[EM] Losing Votes (equal-ranking whole)
C.Benham
cbenham at adam.com.au
Sat Jun 1 05:46:26 PDT 2019
Jim,
Yes.
Chris Benham
On 1/06/2019 9:45 pm, Faran, James wrote:
> 51 A>B>C>D
> 49 B>C>D>A
>
> Is A a better choice than B?
>
> 1. Yes. Plurality demands it. Moreover, B beats C and D on all
> ballots, so C and D can be ignored and the pairwise race is all that's
> left.
>
> 2. No. A is ranked bottom on 49% of ballots, B ranked at least second
> on 100%, top on almost half.
>
> Are C and D Irrelevant Alternatives?
>
> Jim Faran
>
> On Jun 1, 2019 5:28 AM, "C.Benham" <cbenham at adam.com.au> wrote:
>
> Toby,
>
> I didn't coin the Plurality criterion, and I do somewhat prefer your
> suggested alternative wording. To take account of equal-top ranking being
> allowed, I would specify the fractional interpretation of "number of
> ballots ranking A as the first preference". The original coiner of
> the criterion
> was operating on the assumption that no equal-ranking would be
> allowed (except at the bottom implied by truncation which would be
> allowed)
> and perhaps also that no-one would needlessly mark a candidate
> strictly bottom when they could just truncate.
>
> I think in part the criterion is tailor-made for voters accustomed to
> and content with plurality voting, and after some new election on ballots
> that allow voters to rank the candidates is used, they want to know
> why B won while their favourite candidate A was voted (alone) in first
> place
> on more ballots than B was voted above bottom. And I like the
> criterion because I agree that there can't be a good enough answer.
>
> A standard (and possible criterion) I like says that if A both
> positionally dominates and pairwise beats B then B can't win. That
> implies Plurality.
>
> 35: A
> 10: A=B
> 30: B>C
> 25: C
>
> Here no ballots vote A or B below equal-top. A has more top (or first)
> place votes than B so positionally dominates and pairwise beats B.
> Do you think B is an acceptable winner?
>
> Chris Benham
>
>
>
> On 29/05/2019 10:37 pm, Toby Pereira wrote:
>> I don't have a definite answer to the question of equally ranked
>> ballots, and to me I suppose it's still an open question exactly what
>> the best way forwards is, even if you make a good argument against
>> margins.
>>
>> I don't have an example where the plurality criterion bars from
>> winning the candidate that I think should have won. Looking at the
>> definition on the Wikipedia: "If the number of ballots ranking A as
>> the first preference is greater than the number of ballots on which
>> another candidate B is given any preference, then A's probability of
>> winning must be no less than B's.", it's more that I would disagree
>> with the terminology "given any preference."
>>
>> If the definition was "If the number of ballots ranking A as the
>> first preference is greater than the number of ballots on which
>> another candidate B is ranked anything other than last or joint last
>> (either explicitly or through implication on a truncated ballot),
>> then A's probability of winning must be no less than B's." then I'd
>> be less critical of it. I think the way it's worded implies an
>> approval cut-off even if in practice it makes no difference.
>>
>> Toby
>>
>>
>> ------------------------------------------------------------------------
>> *From:* C.Benham <cbenham at adam.com.au>
>> *To:* Toby Pereira <tdp201b at yahoo.co.uk>; "cbenham at adam.com.au"
>> <cbenham at adam.com.au>; "election-methods at lists.electorama.com"
>> <election-methods at lists.electorama.com>
>> *Sent:* Sunday, 26 May 2019, 20:19
>> *Subject:* Re: [EM] Losing Votes (equal-ranking whole)
>>
>> Toby,
>>
>> If you try to give that calculator a truncated ballot it will just
>> turn it into the sort of ballot you like.
>>
>> How do you think equally-ranked ballots should be counted in a
>> pairwise comparison? A half-vote to
>> each or zero to both?
