Alternative alternative voting systems, part seven: 3CV

3CV stands for ‘Three-Criteria Voting’. This is another voting system of my own invention. How does it work?

  • It’s a one-member-constituency system.
  • Voters can vote for two candidates, marking their choices with a cross next to each name. They can vote for just one candidate if they prefer.
  • Voters are also invited to indicate which of their two candidates they would prefer to go through to a second round of counting if no candidate obtains the support of a majority of voters. They can do this by marking an extra cross for that candidate in an additional column on the ballot paper. If they selected only one candidate for the first round, their vote for that candidate automatically goes forward to the second count.
  • If only one candidate obtains the votes of a majority in the first round of counting, that candidate wins. If more than one candidate obtains a majority (which is possible with two votes per voter), the winner is the candidate obtaining the most votes. This ‘majority criterion‘ is the first of the three criteria referred to in the name of the system.
  • If no candidate obtains a majority, the votes for the most preferred candidates (the ones that voters indicate with the extra cross) are then counted and the votes for the less preferred candidates are excluded. In order for there to be a winner, one candidate must either obtain a majority or else a plurality (largest minority) that is at least ten-percentage points above the next-highest candidate. I.e. a candidate could win on 40% of the vote, but only if the next-nearest candidate obtained 30% or less. This is the second criterion, which you could call the ‘substantial-plurality principle’.
  • If there is still no winner at this stage, points are awarded to each candidate, with the preferred votes for each candidate (the vote carried forward into a second count) generating two points and the discarded votes for each candidate generating one point. The winner is then the candidate gaining the highest total of points. This third criterion is basically a simple score or range vote.

What are the underlying principles behind this method? The main idea is that 3CV gives expression to the two main types of ‘preference’ that voters actually have in elections. A premise behind preferential systems such as AV or range methods (where you give a point score to each candidate) is that preference can be quantified: that voters straightforwardly ‘prefer’ one candidate over another and can adequately reflect this by giving a numerical value to each candidate. However, in reality, voters’ preferences are of various types: they like different candidates and parties for different reasons; and it may be impossible for many voters to really say whether they definitely prefer one candidate over another.

I feel that the two main types of preference people have are what you could call ’emotional’ support, or sympathy, and ‘prudential’ support: ‘heart’ and ‘head’. The candidate you support emotionally is one you like individually, and / or whose party and policies you sympathise with. But you may not have voted for that party in the past because they did not have a chance of winning under the First Past the Post system, or because you did not think they could form a credible government, or because you were unsure whether voting for them would be in your interest. These are all ‘prudential’ criteria: the kind of considerations that lead people to vote for one of the larger parties even if they feel more sympathy for a smaller party, because there is a need to be realistic and to ensure that the ‘best’ of the larger parties that can win does win.

3CV allows voters to express both an emotional vote and a prudential vote. The vote people choose to go through to a second round of counting is more likely to be their prudential vote: the candidate who they would probably have voted for under First Past the Post because of the prudential considerations mentioned above. Under 3CV, voters can add a vote for their emotionally preferred candidate alongside the prudential choice. The Alternative Vote (AV) system does this, too. But the difference, with AV, is that votes for the minor parties don’t count for much and often aren’t counted at all because the system effectively just re-allocates them to candidates from the bigger parties or ignores them altogether if voters’ first preferences are for higher-ranked parties. With 3CV, on the other hand, votes for smaller parties are all counted and registered, and smaller parties have a better chance of breaking through if there is a big enough groundswell of support for them, e.g. if enough people who vote for bigger parties use their extra vote for the smaller party in question.

Note that 3CV does things the opposite way round from AV: instead of counting ‘first preferences’ first and then using second preferences if need be, as AV does, 3CV counts first and second preferences together, and then eliminates the ‘second’ preferences if need be, although it does not strictly regard voters’ two choices in the first round as ‘preferences’, whereby voters are forced to artificially rank their selected candidates. So the 3CV count moves from one that is likely to produce a majority for at least one candidate (where voters’ two choices are counted) to one that is more likely to generate only a plurality winner. But that winner is a strong one because (s)he represents voters’ considered choice: in most cases, it would be the candidate / party that, on consideration, most voters would regard as the best realistic option should their emotionally preferred candidate not succeed in garnering enough support. And the fact that the system accepts only pluralities with a margin of victory of at least 10% further ensures that the plurality winner is perceived by the electorate as legitimate.

