Some amateur political theory

As I mentioned, I’m at a conference on Logic, Game Theory and Social Choice. Attending a session on experiments in voting theory (some very interesting ones for which I will try to find links) I started thinking about a case for Instant Runoff/Single Transferable/Preferential systems (like many Australians I’m a big fan of this system which works well for us, with none of the disasters we’ve seen produced in the US and UK by plurality voting). For those interested, an outline of an idea is over the fold. It’s not my field, so I’m quite prepared to be told my argument is wrong, well-known or both.

Update 29/8 The original claim I made was wrong, but now I have one that, I think, works better.

Think about an IRV election where, after the votes have been cast, any candidate has the option to withdraw (there are some potential complications about the order in which this option becomes available to candidates, but I don’t think they matter in the end). Suppose that a candidate will only withdraw if by doing so, they will ensure the election of a candidate preferred by the majority of their voters to the candidate actually elected. I claim that this procedure is a Condorcet method. That is, it always selects the Condorcet winner, the candidate who would beat each of the other candidates in a run-off election, if such a candidate exists.

To see this think about the case of three candidates. IRV elects the Condorcet winner unless she finishes last in the first preference count. For example, there might be three candidates, with the Left and the Right candidate each preferred by 40 per cent of voters and the Centre candidate preferred by 30 per cent. The Centre candidate is preferred by both Left and Right voters to the candidate of opposite orientation, so is the Condorcet winner. The majority of Centre voters prefer the Right candidate. Then the Centre candidate is the Condorcet winner, but, under IRV the Centre candidate will be eliminated, and her transferred votes (second preferences) will elect the Right candidate.

But, if the option of withdrawal is available, the Left candidate, who can’t win, will best serve the preferences of Left voters by withdrawing. This ensures the election of the Centre candidate. So, with three candidates IRV+withdrawal option is a Condorcet method.

To extend to the case of four candidates, we can argue as follows. If the Condorcet winner finishes in the first three places, we have the same case as before. The last-placed candidate is eliminated (or withdraws, it doesn’t matter) and we have a three-candidate race. Suppose that the Condorcet winner finishes fourth. Then (since she’s the Condorcet winner) there must be at least one other candidate whose voters prefer her to the winner under standard IRV. If that candidate withdraws, we are again in a three-candidate race and the previous analysis applies. And so on, recursively, for arbitrary numbers of candidates.

Next observe that if candidates can anticipate votes correctly, and stand only if by doing so they would advance the interests of their own voters, standard IRV will produce the same result, since candidates who would ultimately choose to withdraw will simply not run. We see something like this in the Australian two-party system in seats where there is a strong third-party or independent candidate, but one of the major parties will clearly beat the other in a pairwise choice. The other major party often chooses to run dead, or (mostly in the case of an independent incumbent) not at all, so as to ensure that the other major party is kept out.

If this analysis is correct it seems to me to make a pretty strong case for IRV + withdrawal option and therefore (if decisions not to run roughly match ex post wish to withdraw) for IRV itself. It’s simpler than any other Condorcet method, has actually been used on a large scale, and seems, in practice to work much as claimed in this post.

35 thoughts on “Some amateur political theory

  1. I’m not sure that 2 is entirely correct but it is near enough in practice. Otherwise I agree. IRV is one of the real strenghts of Australian democracy.

    Still we could improve our system in other ways. For instance I like the decentralised power of the Switzerland model. And I’d like to see our central government lose it’s powers of direct taxation as is the case with the EU. I think we should cap average per capita tax revenue for each tier of government and let the people decide directly if the cap should rise or fall (ie TABOR). I think we should allow citizen initiated referendums for repealing (but not making) laws. I think we ought to use term limits. I like many aspects of New Zealands MMP system. We should abolish government funding of parties. There is more but I think I’ll leave it at that for now.

  2. When you enter that voting booth and pull that lever, punch that chad, fill in that bubble, or touch that screen for your candidate, you should be assured your are helping them.
    No voting system should hurt a candidate if they get more votes.

