[EM] Losing Votes (equal-ranking whole)

Wed May 29 06:07:55 PDT 2019

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>
 To: "tdp201b at yahoo.co.uk" <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, 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> 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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