>>
>> So you can't actually point to any election example where the
>> Plurality criterion bars from winning the candidate
>> that you think should have won?
>> 46: A
>> 44: B>C
>> 10: C
>> Returning to this, are you happy with B winning? And if not, why not?
>>
>> Chris Benham
>>
>> On 27/05/2019 3:38 am, Toby Pereira wrote:
>> By unranked candidates, I meant the ones that had not had any sort of
>> "vote" - the ones not explicitly listed by the voter. If there are
>> three candidates in an election, A, B, and C, I might like A but
>> absolutely hate the others. My vote might simply be:
>>
>> A
>>
>> On the other hand, while I might still absolutely hate B and C, I
>> might still hate C more. So my vote might be:
>>
>> A>B
>>
>> But just because I have ranked B on my ballot, this should not be
>> taken as any sort of endorsement of B or a vote "for" B.
>>
>> My vote could also be:
>>
>> A>B>C
>>
>> Does adding C on the end mean that I have in some sense voted for C?
>> I don't think there would actually be any methods where adding C on
>> the end would have any effect on how the winner is calculated, but
>> the plurality criterion would presumably in theory find it acceptable
>> to do so.
>>
>> But this is more a philosophical objection to the assumptions
>> implicit in the plurality criterion than an an objection to the
>> results that a method obeying the criterion would produce in
>> practice. But anyway, I put my thoughts about the plurality criterion
>> a while ago (as did Juho) here:
>> http://election-methods.5485.n7.nabble.com/EM-Fwd-Ordering-defeats-in-Minimax-td34236.html#a34247
>>
>> But anyway, thank you for the link to the calculator.
>>
>> Toby
>>
>>
>>
>>
>> ------------------------------------------------------------------------
>> *From:* Chris Benham <cbenhamau at yahoo.com.au>
>> <mailto:cbenhamau at yahoo.com.au>
>> *To:* "tdp201b at yahoo.co.uk" <mailto:tdp201b at yahoo.co.uk>
>> <tdp201b at yahoo.co.uk> <mailto:tdp201b at yahoo.co.uk>;
>> "cbenham at adam.com.au" <mailto:cbenham at adam.com.au>
>> <cbenham at adam.com.au> <mailto:cbenham at adam.com.au>;
>> "election-methods at lists.electorama.com"
>> <mailto:election-methods at lists.electorama.com>
>> <election-methods at lists.electorama.com>
>> <mailto:election-methods at lists.electorama.com>
>> *Sent:* Sunday, 26 May 2019, 18:08
>> *Subject:* Re: [EM] Losing Votes (equal-ranking whole)
>>
>> Toby,
>>
>> You would like this old online ranked-ballot voting calculator:
>>
>> https://www.cse.wustl.edu/~legrand/rbvote/calc.html
>>
>> What do you think are the "false premises" that the Plurality
>> criterion is based on??? It was coined with the assumption
>> that voters could only strictly rank from the top however many
>> candidates they wish, and those not truncated had in
>> some sense been "voted for". It says that if A has more first-place
>> votes than B has any sort of votes then B can't win.
>> No explicit mention of "unranked candidates".
>>
>> (Adapting it to ballots that allow equal-ranking at the top,?? "first
>> preferences" refers to first-preference score on the
>> ballots symmetrically completed, at least at the top, ballots).
>> To sensibly claim that it is a "mistake" for an algorithm to do (or
>> apparently "assume") something, I think you need to
>> point to something wrong with an actual result of it doing so.
>>
>> My answer to your question is no.
>> Chris Benham
>>
>>
>> On 27/05/2019 1:04 am, Toby Pereira wrote:
>> I think it's a mistake to assume some sort of approval of a ranked
>> candidate. If it's not explicitly part of a method then you should
>> not infer it. As far as I'm concerned:
>>
>> 46: A
>> 44: B>C
>> 10: C
>>
>> Is the same as:
>>
>> 46: A>B=C
>> 44: B>C>A
>> 10: C>A=B
>>
>> Presented with these ballots, does this change who you think the
>> winner should be?