In this respect, the system tries to capture the way people’s thinking processes actually work when they make their voting selection: many voters start with more than one possible candidate in mind and have to weigh up what I’ve called their emotional and prudential choices, eventually plumping for the prudential option (under FPTP), or making their emotional choice their ‘first’ preference and their prudential candidate their ‘second’ preference (under AV). Under 3CV, voters can include both options, and then the system prompts them to whittle down that choice to just one candidate if neither of their selections wins a majority; and that candidate will almost always be the prudential one. The point of this is that the system is likely to make voters feel less cheated in that they’ve had a chance to give voice to both their feelings and their pragmatism, and they’ll accept that the eventual winner is the result of a similar process of elimination and deliberation exercised by their fellow citizens. And it’s for this reason that voters are asked to indicate their second-round choice in an additional column on the ballot paper that does not refer to that candidate as a ‘first’ preference, allowing voters to think of the candidate they give their mark to in that column as the one who, on balance, they feel is the best all-round recipient of their vote.

In any case, voters’ emotionally preferred candidates still have a chance of winning in the event of a third round: if no majority winner is generated in the first round, and if no majority or substantial-plurality winner is produced in the second round. In the final, decisive ‘points round’, the system fairly (I think) gives more weight (i.e. two points) to voters’ prudential choice (the candidate they chose to go through to the second round) than to their emotional choice (one point). But it’s still possible for the emotional choice of many voters to win at the final stage. For instance, in many constituencies at the last UK general election, the Lib Dem candidate would have been the ’emotional’ choice of many voters whose ‘prudential’ choice was either Labour or Conservative (which is how they in fact voted under the prevailing FPTP system). If there had not been enough emotional Lib Dem voters to secure a majority in the first round, but there was also no substantial-plurality winner, it’s possible some Lib Dem candidates would have garnered enough points to win in the third round in that, if they expressed any ‘second’ preference at all, many Tory and Labour voters would have chosen the Lib Dem.

It could perhaps be regarded as inconsistent that the system first includes both emotional and prudential choices, then eliminates the emotional option, and then reinstates it at the last gasp. But this is basically because the system seeks out an authoritative winner that genuinely reflects the key motivations of voters in choosing particular candidates. That is, the winner in most cases will be the candidate that a large minority of voters regards as its prudential choice and a smaller number of voters see as their emotional choice; and the system reflects this either as an overall majority (most convincing winner), a substantial plurality (authoritative winner based only on the prudential considerations) or a points victory (winner that will still appeal to a broad cross-section and large overall number of voters, who’ve voted for the successful candidate for whichever reason). The fact that the points system gives more weight to the prudential candidate (by giving them two points) means that it still reflects a combination of the prudential choice of many voters and the emotional choice of others.

So it’s my view that this system would give rise to greater voter satisfaction than FPTP or AV, whatever the result in each constituency, because it gives more chances to voters’ emotional choices while still giving greater comparative weight to their realistic ones. But unlike FPTP, 3CV does not allow unfair victories based on a minority share of the vote combined with a narrow margin of victory; and unlike AV, it allows authoritative plurality winners while making it more likely for convincing, clear majority winners to emerge. That’s because in most seats in England, 3CV would be likely to produce a majority winner in the first round without all the obscure vote-transfer process of AV, which can produce an eventual winner that commands less overall support than other candidates, as I’ve argued elsewhere.

So how does 3CV stand in relation to the six criteria by which I’ve been comparing different voting systems? First, Does every vote count, and is every vote counted? Here, I’d award 3CV three out of five: one more than AV. This is for the reason set out above: that 3CV does record all votes, including for minor parties, whereas AV does not, meaning that the votes also count for more in that alternative parties have a better chance of winning. However, 3CV does not merit four out of five against this criterion because voters are not as empowered by the system as much as they are in some of the other systems I’ve discussed, which are either proportional or involve more powerful scoring options, including the ability to cast negative votes, as in Net Voting [link].