    Couple examples to ponder:

    Let’s say there is a race, (we will use 1st and 2nd preference as the example will go no farther)
    Here’s where the first election came out:
    (100 votes, but cold also use as %)

    1 2
    39 Sam Manny
    35 Manny Joel
    26 Joel Sam

    In IRV, the candidate with the lowest votes gets eliminated and the voters second choice gets distributed.

    Joel is eliminated thus transferring 26 votes to Sam
    39+26=65 for Sam
    35 for Manny
    Sam Wins

    Sam serves his 4 year term and does a really great job. In the next election, the same competitors enter he race. But since Sam did such a good job, 10 voter who previously voted Manny/Joel think Sam did a great job, so the vote Sam/Manny

    1 2
    49 Sam Manny
    25 Manny Joel
    26 Joel Sam

    In IRV, the candidate with the lowest votes gets eliminated and the voters second choice gets distributed.

    Manny is eliminated thus transferring 25 votes to Joel
    25+26=51 for Joel
    49 for Sam
    Joel Wins

    You could also look at this as a single election, where Sam was able to campaign harder and convince 10 Manny supporters that he was better, but to put Manny second.

    The fact that Sam gets more votes, he is eliminated. Voters went in to support him, but by voting for him, they hurt him.

    This has recently happened in Aspen and will be part of a Federal Lawsuit.

    Now for the pairwise and spoiler effect in IRV:
    The electorate agrees in this:
    40% Cindy > Chuck
    60% Chuck > Cindy

    Now let’s add a third candidate, but we will keep the above the same (pairwise)

    1 2 3
    40% Cindy Mike Chuck
    35% Mike Chuck Cindy
    25% Chuck Cindy Mike

    You can see that 49% still prefer Cindy over Chuck, and 60% (35% + 25%) prefer Chuck over Cindy.

    Let’s run this through IRV.
    In IRV, the candidate with the lowest votes gets eliminated and the voters second choice gets distributed.
    Chuck has the lowest votes, so he is eliminated, thus transferring 25 votes to Cindy.
    Giving us:

    Cindy 40 + 25(transfered) = 65%
    Mike 35%

    Cindy WINS!?

    Consider this: an election is held with a Republican, a Libertarian and a Democrat
    Due to specific positions the candidates take, environment, education, taxes, etc. the votes happen as follow:
    1 2 3
    417 Liber Dem Rep
    82 Liber Rep Dem
    143 Dem Liber Rep
    357 Dem Rep Liber
    285 Rep Liber Dem
    324 Rep Dem Liber

    1st Round:
    Libertarians get 499
    Democrats get 500
    Republican get 609

    WIth IRV, the candidate with the lowest vote gets eliminated, and the voters second choice is distributed, in this case the Libertarian gets eliminated and 417 votes goes to the Democrats, 82 go to the Republicans, leaving:

    2nd Round:
    Democrats: 917
    Republicans: 691

    Democrats WIN.

    But, there was a old bus from the local commune that had 100 voters going to the polls after a hard day of group living. The were planning on voting just for the Libertarian as Rank 1, and the Democrat as Rank 2, and was no way in hell going to even vote for the Republican for #3 but leave it blank. Unfortunately, their bus broke down and they never got a the chance. But, in the end, their Second favored candidate won, so they were fairly happy.

    Now let’s suppose their bus didn’t break down and they made it to the polls. It turns out like this:

    1 2 3
    100 Liber Dem
    417 Liber Dem Rep
    82 Liber Rep Dem
    143 Dem Liber Rep
    357 Dem Rep Liber
    285 Rep Liber Dem
    324 Rep Dem Liber

    1st Round:
    Libertarians get 599
    Democrats get 500
    Republicans get 609

    WIth IRV, the candidate with the lowest vote gets eliminated, and the voters second choice is distributed, in this case the Democrat gets eliminated and 357 goes to the Republicans, 285 go to the Libertarian, leaving:

    2nd Round:
    Libertarians: 742
    Republicans: 966

    Republicans WIN.

    So, because they voted, they propelled their hated candidate to a win. They didn’t event vote for that candidate but due to the method of redistributing the votes.

    Many municipalities in the US are looking at trying IRV and the promoters have looked at Ireland and other countries as models. All the cool kids are doing it. Put the fact remains – your vote should COUNT.