>>
>> This isn't a defence of margins by me or an argument against anything
>> else in your post, but I think the plurality criterion, by talking
>> about unranked candidates, is based on false premises.
>>
>> Toby
>>
>> On Sat, 25 May 2019 at 15:31, C.Benham
>> <cbenham at adam.com.au> <mailto:cbenham at adam.com.au> wrote:
>> There are several Condorcet algorithms that decide the winner by
>> weighing "defeat strengths" and they
>> are all equivalent to MinMax when there are no more than 3
>> candidates.
>>
>> The ones I have in mind that are equal or very nearly equal in
>> merit are
>> River, Schulze, Ranked Pairs, Smith//MinMax.
>> In public political elections they are very very unlikely to give
>> different winners. River and Smith//MinMax seem to me
>> to be the easiest to understand and explain and use. The other
>> two are
>> perhaps a bit more elegant and have their
>> enthusiastic supporters.
>>
>> This is to make the case that measuring pairwise defeat strength
>> by the
>> number of votes on the losing side with above-bottom
>> equal-ranking contributing a whole vote to each side (and
>> otherwise as
>> with normal Winning Votes) is much better than either
>> Winning Votes or Margins.
>>
>> The case for Losing Votes(erw) against Margins is that it (in common
>> with WV) it meets the Plurality criterion and the Non-Drastic
>> Defense criterion.
>>
>> The case for Losing Votes(erw) against Winning Votes is that it
>> meets
>> the Chicken Dilemma criterion and that is much less likely
>> to fail to elect a positionally dominant uncovered candidate. (I
>> don't
>> see how it can fail to elect such a candidate in the 3-candidate
>> case.)
>>
>> For those who think that Margins might be acceptable:
>>
>> 46: A
>> 44: B>C
>> 10: C
>>
>> A>B 46-44 (margin=2), B>C 44-10 (margin=34), C>A 54-46 (margin=8).
>>
>> Using Losing Votes (erw) as the measure of defeat strength, the
>> weakest
>> defeat is the one with the most votes on the losing side.
>> That is the C>A defeat so MinMax drops that and A wins.
>> Conversely the
>> strongest defeat is the one with the fewest votes on the
>> losing side. That is the B>C defeat so River and Ranked Pairs lock
>> that. The second strongest is the A>B defeat so those methods
>> also lock that. All but one candidate has been thereby
>> disqualified so B
>> wins, or we ignore the third pairwise defeat because that
>> makes a cycle, so give a final order A>B>C and A wins.
>>
>> To meet both of the Plurality criterion and the Chicken Dilemma
>> criterion A must win.
>>
>> Winning Votes elects C, violating Chicken Dilemma (which it has
>> to do to
>> meet the previously fashionable Minimal Defense criterion).
>>
>> Margins elects B. This fails the Plurality criterion because A
>> has more
>> exclusive first-place votes than B has any sort of above-bottom
>> votes. It is also an egregious and outrageous failure of
>> Later-no-Help
>> (assuming that if all the ballots just vote for one candidate we
>> elect the plurality winner).
>>
>> To anyone who is remotely positionally or strategically minded or
>> has
>> any common sense and isn't blind to everything except the
>> Margins pairwise matrix, B is clearly the weakest candidate and a
>> completely unacceptable winner.
>>
>> 35: A
>> 10: A=B
>> 30: B>C
>> 25: C
>>
>> A>B 45-40 (erw, "normally" 35-30, margin=5), B>C 40-25 (margin=15),
>> C>A 55-45 (margin=10).
>>
>> Voted at least equal-top (or Top Ratings) scores: A45, B40, C25.
>> Voted above bottom (or Approval) scores: A45, B40, C55
>>
>> An old Kevin Venzke example. B is neither the most top-rated
>> candidate
>> or the most approved candidate and is
>> pairwise-beaten and positionally dominated by A (the most top-rated).
