[EM] Bucklin/IRV hybrid? Motivated by MSV strategy

C.Benham cbenham at adam.com.au
Wed Nov 2 21:57:30 PDT 2016


On 11/3/2016 8:44 AM, Michael Ossipoff wrote:

> x: A
> 1: C=A
> 1: C=B
> x: B
>
> x = any number greater than 1.   MMPO  elects C.
>
> (enduote)
>
> 1. When I asked who is wronged, you said that the A voters are 
> wronged, because, rightfully, it should be an A&B tie, and the A 
> voters should have a 50% probability of their favorite winning. 

All the voters except 2 are seriously "wronged" because their exclusive 
favourite (A or B) should be elected with 50% probability (instead of 0%),

(And after randomly choosing one of A and B, only one of the two who 
voted C equal-top will not have one of their equal-favourites elected.)

> Wronged? Sure. Significantly-wronged? No. It certainly can't be called 
> an outrage.

That's right. Having your favourite top-voted on half of the millions of 
ballots lose to a candidate that is voted above bottom on only two ballots
certainly can't be called an outrage.

> Ridiculous result? Sure. ...caused by ridiculous voting.
>
> ...in an implausible example.

The voting isn't ridiculous. The idea that the A and B voters should 
have bothered to "cooperate" against such a minor candidate is ridiculous.

The example's "implausibility" is forgiven by its extreme simplicity.  I 
think of a voting method algorithm as a quasi-intelligent device. It is more
understandable and maybe forgiveable if the device is "confused" by a 
relatively complicated example (say with lots of candidates in the Smith set
and/or cycles within cycles), but anything that gets it so wrong in such 
a simple example is unforgivably "stupid" and should be binned.

> That being said, I admit that the bad-example shows that MMPO has a 
> wrong-looking-result-vulnerability.
>
> They go with methods that have deluxe properties. 

I don't think I agree with that premise, or that MMPO has "deluxe 
properties" (presumably you mean 'deluxe strategy properties').

I don't like random-fill incentive and consider Later-no-Harm to be a 
mixed blessing, and I'm not very impressed by "Winning Votes
  strategy".

I like that it meets FBC.