    As more elections occur in the US, these examples are happening and are pissing people (and loosing candidates) off. Several cities have referendums on their ballots to get rid of IRV after just one try. Lots of buyers remorse.

    I’m glad you are keeping an open mind on this.

  3. Approval voting actually requires a complex strategic choice. Since there’s no option of leaving the seat vacant, it makes no sense to say “vote for candidates of whom you approve”. Instead, you have to divide the candidates into two groups, based on a guess that the member of the first group who gets most votes will be preferable to the member of the second group who gets most votes.

  4. Pr Q says:

    (like many Australians I’m a big fan of this system which works well for us, with none of the disasters we’ve seen produced in the US and UK by plurality voting)

    I am a big fan of preferential voting too, along with most of our early consitutional ideas. It embodies an instinctive notion of fairness by giving all parties a say in the overall distribution of votes. But it avoids the chaos of proportional representation, thereby assuring conservative forms of government.

    We really lucked in with our Founding Fathers.

    BTW what are the “disasters we’ve seen produced in the US and UK by plurality voting”? Are they just disasters because Right-wingers may have benefitted?

  5. @Jack Strocchi

    what are the “disasters we’ve seen produced in the US and UK by plurality voting”? Are they just disasters because Right-wingers may have benefitted?

    Disasters: first, because some wrong guys got elected. second because one such wrong guy was George W Bush, third because George W Bush was nominally right wing, despite a fiscal policy that belied the label.

    But yes, we lucked in with our founding fathers. The bicameral pref/prop system is pretty good. A shame that its recent above-the-line impairment allowed one idiot (Conroy) to spawn an even greater one (Fielding).

  6. I don’t think preferential voting was one of the founding features of Australia’s system of government. For the first few decades after Federation I believe simple plurality voting was still used for the House of Representatives (even in the Senate, where it tended to produce winner-take-all outcomes).

    The Nationalist Party and the Country Party usually worked out an arrangement of not contesting the same seats so as not to split the non-Labor vote.

  7. All that the views on current Australian voting systems really show is, people used to them like them – just as my own (relative) approval of first past the post shows that my background encouraged me to like transparency and definiteness more than its particular anomalies.

    For what it’s worth, my favoured system (drawing on a knowledge of Arrow’s Theorem as well as my personal tastes) is:-

    – Have two quite distinct election methods for each house of a bicameral system (with many office holders in each), so that each Arrow’s Theorem criterion is met at least somewhere.

    – Have one house short term, with term limits and elected by cumulative voting in multi-member constituencies (not necessarily all geographical, e.g. some just for public servants, and without aiming for heterogeneity in the constituencies – the multi-member side of things avoids unfairness); Britain actually approximated this until “reforms” by former minor parties and interests kicked away this ladder that had let those parties and interests in.

    – Have the other house long term like the Canadian Senate, with some additional ex officio non-voting positions (to provide observers/advisers).

    – Have a bar on anyone ever nominating for or serving in either house ever being eligible for the other (to avoid groupthink).

    – Have no tie break method as between houses but rather give the long term house only a delaying power until after a new short term house election (which might be triggered for certain types of bills and/or majorities), to allow a mandate to be requested.

    I can see the short term house being a joint sitting of state level houses, to save multiple layers in a federal structure. I would also recommend only paying members from dedicated and endowed revenue earning funds, and not from hypothecated revenue falling on taxes (with any pensions forming a charge on current serving members). Non-geographical public servant constituencies were actually tried in Victoria, and only “failed” in the sense that they achieved their aim so well that they provoked a backlash. I would also allow citizen initiated referenda, with two further features:-

    – Results only to be binding by a large special majority or if the same identical referendum (with no options changed) were passed after a special interval of the order of a generation (with no second chances at confirming a referendum, and lapsing if the referendum were not held before a cut off or if another referendum on any subject were held in the interim – or even proposed by either house).

    – Alternative options could be added by either house, except for a confirming referendum.

    For single specific posts, I prefer the French system for presidents, with an explicit run off election for leading contenders who have not outright won.

