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Technical discussion of election methods

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Poll, preliminary ballots

KM
Kristofer Munsterhjelm
Mon, May 13, 2024 3:18 PM

On 2024-05-01 17:19, fdpk69p6uq@snkmail.com wrote:

OK, here is my ballot:

  1. STAR
  2. Smith//Score
  3. Condorcet methods (Baldwin, Benham, Black, Copeland//Borda, Gross
    Loser Elimination, MinMax(wv), RP(wv), Schulze, Schwartz-Woodall,
    Smith//Approval (explicit & implicit), Smith//DAC, Woodall)
  4. Approval with manual runoff
  5. Approval
  6. ---- Approval cutoff ----
  7. RCIPE
  8. Double Defeat, Hare
  9. Majority Judgement
  10. IRV
  11. Plurality

(If I made a mistake in the Condorcet line, let me know.)

Margins-Sorted Approval,  Margins-Sorted Minimum Losing Votes, and Max
Strength Transitive Beatpath are also Condorcet methods. Are you ranking
them third as well?

-km

On 2024-05-01 17:19, fdpk69p6uq@snkmail.com wrote: > OK, here is my ballot: > > 1. STAR > 2. Smith//Score > 3. Condorcet methods (Baldwin, Benham, Black, Copeland//Borda, Gross > Loser Elimination, MinMax(wv), RP(wv), Schulze, Schwartz-Woodall, > Smith//Approval (explicit & implicit), Smith//DAC, Woodall) > 4. Approval with manual runoff > 5. Approval > 6. ---- Approval cutoff ---- > 7. RCIPE > 8. Double Defeat, Hare > 9. Majority Judgement > 10. IRV > 11. Plurality > > > (If I made a mistake in the Condorcet line, let me know.) Margins-Sorted Approval, Margins-Sorted Minimum Losing Votes, and Max Strength Transitive Beatpath are also Condorcet methods. Are you ranking them third as well? -km
CL
Closed Limelike Curves
Mon, May 13, 2024 9:30 PM
  1. STAR
  2. Smith//Score
  3. Score
  4. Highest medians
  5. Approval, anything else that's cardinal
  6. Approval with runoff
    ---- Approval cutoff ----
  7. Ranked Pairs
  8. Schulze
  9. Any Smith-efficients that satisfy weak defensive strategy criterion
    ---- Second, bigger approval cutoff* ----
  10. Any other Smith-efficients
  11. Any non-Smith Condorcet methods
  12. RCIPE
  13. IRV
  14. Plurality

*I don't like approval cutoffs. I need at least 3-4 bins. The first one is
what I'd do if I wanted to provide the most information, the latter is
"what I'd actually accept". Use the first one, I guess.

On Mon, May 13, 2024 at 8:26 AM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:

On 2024-05-01 17:19, fdpk69p6uq@snkmail.com wrote:

OK, here is my ballot:

  1. STAR
  2. Smith//Score
  3. Condorcet methods (Baldwin, Benham, Black, Copeland//Borda, Gross
    Loser Elimination, MinMax(wv), RP(wv), Schulze, Schwartz-Woodall,
    Smith//Approval (explicit & implicit), Smith//DAC, Woodall)
  4. Approval with manual runoff
  5. Approval
  6. ---- Approval cutoff ----
  7. RCIPE
  8. Double Defeat, Hare
  9. Majority Judgement
  10. IRV
  11. Plurality

(If I made a mistake in the Condorcet line, let me know.)

Margins-Sorted Approval,  Margins-Sorted Minimum Losing Votes, and Max
Strength Transitive Beatpath are also Condorcet methods. Are you ranking
them third as well?

