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Cardinal voting

Dear party,
    I'd like to know your thoughts on cardinal voting systems and whether we could use them internally. There are several desirable mathematical criteria that a good voting system should have. Some criteria are not desirable and some subtly contradict other criteria due to things like Arrow's paradox. It is quite clear that plurality voting and other ordinal voting systems are generally a poor reflection of the choice that satisfies most overall, whereas cardinal voting more accurately reflects the best choice and is much less subject to the pitfalls of strategic voting.
    Two such cardinal systems are range voting and approval voting. For single-winner positions and decisions such as internal elections for Pirate Party roles, range voting or approval voting are probably the most optimal. The latter effectively just being a simplified version of the former (which loses the later-no-harm criterion for being less accurate, effectively signal aliasing). Approval voting ballot papers would appear no more complex to the voter than a conventional plurality ballot paper, only you get to cross any number of boxes. The result of either of these 2 systems would be to achieve desirable criteria such as the independence of clones criterion and would elect a candidate that is more likely to be the optimal choice for overall satisfaction. They essentially significantly weaken the problem of strategic voting and voters that don't get their first choice are likely to be more satisfied than they would if the vote was ordinal. Cardinal systems are closer to a ‘perfect compromise’. Naturally, I'd like to see them get used more often.
    I would like to see either of these 2 systems used internally. I hold this issue above all others because it is our ability to vote in a democracy that allows us to decide on other issues; a better voting system would help strengthen our democratic decision making giving fairer outcomes for issues in general.
    If you've not heard of cardinal voting before, please check out these resources:
      * https://en.wikipedia.org/wiki/Cardinal_voting_systems
      * https://en.wikipedia.org/wiki/Range_voting
      * https://en.wikipedia.org/wiki/Approval_voting
      * ‘Score Versus Caveman Voting’ – a walkthrough introduction to range voting and explanation of the problems that it solves:
          * https://youtu.be/AuKDXeJt7KA (part 1 of 3)
          * https://youtu.be/JnjJhy-YanQ (part 2 of 3)
          * https://youtu.be/E0u9QXkn5uI (part 3 of 3)
      * https://en.wikipedia.org/wiki/Voting_system#Evaluating_voting_systems_using_criteria
    As for what would be the best voting system for a general election, I think that it requires some more research. I've been a proponent of proportional representation since before finding out about cardinal voting. Unfortunately, I'm not aware of any multiwinner cardinal voting system, and it is obvious that simply using approval or range voting as a multiwinner system would lose the independence of clones criterion and possibly others. It would seem that this criterion could be reinstated by weighting the vote by dividing each voter's selection by the total of the absolute value of each vote in the selection, but I'm not an expert on voting theory and don't know how to prove such a hypothesis. If this works as intended, then the resultant multiwinner proportions could then be used to balance local single-winner votes such that the proportions are met evenly, and this would form a proportional representation cardinal voting system.
    In case someone reading this happens to be an expert in this, I'd like to share a couple more thoughts on this. The theoretically ideal extension of range/approval voting to be multiwinner I imagine to be a range/approval vote where there's an option for each combination of candidates. This of course would offer an infeasibly large number of possible options even for a fairly small number of candidates, so the question is whether a reasonable approximation to this esoteric adaption can be sought. Maybe the weighting that I described above is already the best approximation and satisfies all the same criteria as the normal single-winner range/approval voting.
    So multiwinner cardinal voting for proportional representation requires some more thought and some mathematical research, but for internal matters, which are single-winner anyway, range/approval voting would be excellent. Also, if we use a better voting system internally then at least we are leading by example – this could well lead to further interest in better voting systems and sorting out the drastically suboptimal ordinal voting systems used for general elections and elsewhere.

Yours sincerely,
James Haigh.

P.s., I've just discovered that the weighted adaptation of range or approval voting is called cumulative voting (https://en.wikipedia.org/wiki/Cumulative_voting ) which is at least ‘semiproportional’, so indeed there already is a somewhat researched multiwinner cardinal voting system! Brilliant!


  • Hi James,

    Thank you for this. I've not yet watched the videos but they are on my to do list.

    In order to help anyone else reading this thread, can you go into more detail as to why ERS97 STV isn't fit for internal elections?
  • Hi,
        The video explains it better than I can. It's actually a single half-hour video that has been split into 3 parts, each just less than 10 minutes long. The first half of it explains the problems with existing systems, including even why this is important on a smaller scale. So it should answer your question nicely.