    However, I do not consider that any of this confers legitimacy except over those who truly do agree with the idea of indirect representative democracy. For the rest (including me), it only offers amelioration.

  8. I prefer the idea of sortition + deliberative voting for a unicameral assembly + direct democracy to set overall policy direction and resolve deadlocks on policy issues.

    Essentially, random people who had indicated an interest in serving on their voter enrolment would be selected about two years out. Anyone with a clear conflict of interest could be either let go, or could resolve it. Each could be given resources to develop and publicise their ideas, requisite training, a stipend similar to their wage or average wage (whichever was the higher) and could run a blog (with help) in which they would communicate with potential voters.

    At various points in time (say every six months) there would be deliberative votes where people would rate the candidate’s policies in terms of importance, feasibility and the belief they had in the candidate and his or her competence to do the job. Depending on how this played out, each candidate would get a certain number of winning tokens which would on election day be placed in a barrel alongside all the winning tokens of all the other candidates who were still running. Then the winner would be selected at random.

    Statistically, this would result in a skew towards candidates whom most people found credible but people with somewhat more challenging ideas or different social backgrounds would not automatically be excluded. More importantly still, a much broader policy discussion would result with much more focus on issues rather than personalities. Every person who was seriously interested in making a difference could believe that they could stand and be elected without kissing up to powerful interests or getting involved in shady dealings, and because it couldn’t be a career (getting elected twice would be statistically improbable) candidates couldn’t forget who they were or why they were there. On election day, while people might wish that their person had got up there would be no large bands of people feeling that their side had lost, or that next time, if they managed to persuade enough people of the justice of their cause, that people wouldn’t be elected who shared their views.

    There would be no direct role for parties in this system either. All a party could really do is to seek to influence the total potential candidate pool by discussing (shock horror) ideas. Imagine that. Political parties trying to get people talking about policies rather than personalities! And of course the legislature would really be both representative of the populace and indifferent to party discipline — so people who were incompetent or malfeasant could find no cover. At the same time, there’d be no reason for “gotcha” politics if people in power made honest mistakes. They could say “look, I screwed up, but here’s what I’m going to do now” knowing that the next election wasn’t an issue for them personally or any party. People could write to their pollie expecting a sensible response.

    Groups in the legislature could eventually coalesce around common policies and organise interest groups in the populace to support various ideas.

    I doubt anyone in the elite would see this as in their interest however …

  9. I am much closer to your views Fran than the others, which are still basically ‘follow the leader’. The only problem with moving to a substantively democratic political system is that entrenched power must also be challenged in the corporate and bureaucratic arenas. Otherwise we end up with weaker govt and correspondingly stronger corporate and bureaucratic power. Participation must be extended far more widely than elected govt alone.
    But your suggestion would make a great start 🙂

  10. Most of the utopias proposed above have a literature (largely condemnatory). But isn’t the topic voluntary withdrawal after the IRV ballot? This I have never heard of.

    Doesn’t it resolve your anomalies, BobT? In his first instance Manny would resign and Joel, not Sam, would win. Rightly so since 61% prefer Joel to Sam.

    In the next follow-up election Sam would voluntarily withdraw and Manny, not Joel, wins – rightly since 74% prefer him to Joel.

    In the next three-way example Mike would hasten to withdraw and so push the election to Chuck – rightly since preferred by 60% of the electorate.

    The other examples the numbers are too big for my lazy brain. Presumably they would also be resolved. (Why didn’t you stick to percentages Bob?)

    The examples are somewhat artificial since in practice not all second preferences flow to the same candidate. Probably this would not change the principle but it would make the calculation messier.

    To Jack Strocchi. One disaster would be Northern Ireland. The disaster in NI was caused by first past the post elections. Not by sectarianism, but by the electoral system. After 50 years of polarisation the UK govt tried to introduce PR in the early 80s. It didn’t take. They tried again in the late 90s. Still didn’t work. Then in about 2004 they had another go at PR and it seems to be sticking.

    There is now PR in Greater London, PR in Wales and PR in Scotland. If you have only one chamber, PR is essential. Witness the chaos in PNG, Vanuatu and the Solomons. As long as those countries have majoritarian single chambers, they will never be viable.

