to what is usually said about it: it doesn’t always pick a winner obtaining a majority plus can fail to pick another candidate – and sometimes the only candidate – that does win a majority. That’s a major major flaw that Bucklin doesn’t share with it: Bucklin finds the largest available majority or plurality relative to each round of counting (i.e. stopping once a majority of higher preferences has been found).

      And that’s not to mention AV’s vulnerability to tactical voting scenarios of the kind I describe in my post on those (two days ago).

  3. I have been reading your articles in search of the name of a certain voting system and figured I would just ask if you are familiar with any formal voting system with these criteria.

    Multiple voter system.
    There are only two posible outcomes.
    Votes for option 1 are assumed and do not require active participation.
    A single vote for option 2 overrides any number of votes for option 1.

    Example. A family of four is on a car trip. When a rest stop approaches they all have the ability to to say they need to go to the bathroom and the whole family will stop at the rest stop. One or all of the family can vote to use the rest stop but it requires a unanimous vote to pass the reststop.

    • Sounds a bit like conditional majority voting, in which the dissent of a minority can override the decision of the majority – used in federal systems, so that the divergent needs of smaller parts of the federation are not ignored.

  4. One single member PR system you have not evaluated yet is Direct Party and Representative Voting. (Google dpr voting or http://www.dprvoting.org ) I hope you will have a look at this and include it in your table. I think it would score very strongly for the following reasons.

    Does every vote count?
    Every vote counts and makes an equal difference.
    For this reason there are no marginal constituencies, so the campaign would have to be conducted nationwide because each vote is equally valuable.

    Is the system proportional?
    The system is almost precisely proportional, as far as the significant parties are concerned.
    There is something of a barrier to the small parties which would not be represented under FPTP, but this system is fairer than FPTP both to very small parties and independents, for reasons that take a little longer to explain.

    Does the system foster accountability?
    Yes, because the MP can no longer rely on being elected for party label reasons. A disgruntled electorate could cast a majority of their votes for Party A, but choose an MP from another party (or an Independent) to represent them.
    For this reason there are no safe seats for the MP.

    Does the system let voters express their views?
    Yes, because the voter can vote for a party of their choice, (even when there is no candidate from the party of their choice standing in the constituency) and also vote for the candidate they want to represent them, regardless of party.

    Does the system mitigate tactical voting?
    Yes, there is not rationale for tactical voting. Your vote can only benefit the party you vote for.

    How user-friendly is the system
    Very. It is straightforward to vote – One vote in the party section, for your choice of party to from the Government, and one vote in the representative section to select the candidate to become the MP.
    It is very quick and simple to count, practically as quick as FPTP.

    Existing constituency boundaries could be retained (or changed). The system is not sensitive to constituency size or boundaries and there would be no party advantage for any change of boundaries.

    I would be pleased to answer any queries you may have.

  5. I’ve put some code to implement a PR version of Bucklin voting (with whole votes, not fractional as you use above) on GitHub. You may be interested in checking it out.

    https://github.com/dodecatheon/Majority-Choice-Approval–M–Transferable-Vote

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