  • edited November 2014
    Hi James

    Given the low rate of member participation in party votes, why do you feel moving towards a complex system that creates only a very slight amount of potential additional enfranchisement would be worth (the estimated) barrier to participating that the added complexity would add?

    Also how would you respond to other major online voting systems such as Youtube's who gave up with the 5 star system in favour of up/down? I consider this as evidence of the fact people are not interested in 'grading' votes.

    Related, I'm a member of another organisation who is interested in building AI's to perform voting related tasks for us, because it's simply too much effort to vote all the time under such complex conditions.
  • Hi Deku,
        YouTube's rating system is still cardinal, only with 2 grades + abstaining. That's exactly the same as approval voting and it's as simple as it gets. It's no more complex than allowing only 1 vote – it simply removes a constraint. Please don't confuse my theorising about the resultant properties as complexity for implementation or for the voter to use it. Having finer granularity (as in range voting) is what adds some complexity but even then, it's still entirely a summation. If range voting is considered too detailed, go for approval voting.
        Of course, the benefits aren't obvious when we have elections consisting of a single candidate but it's still important because we'll be leading by example and we'll be ready for the party to grow. As soon as you get to elections of 3 or more candidates the negative effects of ordinal voting become more obvious, but even with just 2 candidates, there is more of a barrier to voting in an ordinal system – if I prefer both candidates roughly equally, in an ordinal system, the only option to express that is to abstain. With cardinal voting, including approval voting, I can express that same information without abstaining, and therefore show that I do care to vote but that I happen not to have a preference.
        I don't think voters are as stupid as you make out otherwise there wouldn't be such a thing as strategic voting. Having a cardinal voting system would resist the strategic voting but also cater for those voters who wish to express a little more information about how their preference is distributed. Voters that aren't interested in the ability to vote for more than 1 candidate can just use it exactly like they are used to, i.e. vote for only 1 candidate. However, cardinal voting actually takes a great deal of unnecessary work out of the decision of who to vote for if the voter sees a tie in their preference. Rather than spending a large amount of time trying to decide who has that slight edge, they can simply approve them both and be done with it.

  • Would this be able to handle an election with say 20 candidates standing for 12 available vacancies (i.e. Board elections) ?
  • Yes. Range/approval voting are single-winner but there are also multiwinner cardinal votings systems such as cumulative voting. Cumulative voting, as I understand, partially restores the independence of clones criterion that would be lost if range/approval voting was to be used for multiwinner decisions as-is. It is either done by dividing the voters' votes by their total number of votes or by placing a contraint on the total number of votes a voter can use. The latter implementation is entirely addition-based but requires validation (effectively the voter is required to divide up their votes as desired). Seeing as division isn't difficult if the votes are aggregated by a computer, the former method is probably a lot easier for the voter. Note that this can still be done with basic yes/no votes as with approval voting by assigning numeric values to yes, no, and abstain/blank/pass. Although I'm dead sure about single-winner range/approval voting, I'm not so familiar with multiwinner cardinal voting. I've just noticed that because division is an inate part of cumulative voting, the multiplicative identity, zero, becomes relevant and breaks the symmetry unless negative voting is used. This is something that I'd like to investigate before recommending cumulative voting specifically as there may well be a better way to form a multiwinner cardinal voting system. My preliminary thoughts are that cumulative voting is still a lot better than ordinal multiwinner alternatives, but isn't as good as range or approval voting is for single-winner decisions.
  • It might be a bit flippant, but reading these explanations I imagine what the 'No to AV' camp thought AV would look like o_O
  • I would love us to go for a PR system as FPTP is dead now. However in today's Ashcroft poll he asked a simple question on what system people preferred and simple majority (FPTP) won by 60%.

    Like in the farce that was the AV campaign it is difficult to explain to a disillusioned public as to why PR would be better for everyone and I would argue all parties.

    So I ask a question, to change the system and cardinal looks interesting do we need a referendum, I am not a big fan of them anyway.
  • I think AV is the winner, STV could be better but we have enough MPs as it is. anything is better than first past the post though. I really think AV really takes away peoples fears of "wasted votes". We could go German and go MMP but I still feel AV would be better not perfect still open Gerrymandering. I think with AV people will vote for the party they like not the party they least hate.
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