  11. The ability to withdraw “prior to” the vote tally would, though seen as a noble gesture by some, would be used as a method to “game” the system. Back room consultants would run slates, making promises of senior staff positions, etc.) The ability to withdraw after the votes tallied and presumably a winner shown, is certainly a method to game the results.

    The fact remains, IRV on its face has fundamental (as shown) and constitutional problems and soon will be challenged in Federal Courts in the USA.

    Mike, you are right that the second choice does not always go to the same person, but was done so to simplify the example. A REAL LIFE EXAMPLE, is shown in the links, with the true vote tallies. Take a look.

  12. I agree Nanks and indeed, I would see such a system as also well-suited to the operation of public services, co-ops etc. You do need professional bureaucrats of course, but this system could make them more accountable because part of their power comes from the cosy relationships they develop with the political arms of government.

  13. BobT – the real example is a bit complex. I will have to take their word for it that his supporters caused his defeat by voting for him. That’s okay for your example above is clear evidence that that can happen.

    But it is true, isn’t it, that voluntary withdrawal would resolve the problem completely?

    I don’t know about gaming the system. I don’t see how it is especially open to it. The candidates just look at the 1st preference tally and act according to their political interests.

  14. In traditional IRV the first candidate to drop out of the race is the one with the least number of primary votes. This could be amended such that the candidate to drop out is the one that is put last by most candidates. This does however require that voters fill in all boxes. It would improve the prospects of finding the condorcet winner.

    Fran introduced an element of lottery to candidate appointment. Whilst I don’t like the approach specified I do like the idea of a random element.

    One way to get a representative body would be to require candidates to collect 1000 signatures from citizens willing to vouch that the candidate is worthy of the office and supporting their candidacy. Then we randomly select which of the candidates become MPs by pulling names from a hat until we have the required number. Nobody could argue that the result woudn’t be at least as representative as running elections. After all opinion polls are considered representative and they involve the views of a random group of people. And juries are selected in part by random chance and they make some very serious decisions. The benefits of this approach include avoiding the cost of elections. We could call it democracy without elections.

  15. The problem I’d have with that method Terje is that there would be too much randomness in them. Of course, as we see from branch stacking, those 1000 names might have nothing to them at all.

    What we want from democracy are two basic things:

    1. Governance mainly by people who strongly resemble the political and social composition of the governed. This is not merely democractic of course but offers policy continuity which is important for good governance (see below)
    2. Governance that includes, significant dissent from the consensus where it exists, respects minorities, allows scope for non-mainstream ideas to get a hearing etc

    And from good governance we hope for people who are honest and competent and are capable of supporting some continuity on programs that need to run their course to be evaluated.

    We also want to create an informed polity and connect this “building an informed polity” with the business of governance so that means and ends are reconciled.

    My system addresses each of these and discourages any group from seeing the outcome of each new iteration of governance as a win or a loss, but as something to be evaluated on the basis of substantive matters. In short, it should build a sense of ownership of the governance process even where people are dissatisfied with a particular policy.

  16. @Fran Barlow
    How would you moderate the influence of corporations – through their ability to dominate the flow of information – and similarly how would you control aggregation of power in the public service.

  17. Fran – thanks for the feedback. My comment was more of a brain storming exercise than a finished product. I agree that it might disconnect people from any sense of owning the process. Either way I do agree with your view that randomness can be harnessed as a way to remove a lot of the wasteful tribalism from politics. Do you know of any representative bodies in the world that are appointed using partially random methods?

  18. @nanks

    How would you moderate the influence of corporations – through their ability to dominate the flow of information?

    I think the flow of information is becoming more fragmented by the day. Murdoch is thinking of charging for content, papers are going bankrupt, and you can watch TV and listen to radio in any country these days. You can design and publish your own podcasts and of course blogsites are everywhere.

    Combine that with a far more engaged and informed public and I don’t think this would be a problem in practice. I suspect anyone trying to control a n information system like this would be attempting to herd cats.

    similarly how would you control aggregation of power in the public service

    Again, I see the process as organic — so two words — changing culture. At the moment, the public service is out of sight, most of the time. The whole Goblin Grech thing couldn’t have happened if we’d had openness about process and a large pool of people who were able to and interested in, tracvking the work of our functionaries. Plainly, there would still have to be some firewalls to protect legitimate privacy concerns, investigations into probity and perhaps legitimate commercial-in-confidence or cabinet matters and so forth but these things aside I’d be for the open publication in near real time of departmental memos and correspondence.

