[EM] A few more Bucklin variants, because why not?
Chris Benham
cbenhamau at yahoo.com.au
Fri Oct 18 05:43:58 PDT 2024
Etjon,
Your Iterated Bucklin method appeals to me more than normal Bucklin.
You have gotten rid of at least some of the Irrelevant Ballots problem.
In my first example below, deleting the 2X ballots changes the Bucklin
winner from B to A.
But among methods that interpret not-truncated as approval, I don't see
it as a serious contender. I much prefer Margins-Sorted Approval and
Smith//Approval and Condorcet//Approval. Also close to being in that
category is Smith//Descending Acquiescing Coalitions.
Chris B.
On 18/10/2024 3:36 pm, Etjon Basha wrote:
>
> Hi Chris,
>
> Thank you for your feedback.
>
> On the LNHa failure on the margin scenario (absolute margins was what
> I was thinking indeed), A should win.
>
>
> Now, I put somewhat less weight on LHNa since we’re operating in the
> “truncation allowed” paradigm, and all candidates explicitly ranked
> are candidates explicitly endorsed. I would be halfway OK with my
> favorite losing to my second favorite in this case. In this case,
> those A voters who gave B the win are hopefully seeing B as the one
> most likely to win, and although they prefer A, they would think A has
> far fewer chances to win. If they had a proper indication of the
> relative support of the two, they would hopefully not have ranked B.
>
>
> Of course, this means that the method is on par with Approval in this
> case, defeating the point of ranking in the first place. But in
> practice, I hope it wouldn’t fail LNHa as often as approval (and
> require less strategising of the voter), though it may well fail it
> more often the Iterated Bucklin or the other versions electing from
> the SCS. I think it elects Condorcet more often than all of them though.
>
>
> Point taken on clones too, about whom I didn’t even think about. These
> defeat the whole point of the universal cutoff underpinning the whole
> set, a pretty serious failure indeed.
>
>
> Somewhat interestingly, my original favorite – electing the candidate
> who wins by the least votes – produces A or Y in both cases, but the
> method elects the Condorcet loser (B) in 3A, 6BC, 4C, 5ACB, a very
> serious failure as well. I suppose then between clones and the CL,
> none of these appear to be much better than Iterated Bucklin at least.
>
> Regards,
>
> Etjon
>
>
> On Fri, Oct 18, 2024 at 2:48 PM Chris Benham <cbenhamau at yahoo.com.au>
> wrote:
>
> Etjon,
>
>> 3. Electing the Serious Candidate that wins their cutoff count by
>> the most approvals *compared to the runner up*. May fail Condorcet the
>> least. Likely the most sensible of the bunch.
> Does "compared to the runner up" refer to the absolute margin or
> the relative margin? In other words, are we talking about the
> margin by the greatest number or the greatest percentage or ratio?
>
> Here is my example (from my 2 November 2024 EM post) designed to
> highlight the disadvantages of Bucklin compared with Hare:
>
> 40 A>B
> 30 B
> 09 C
> 02 X
>
> 81 ballots
>
> Here your "Serious Candidate" set is A,B and your "likely most sensible" method 3 elects B (70-40 versus 40-30), but I find it absurd and unacceptable to not elect A.
>
> A is a "Dominant Candidate", the number of ballots on which A is voted above all other candidates is greater than A's maximum pairwise opposition.
>
> It seems that your Iterated Bucklin method elects A here.
>
> https://electowiki.org/wiki/Iterated_Bucklin
>
>> 5. Electing the Serious Candidate that wins the election if the
>> cutoff is set at the FPP winner.
>
>
> This would elect A here but (like FPP) fails Clone-Winner.
>
> 29 A>Y>B
> 11 Y>A>B
> 30 B
> 09 C
> 02 X
>
> Y is clone of A. Adding this candidate changes the winner from A to B. (Iterated Bucklin still elects A.)
>
> Chris B.
