[EM] Losing Votes (equal-ranking whole)
Chris Benham
cbenhamau at yahoo.com.au
Sun May 26 10:08:19 PDT 2019
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> 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
>
>
>
>
>
>
>
>
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