  19. Terje

    “In traditional IRV the first candidate to drop out of the race is the one with the least number of primary votes. This could be amended such that the candidate to drop out is the one that is put last by most candidates. This does however require that voters fill in all boxes. It would improve the prospects of finding the condorcet winner.”

    Why bother? If merely allowing voluntary withdrawal does the job why invent complicated rules which “improve the prospect”? JQ put up a suggestion which is very simple and apparently works perfectly. Can you show that it doesn’t? It also looks as though it could be easily introduced.

    Fran – you are using governance where you mean government.

  20. Mike – I’m not sure why you say “why bother” in an open ended conversation. I’m not trying to beat the proposal put forward by JQ merely sharing alternatives. In any case not every competition is going to have a Condorcet winner so two systems that guarantee to find the Condorcet winner might be compared using other criteria. JQs assertion is as yet unproven and as far as I know it is not even published in the peer reviewed literature.

    The proposal that I made regarding a modified IRV, in which the most unpopular candidate is removed at each round rather than the least popular, actually has a formal name. Apparantly it isn’t guaranteed to find the condorcet winner. Even so I think it is an improvement on traditional IRV. Details on the scheme below:-

    The following article suggests that there are several established systems that find Condorcet winners.

    Perhaps we should vote on which system is best?

  21. p.s. For what it is worth I don’t think IRV gets it wrong often enough to bother with reforming it. Our biggest problem in terms of creating a body that is representative of the people is that we have single member electorates such that parliament nicely represent everybody in the centre of politics and hardly anybody else. The result is mediocre policy challenged by mediocre counter arguments. The New Zealand system does a better job and essentially uses plurality voting within an MMP framework.

  22. Terje “For what it is worth I don’t think IRV gets it wrong often enough to bother with reforming it.”

    My feeling too. Still, the availability of voluntary withdrawal could only improve it.

    Yes, parliament composed of single member electorates is basically a failure. A rule of thumb (Duverger’s rule) says it makes for two-party polarised politics and most political scientist would agree that that is the tendency.

    As I pointed out above (#11), left to itself it doesn’t work (breeds civil war) and needs to be supplemented by a second chamber.

    Yet there is ongoing activism in NZ for a return to majoritarian elections. Stupidity or ignorance in my view.

    Given a second chamber, debate in the single-member chamber is worthless – just theatre. Its sittings could be discontinued and the clerk issued with a rubber stamp saying PASSED. That would save a lot of money and the MPs could go back to their electorates and play social worker – which for most of them is what they prefer anyway.

  23. Imagine an election using John Quiggins IRV method in which the Liberal candidate is ahead of the Labor candidate at the end of the count but not if the third party independent, lets call her Helen, voluntarily withdraws. If Helen decides to withdraw then she signals to the world that she favours the Labor party and many of her followers who lean toward the Liberals will be disillusioned. If however she decides not to withdraw then she signals to the world that she favours the Liberal party and all her followers that lean towards the Labour party will be disillusioned. Either way her claim to being an independent third party alternative is compromised. As such it seems to me that the reform proposed by JQ simply leads to a more deeply polarised political culture. As such I would regard it as a backward step.

    The point above is not merely theoretical. I was a candidate for the LDP during the last federal election. We had to give preferences to other parties as part of the senate preference process for each state. Whilst we tried hard to be reasonably neutral towards the various parties the system essentially forced us to rank our choice between them and also signal our position regarding the major parties (Labor and Liberal) in each state. By forcing us into this game the system essentially guaranteed that we would annoy a significant number of our followers, and fuel our critics, one way or another. And in fact this is exactly what happened. Forcing parties to choose between other parties creates a very compromising process that simply reinforces the old left / right mentality and helps to futher undermine conversations centred on policies.