>
>
>
> *Etjon Basha*etjonbasha at gmail.com
> <mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20A%20few%20more%20Bucklin%20variants%2C%20because%20why%20not%3F&In-Reply-To=%3CCA%2BEJN6Qj5tsq3%2BR6B_5YLDRA%3DzfRu0DOgMwBXJy7N0RA0Z0RYQ%40mail.gmail.com%3E>
>
> /Sat Sep 21 04:53:21 PDT 2024/
>
> *
>
>
> ------------------------------------------------------------------------
>
> Dear gentlemen,
>
>
> A while ago I did write here about the Iterated Bucklin
> <https://electowiki.org/wiki/Iterated_Bucklin> method on which I’ve
> recently had a chance to think and generalize about a bit more. Maybe some
> of the below could be novel or otherwise of interest.
>
>
> First, and for our purposes today, let's define the *Serious Candidates Set*
> in the context of a ranked ballot, to include those candidates who would
> win an approval count if they served as the approval cutoff across all
> ballots.
>
>
> In the [2:A>B, 3:C>A, 4:A>B] election as an example, the Set would include
> A and B only, as applying the cutoff at C would still elect B.
>
>
> I’ve been checking some random simulations from Kevin Venzke’s
> votingmethods.net <http://votingmethods.net>, and here are some properties of this Set that I
> *suspect*:
>
> 1. If there is a Condorcet Winner, this Set should always include
> them.
>
> 2. Otherwise, this Set should always partially overlap with the
> Smith Set.
>
> Now, quite a few methods emerge once the Serious Candidate Set is isolated
> (by actually checking the approval winner once every candidate is used as a
> cutoff). The five below allow truncation and equal ranking, and have been
> checked (again courtesy ofvotingmethods.net <http://votingmethods.net>) to ensure that they are
> different from one-another and the 40-odd other methods Kevin has
> aggregated over there.
>
>
> So, which member of the Serious Candidate Set should be elected?
>
> 1. Electing the Serious Candidate that wins their cutoff count by
> the most approvals. Rather obvious but not too much of an improvement over
> Approval (if any at all). Terrible Later No Harm failures, though this is
> in the context where truncation is allowed. Fails Condorcet.
>
> 2. Electing the Serious Candidate that wins their cutoff count by
> the *least* approvals. A bit counterintuitive, but winning by the least
> means that the winner had to “dip” the least into each approver’s rankings.
> If this is not compliant with Later No Harm, it should at least fail
> rarely. It would fail Later No Help spectacularly though, indeed having a
> huge incentive to always rank your least favorite candidate that is still
> likely to win last, instead of leaving them unranked. Unfortunately, I’ve
> seen it elect the Condorcet Loser at least once.
>
> 3. Electing the Serious Candidate that wins their cutoff count by
> the most approvals *compared to the runner up*. May fail Condorcet the
> least. Likely the most sensible of the bunch.
>
> 4. Iterated Bucklin (now fitting into this generalised family) will
> always elect a member of the Set, but it seems to be neither of the three
> above with consistency. I cannot seem to find the pattern the method lands
> on.
>
> 5. Electing the Serious Candidate that wins the election if the
> cutoff is set at the FPP winner. If the FPP winner is in the Set to begin
> with, they will be elected. Otherwise, again a method that elects a winner
> from the set through no obvious pattern. Of particular interest to me since
> it’s the only method in here that can be hand-counted with relative ease
> (it’s just an FPP count and an approval count after that).
>
> For reference, standard Bucklin may not always elect members of the Set so
> cannot be retconned into this tree. I've tested quite a few other methods,
> and there are some for which I'm still to find a failure to elect from the
> Serious Candidates Set, including Borda and, unsurprisingly, many approval
> variations and Approval-Condorcet hybrids.
>
> Just some preliminary thoughts above, hopefully of some interest.
>
>
> Best regards,
>
> Etjon Basha
>
>
> ----
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