3CV also scores three out of five in relation to the question, Is the system proportional? 3CV is not intrinsically proportional, by virtue of its being a one-member-constituency system, which allows bigger parties to amass a larger share of seats nationwide than is merited by their overall share of the vote. However, 3CV would be more proportional than FPTP and, arguably, than AV (hence the higher score), in that it allows ‘natural’ majorities in favour of particular parties to emerge. For example, in seats that are three-horse races between the UK’s largest parties, it would be possible for one party (e.g. the Conservatives) to win on, say, 35% of the vote under FPTP. Under AV, the winner would be dependent on the lottery of who finished third on first preferences. For example, if the Tory came third, the Lib Dem candidate would win (as most Tory voters would transfer their votes to the Lib Dem), even though there might be more overall support for the Labour candidate, in that Lib Dem voters’ second choices (not counted) could well be mainly for Labour. Under 3CV, this natural majority in favour of Labour would emerge, particularly if more left-wing Lib Dem voters were motivated to indicate Labour as one of their two votes in order to ensure the Tory candidate was defeated.

As for the third criterion, Does the system foster accountability?, I’d say 3CV scores four out of five. There’s a high degree of accountability that is intrinsic to one-member-constituency systems, in that MPs are directly accountable to their voters. However, 3CV improves on FPTP and AV in that MPs would be even more dependent on appealing to supporters of other parties, whose second vote would be needed for MPs to secure a majority. This is also the case with AV; but with 3CV, all ‘second’ preferences are counted, which is not what happens with AV. Seats would be less safe, and MPs would have to work harder to serve the interests of all their constituents.

Criterion No. 4 is, Does the voting system allow voters to express the full range of their political and personal preferences, and send a message to politicians? Here, 3CV scores three out of five (compared with two for AV). 3CV is designed to map to voters’ decision-making processes (weighing up emotional versus prudential choices) in the manner described above; so it does allow voters to express a range of views. However, this range is quite limited compared with other systems, and the potential for voters to bring about electoral shocks and so punish politicians is also restricted – arguably even more so than under FPTP, because even if some of a party’s core vote deserts it, with 3CV it can count on both emotional and prudential support from other voters. However, voters can still send quite a powerful message to politicians via their emotional choices.

Against the fifth criterion, Does the system mitigate tactical voting?, I’d also give 3CV three out of five. There is a degree of tactical voting involved in voters’ decision about which of their two candidates to carry forward to a second count. However, this decision does not involve merely tactical voting (i.e. backing a tolerable winner) but includes other factors such as self-interest and wanting to elect a credible national government. Plus the prudential vote, under 3CV, does not require voters to abandon the party they support emotionally, who they can still back in both the first and potential third round of the count. So, as a non-proportional system, there is a degree of pressure to vote tactically with 3CV, but this does not exclude people’s real preferences.

Finally, How easy is the system for voters to understand, trust and use effectively? Again, I’d give 3CV three out of five. It’s quite a simple system for voters to understand in the polling booth once it’s been explained to them: ‘you can vote for two candidates, and then in the second column you can pick just one of those two who you’d like to go into a second count if no candidate wins an overall majority’. People might be confused for a while about whether that second-round candidate was supposed to be their first or second preference; but it could be explained that the candidate to select there is the one you’d probably choose if you’d only had one choice to begin with. I think people would get it quite soon, and they’d understand that they could vote with both their hearts and heads while also being free to choose which of those two criteria was most important to them.

So, to recap, here’s how 3CV stands in relation to the other systems discussed in this series:

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

3

2

3

4

4

3

4

3

Is the system proportional?

1

2

2

3

3

3

3

3

Does the system foster accountability?

3

3

4

4

4

4

4

4

Does the system let voters express their views?

1

2

3

4

4

3

4

3

Does the system mitigate tactical voting?

1

2

2

3

4

2

3

3

How user-friendly is the system?