Chris Benham

>
> Chris--
>
> I'd said:
>
>>
>>     For #2, it really takes something with a lot of valuable &
>>     otherwise-unobtainable properties, to justify replacing Approval,
>>     Score or Bucklin with it.
>>
>>     I suggest that only Plain MMPO qualifies.
>
>
> You replied:
>
> Say you ask people who are used to and/or like any of  Approval, 
> Score,  Bucklin,  or  plurality (aka FPP) or Top-Two Runoff or IRV or 
> Benham:
>
> (a) Would you accept a method that in a 3-candidate election with 20 
> million voters can elect a candidate that is voted above equal-bottom
> on only two ballots?
>
> x: A
> 1: C=A
> 1: C=B
> x: B
>
> x = any number greater than 1.   MMPO  elects C.
>
> (enduote)
>
> 1. When I asked who is wronged, you said that the A voters are 
> wronged, because, rightfully, it should be an A&B tie, and the A 
> voters should have a 50% probability of their favorite winning.
>
> My answer to that was & is that the A voters have indicated that they 
> don't consider B any better than C. They're indifferent between C and 
> the other candidate whom they'd like to have a 50% probability of 
> winning. Wronged? Sure. Significantly-wronged? No. It certainly can't 
> be called an outrage.
>
> 2, You make it sound as if what happened in that example is entirely 
> the fault of the voting-system, and maybe the two A=C and B=C voters..
>
> But it was done by the all A voters and B voters. In a method known to 
> look only at pairwise opposition, those voters ensured that A & B will 
> have as much pairwise opposition as anyone can have, because they 
> refused to rank eachother's candidate over C.
>
> Refusal to co-operate with a rival can be a mistake in any method. 
> It's hardly surprising if it's a mistake in MMPO too.
>
> So don't let the A voters & B voters convince, you when they whine 
> about that result.   ...the result of their refusal to co-operate with 
> eachother.
>
> Think of it as the chicken-dilemma defection-blunder magnified.
>
> Ridiculous result? Sure. ...caused by ridiculous voting.
>
> ...in an implausible example.
>
> --------------------------------------------------------------------------------------------
>
> That being said, I admit that the bad-example shows that MMPO has a 
> wrong-looking-result-vulnerability.
>
> They go with methods that have deluxe properties. What else is new.
>
> The problem is that, of course, MMPO gets its unqualled 
> properties-combination by looking only at pairwise opposition.
>
> For one thing, that means that it disregards how much positive support 
> a candidate has. So it was possible to write a bad-example in which 
> someone wins with practically no positive support...without that 
> example's result seriously wronging anyone.
>
> Also, because it's _pairwise_ opposition, a candidate with two 
> factions each ranking a different candidate over C, the method ignores 
> the fact that C has _two_ candidates ranked over hir by a large number 
> of voters, whereas A & B each have only one candidate ranked over them 
> (by just one more voter).
>
> MMPO doesn't count how many candidates are ranked over C, or the total 
> number of voters who rank C lower. Thereby we get the wrong-looking 
> result where C has both of the other candidates ranked over hir by a 
> lot of people, but still beats A & B, each of which have just one 
> candidate ranked over hir--by one more voter..
>
> These are obvious inevitable results of looking only at pairwise 
> opposition.
>
> But, even with those wrong-result vulnerabilities, the resulting 
> bad-example doesn't significantly wrong anyone.
>
> Even though no serious wrong is done by those wrong-looking results, 
> what can be done to avoid them?
>
> * Rank some in-between compromise candidates over the worst one, ok? 
> Is that too much to ask?
>
> In that way, you rank eachother's candidate over the worst one, giving 
> hir more people ranking those candidates over hir, to give hir more 
> pairwise opposition than the candidates you like better.
>
> Set your rivalry aside and do that.
>
> * Don't allow write-ins.  Or, if you do allow write-ins, make sure 
> that you rank compromises, not just your favorite, so that you're all 
> voting eachother over whatever unknown write-in comes along, so  that 
> hir individual pairwise oppositions won't be less than those of the 
> candidates you like more..
>
> All the rank methods have strategy problems, to go with the deluxe 
> properties that they bring. The more deluxe properties, the more kinds 
> of wrong-looking results are possible. You get what you pay for.
>
> So you deal with those special  vulnerabilities, as the price of the 
> deluxe properties.
>
> Michael Ossipoff
>
>
>
>
>
>
>
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>
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>
>
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>
>
>
>
> (b) Do you think it is fair and sensible that a voter who is only 
> interested in getting their favourite elected can increase the chance 
> of that
> happening by fully ranking (below top) all the other candidates at 
> random?
>
>
>
> What response do you think you will get?
>
> I don't live in the US, but I would think that most people wouldn't 
> even believe that question (a) is serious, and that anyone who tries to
> tell them that that example only "looks bad" would blow their credibility.