  24. “Imagine an election using John Quiggins IRV method in which the Liberal candidate is ahead of the Labor candidate at the end of the count but not if the third party independent, lets call her Helen, voluntarily withdraws.”

    So Helen came in second on the 1st preference tally and Labor came third. (Is that what you meant? I am not sure it was, but if she came third then her withdrawal would be involuntary and obviously she did not come first.) The people who voted for Helen put second preference to Labor (mostly). The people who voted for Labor, however, must put their second preferences to Liberal – otherwise Helen would win the election. Pressing on…

    Helen has no big decision to make. She will withdraw. For if she did not then she would allow the Lib to win contrary to the wishes of her supporters. Yes, that minority of her supporters who second preferenced Liberal will be disappointed but with their fellow Helen-voters, not with her. Indeed, they would agree she must withdraw if they think the result should reflect the voters’ wishes.

    So your objection falls away completely. If I am missing something, do demonstrate with some percentage voting figures.

  25. Yes I think you are missing something. However given that the something is apparent even in your own example and you still don’t see it then I’m not sure I can help.

    Perhaps another way to look at this is to ask why Helen has a choice in the matter. If as you say she has no decision to make then why make her decision voluntary at all? Why not insist that she must effectively be withdraw as soon as it is apparant that she hasn’t won at position one or two and if most of her supporters favour candidate number two (but not if they mostly favour candidate number one) and then recount accordingly? This would preserve her independance and achieve the same electoral result you seem to advocate.

  26. Still no numbers, Terje? The electoral result I “seem to advocate” is the one which best reflects the will of the voters.

    Presumably it would be her own supporters who would insist that she withdraw. But yes, why make her decision voluntary? Why not change the rules of elimination of candidates to make it compulsory in order to obtain the optimum result?

    I suspect the rules cannot be consistently worked out. With three candidates it seems plain but where there were four or more you probably get paradoxes. Voluntary withdrawal would leave it up to the candidates to sort out in any instance. Even with three candidates, it may not be plain for that is the situation people set up to illustrate the “Condorcet paradox”.

    That brings up something I have been wondering about. With multiple candidates, would there be race to withdraw? Or would there deals done between candidates for a certain sequence of withdrawing? Declaration of the outcome would have to be delayed to allow time for negotiation.

  27. Mike numbers won’t help. The solution may be perfect in terms of finding the condorcet winner but so what. If you think finding the condorcet winner is the only important aspect of elections then I think you are missing an awful lot. You seem to be locked into an assumption that we are trying to optimise for one election only. The solution on offer undermines for many minor candidates the perception of being independent third party alternatives. At the next election Helen will be a less viable candidate because of the damage done at the previous election. Ultimately the reform works to further narrow the focus of elections to the two major parties. It is hard for me to see any real benefit in this except in some esoteric mathematical sense. At best it is an interesting academic exercise.

  28. So you admit the solution may be perfect. (Did you do a bit of doodling with the numbers?) These comments are up to #34 but it seems the matter rests with my (or JQ’s) resolution at #11 to BobT’s numbers at #3.

    You are concerned for future elections? An election is an understanding that the person elected will be the person most congenial to the electorate (or least uncongenial if you wish). If anyone else is “elected” then the rightful winner has been cheated and not only future elections, but the credibility of the system is undermined. Just look at BobT’s complaint. An electoral system should seek that Condorcet winner, even if it is not always achievable.

    It seems to me that the main reason for standing as a third, fourth, etc candidate (who has no chance of winning) is to dicker over preferences with the two or three main candidates (one of whom will win). Thus the Australian preference system allows smaller groups some influence thereby mitigating the two-party polarisation.

  29. Mike – the solution can’t be perfect in reflecting the will of the voters even within your narrow terms of reference simply because it depends on the voluntary decision of an imperfect candidate. However in the real world context that I’m primarily interested in it is definitely not an improvement. If you could turn voluntary withdrawal into a mandatory rules based withdrawal then it may be a real world improvment but you have indicated that beyond three candidates you have not yet figured out how you would do that. And leaving it to candidates to decide who wins is not reflecting the will of the voters. Witness the senate preference process in Australia and the constant complaints about the way Steve Fielding was elected.

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