>>
>> Winning Votes and Margins both elect the clearly weakest
>> candidate, B.
>> Losing Votes(erw) elects A.
>>
>> For those who prefer to have a method comply with Minimal Defense
>> (which
>> says that if on more than half the ballots
>> C is voted above A and A no higher than equal-bottom then A can't
>> win)
>> rather than Chicken Dilemma another method
>> I prefer to WV is Smith//Approval which here elects C.
>>
>> 25: A>B
>> 26: B>C
>> 23: C>A
>> 26: C
>>
>> C>A 75-25 (margin=50), A>B 48-26 (margin=22), B>C 51-49 (margin=2).
>>
>> Voted at least equal-top (or Top Ratings) scores: C49, B26, A25.
>> Voted above bottom (or Approval) scores: C75, B51, A48.
>>
>> C is an overwhelmingly positionally dominant uncovered candidate.
>> Margins and Losing Votes elect C.
>> WV and IRV elect B.
>>
>> Now say we change 4 of the 26 C ballots to A>C, thereby making C
>> a bit
>> weaker.
>>
>> 25: A>B
>> 26: B>C
>> 23: C>A
>> 22: C
>> 04: A>C
>>
>> C>A 71-29 (margin=42), A>B 52-26 (margin=26), B>C 51-49 (margin=2).
>>
>> Voted at least equal-top (or Top Ratings) scores: C45, B26, A29.
>> Voted above bottom (or Approval) scores: C75, B51, A52.
>>
>>
>> The weakening of C has caused WV and IRV to change from B to C, now
>> agreeing with LV and Margins.
>> Assuming the change was from sincere to insincere, those very lucky
>> and/or very well informed 4 voters
>> have pulled off a Push-over strategy.
>>
>> This is a failure of Mono-raise-delete (more obvious if we
>> reverse the
>> order of the two situations), which
>> is one of Woodall's mononicity criteria that he says is incompatible
>> with Condorcet.
>>
>> Nonetheless in this case C is still the positionally dominant
>> uncovered
>> candidate and Losing Votes (erw)
>> and Margins both still elect C.
>>
>> Steve Eppley's old example to illustrate (I think his) Non-Drastic
>> Defense criterion, which says that if
>> on more than half the ballots B is voted no lower than equal-top and
>> above A then A can't win.
>>
>> 46: A>C (sincere may be A>B)
>> 10: B>A
>> 10: B>C
>> 34: C=B (the "defenders", sincere may be C>B)
>>
>> B>A 54-46 (m=8), A>C 56-44 (m=12), C>B (80-54 erw, "normally"
>> 46-20, m=26).
>>
>> Voted at least equal-top (or Top Ratings) scores: B54, A46, C34.
>> Voted above bottom (or Approval) scores: B54, A56, C90.
>>
>> B is the only candidate top-rated on more than half the ballots.
>> More
>> than half the voters voted B
>> above A and B not lower than equal-top. Margins and Losing Votes
>> without my recommended
>> "above-bottom equal-ranking whole" bit elect A, violating the
>> Non-Drastic Defense criterion.
>>
>> Losing Votes (erw) and WV elect B.
>>
>> If anyone has some counter-examples where they think that Winning
>> Votes
>> does better than
>> Losing Votes (erw), I'd be interested in seeing them.
>>
>> Chris Benham
>>
>>
>>
>>
>>
>>
>>
>>
>>
>> ----
>> Election-Methods mailing list - see https://electorama.com/em
>> <https://electorama.com/em>for list info
>>
>>
>> <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient>
>> Virus-free. www.avg.com
>> <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient>
>>
>>
>>
>>
>>
>>
---
This email has been checked for viruses by AVG.
https://www.avg.com
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20190601/8c159ac1/attachment-0001.html>
More information about the Election-Methods
mailing list