>
> Chris Benham
>
>
>
>
>>     Jameson--
>>
>>
>>     On Sat, Oct 29, 2016 at 11:16 AM, Jameson Quinn
>>     <jameson.quinn at gmail.com <mailto:jameson.quinn at gmail.com>> wrote:
>>
>>
>>         ....Here's my "ideal characteristics" for a political
>>         single-winner election system, more or less in descending
>>         order of importance:
>>
>>          1. FBC
>>
>>
>>     Yes, I consider FBC to be #!.
>>
>>         1.
>>
>>
>>          2. Handles center squeeze (ie, some form of weakened
>>             Condorcet guarantee that's compatible with FBC)
>>
>>     But maybe the goal of electing the CWs unnecessarily complicates
>>     votiing. Maybe someday, there won't be a bottom set, for most
>>     voters, and, with honest elections & honest, open media, it will
>>     be clear who's the CWs. But now, Approval's best strategy doesn't
>>     require that. Brams pointed out that Approval's results can be
>>     better than the CWs.
>>
>>     But, when it's desirable to elect the CWs, and it isn't obvious
>>     who's the CWs, then the wv methods, and methods with wv-like
>>     strategy (such as MMPO), are the methods that make it easiest to
>>     protect the CWs.
>>
>>     Also, it should be noted that you can't be sure how often there
>>     will be a CWs, under different and better conditions.
>>
>>         1.
>>
>>
>>          2. Relatively simple to explain
>>
>>
>>     Approval & Score are easy to explain. I've had conversations in
>>     which only Approval & Score were accepted as being plain &
>>     un-elaborate enough to be acceptable..
>>
>>     You know that SARA & XA are complicated and not easy to explain.
>>     I've tried explaining them.
>>
>>     MMPO?:
>>
>>     "The winner is the candidate who has fewest people voting someone
>>     else over hir."
>>
>>     {...some same other candidate)
>>
>>         1.
>>
>>
>>          2. Minimal strategic burden
>>
>>
>>     We often hear it said that Approval has a large strategic burden,
>>     but, for most people, with our current candidate-lineup, there's
>>     nothing difficult about it: Approve (only) the progressive
>>     candidates. That's optimal for most people.
>>
>>     And if the time comes when, for most people, there isn't a
>>     bottom-set, then that will be a happy circumstance, in which it
>>     doesn't matter terribly anyway, which candidate wins.
>>
>>     In such conditions, with honest elections and honest, open media,
>>     it will likely be pretty obvious who's the CWs, and, in the
>>     absence of tep-set/bottom-set, the best strategy will be to just
>>     approve down to the CWs.
>>
>>     And, if there were no bottom-set, and if it happened that it
>>     _wasn't_ clear who the CWs was, and it was 0-info, then it would
>>     just be a matter of approving down to the expected winning
>>     merit-level. Maybe, under those conditions, that would be the
>>     candidate-mean.  Or maybe (as now)  the estimated mean merit of
>>     what voters want (which can be estimated by the candidates'
>>     merit-midrange, if the election is 1D.  ....but it might not
>>     remain 1D under different and better conditions).
>>
>>     ..but I repeat that, with only your former top-set remaining as
>>     winnable candidates, it won't make as much difference which one
>>     wins anyway.
>>
>>     People often consider Approval voting more difficult than it is.
>>
>>
>>          1. Summable (ideally O(N), no worse than O(N²) in practice,
>>             though I might accept some special pleading for the use
>>             of prior polling to reduce to O(N²).)
>>          2. Handles CD, or at least, CD offensive strategies don't in
>>             practice mess up the center squeeze properties.
>>
>>
>>     MMPO meets Weak CD.
>>
>>         1.
>>
>>
>>          2. Some arguable track record
>>
>>
>>     Of course at EM we discuss two completely separate and different
>>     method proposal choices:
>>
>>     1. Proposals to electorates who have only had Plurality.
>>
>>     2. Later proposals to replace one better voting system with another.
>>
>>     If we're talking about #1, then there are only a few to choose from:
>>
>>     Approval, Score, and Bucklin.
>>
>>
>>     I suggest that all 3 of those should be offered to
>>     initiative-proposal committees, and that the public should be
>>     polled, or consulted in "focus-groups", regarding which of those
>>     3 methods they'd  accept
>>
>>
>>     For #2, it really takes something with a lot of valuable &
>>     otherwise-unobtainable properties, to justify replacing Approval,
>>     Score or Bucklin with it.
>>
>>     I suggest that only Plain MMPO qualifies.
>>
>>
>>
>>         1.
>>
>>
>>
>>
>>          Approval does well on 1,3,4, and 6, is OK on 2, and bad on 4
>>         and 5.
>>
>>
>>
>>     No. Contrary to what we so often hear, Approval doesn't have a
>>     high strategic burden, as I discussed above.
>>
>>     Other than MMPO's CD, improvements over Approval by more
>>     complicated methods are illusory.
>>
>>     And your standard #5 was summability and count-complexity.
>>     Approval is precinct-summable, and its count is the easiest and
>>     least computation-intensive, among voting-systems.
>>
>>     Michael Ossipoff
>>
>>
>>
>>
>>
>>
>
>
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