3

2

4

3

3

3

3

3

Total scored out of a maximum of 30

12

13

18

21

22

18

21

19

3CV obtains a comparable score to the single member-constituency Approval Voting system, and the more proportional, modified variant of AV that is AV+. It is streaks ahead of AV itself but behind the proportional two-member-constituency TMPR system, the empowering Net Voting method and the score-voting ARV. Certainly worth throwing into the hat compared with AV, I’d say.

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6 Responses

  1. Your scoring isn’t objective, it’s based on your estimates of value, which could very well be wrong.

    The RIGHT way to calculate performance is to use Baesian regret. Then you get at OBJECTIVELY measuring the effectiveness with which various voting methods satisfy the SUBJECTIVE preferences of voters with regard to the CANDIDATES.

    A really clear-cut problem with your scoring is that you have a “mitigate tactical voting” score, which I assume you have no basis for. Only by looking at the impact of tactical voting on Bayesian regret values can you objectively measure the significance of tactical behavior in a given voting method. E.g.

    http://ScoreVoting.net/BayRegsFig.html

    • Clay, we’ve had this discussion before, haven’t we? I’m not pretending my analysis is absolutely objective, if such a thing exists. I’m not convinced that you can measure things like regret and voter satisfaction, which are highly elusive and fickle qualities, through a mathematical method. My analysis is based on an understanding of how British, and more specifically English, voters actually behave in elections, based on the unique features of English party politics and the pattern of past elections. So it’s a more concrete and pragmatic approach that English readers can relate to more easily.

      In relation to tactical voting, I should perhaps write ‘obviate tactical voting’, rather than ‘mitigate’. I’m looking at the potential of the system to nullify tactical voting by making it unnecessary. With 3CV, the ‘tactical’ choice is re-framed as a realistic one, which voters should feel more reconciled to, having had the opportunity to also make their more emotional vote in a format that enables that vote to make more of an impact than, say, under AV. That at least is the intention behind it; whether it would work out that way in reality is another matter, and 3CV obviously doesn’t go far enough, as voters for smaller parties will still be grossly under-represented nationwide.

    • David,

      You don’t “measure” Bayesian regret, you calculate it. Here’s an extremely simplified example of the process.
      ScoreVoting.net/BRworked.txt

      In the figures I cite, there are various utility generators used, different ratios of tactical vs. sincere voters, varying numbers of candidates, etc.

      As for “obviating” tactical voting, it is mathematically proven that cannot be done with any deterministic voting method.

      Also, it’s wrong to prioritize tactical voting qua tactical voting. The relevant issue is the decrease in voter satisfaction caused as a _result_ of the tactical voting.

      A simple example to highlight that would be to look at the Bayesian regret for Instant Runoff Voting with 100% sincere voters, vs. Score Voting with 100% _tactical_ voters. There are models in which Score Voting still does better, even in that unrealistically tilted tactical voting scenario. That is, even if IRV had some magical property that caused it to be 100% sincere, it would still be worse than Score Voting.

      Moral: focus on utility, not intermediate qualities whose effect on utility you have little means to objective quantify.

      • Thanks for the clarification, Clay. I see what you’re saying but I still think there’s some merit in speculating in more ordinary language about how voters would behave and feel about different systems if they were introduced, even if this is not scientific or ‘objective’. I actually agree with you that score voting systems are better than instant run-off, which is clearly rubbish and produces skewed results.

  2. I agree that there’s merit in talking in ordinary language about the issues. But by giving a “score” based on various properties, I think you go further, giving the impression that this is quantitative when it’s really more qualitative. Perhaps just discussing the criteria pass/fail list, without assigning scores, is a better way to go.

    Of course there are things like cost/complexity/spoilage which are not encompassed within the Bayesian regret calculations, and so they have to be talked about independently.

    Overall I think there’s a lot of good material here.

    Thanks for your feedback.

    • Thanks for your generous response, Clay. Yes, giving these criteria a score is a bit arbitrary and subjective. It’s partly intended to be polemical: trying to make the point that AV is inadequate in so many departments compared with alternatives that could have been considered in the UK.

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