-km

Election-Methods mailing list - see https://electorama.com/em for list
info

1. STAR 2. Smith//Score 3. Score 4. Highest medians 5. Approval, anything else that's cardinal 6. Approval with runoff ---- Approval cutoff ---- 7. Ranked Pairs 8. Schulze 9. Any Smith-efficients that satisfy weak defensive strategy criterion ---- Second, bigger approval cutoff* ---- 10. Any other Smith-efficients 11. Any non-Smith Condorcet methods 12. RCIPE 13. IRV 14. Plurality *I don't like approval cutoffs. I need at least 3-4 bins. The first one is what I'd do if I wanted to provide the most information, the latter is "what I'd actually accept". Use the first one, I guess. On Mon, May 13, 2024 at 8:26 AM Kristofer Munsterhjelm <km_elmet@t-online.de> wrote: > On 2024-05-01 17:19, fdpk69p6uq@snkmail.com wrote: > > OK, here is my ballot: > > > > 1. STAR > > 2. Smith//Score > > 3. Condorcet methods (Baldwin, Benham, Black, Copeland//Borda, Gross > > Loser Elimination, MinMax(wv), RP(wv), Schulze, Schwartz-Woodall, > > Smith//Approval (explicit & implicit), Smith//DAC, Woodall) > > 4. Approval with manual runoff > > 5. Approval > > 6. ---- Approval cutoff ---- > > 7. RCIPE > > 8. Double Defeat, Hare > > 9. Majority Judgement > > 10. IRV > > 11. Plurality > > > > > > (If I made a mistake in the Condorcet line, let me know.) > > Margins-Sorted Approval, Margins-Sorted Minimum Losing Votes, and Max > Strength Transitive Beatpath are also Condorcet methods. Are you ranking > them third as well? > > -km > ---- > Election-Methods mailing list - see https://electorama.com/em for list > info >
KM
Kristofer Munsterhjelm
Tue, May 14, 2024 3:03 PM

On 2024-05-13 23:30, Closed Limelike Curves wrote:

  1. STAR
  2. Smith//Score
  3. Score
  4. Highest medians
  5. Approval, anything else that's cardinal
  6. Approval with runoff
    ---- Approval cutoff ----
  7. Ranked Pairs
  8. Schulze
  9. Any Smith-efficients that satisfy weak defensive strategy criterion
    ---- Second, bigger approval cutoff* ----
  10. Any other Smith-efficients
  11. Any non-Smith Condorcet methods
  12. RCIPE
  13. IRV
  14. Plurality

Are you counting cardinal hybrids (Smith//Approval, Approval Sorted
Margins, Double Defeat Hare) as being part of the "anything else that's
cardinal" category? I would imagine so, but I want to be sure.

As for WSDC compliance, I'm not all that sure which methods pass, so
I'll ask the other members if they could let me know which of the
methods pass WDSC. If nobody answers, do you want to just equal-rank all
Smith methods equal, specify a more detailed ranking yourself, or
something else?

*I don't like approval cutoffs. I need at least 3-4 bins. The first one
is what I'd do if I wanted to provide the most information, the latter
is "what I'd actually accept". Use the first one, I guess.

Them's the breaks when it comes to Approval. But got it, I'll count
what's above the first cutoff.

-km

On 2024-05-13 23:30, Closed Limelike Curves wrote: > 1. STAR > 2. Smith//Score > 3. Score > 4. Highest medians > 5. Approval, anything else that's cardinal > 6. Approval with runoff > ---- Approval cutoff ---- > 7. Ranked Pairs > 8. Schulze > 9. Any Smith-efficients that satisfy weak defensive strategy criterion > ---- Second, bigger approval cutoff* ---- > 10. Any other Smith-efficients > 11. Any non-Smith Condorcet methods > 12. RCIPE > 13. IRV > 14. Plurality Are you counting cardinal hybrids (Smith//Approval, Approval Sorted Margins, Double Defeat Hare) as being part of the "anything else that's cardinal" category? I would imagine so, but I want to be sure. As for WSDC compliance, I'm not all that sure which methods pass, so I'll ask the other members if they could let me know which of the methods pass WDSC. If nobody answers, do you want to just equal-rank all Smith methods equal, specify a more detailed ranking yourself, or something else? > *I don't like approval cutoffs. I need at least 3-4 bins. The first one > is what I'd do if I wanted to provide the most information, the latter > is "what I'd actually accept". Use the first one, I guess. Them's the breaks when it comes to Approval. But got it, I'll count what's above the first cutoff. -km
CL
Closed Limelike Curves
Tue, May 14, 2024 3:13 PM

Yep, cardinal-Condorcet is included.

On Tue, May 14, 2024 at 8:10 AM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:

On 2024-05-13 23:30, Closed Limelike Curves wrote:

  1. STAR
  2. Smith//Score
  3. Score
  4. Highest medians
  5. Approval, anything else that's cardinal
  6. Approval with runoff
    ---- Approval cutoff ----
  7. Ranked Pairs
  8. Schulze
  9. Any Smith-efficients that satisfy weak defensive strategy criterion
    ---- Second, bigger approval cutoff* ----
  10. Any other Smith-efficients
  11. Any non-Smith Condorcet methods
  12. RCIPE
  13. IRV
  14. Plurality

Are you counting cardinal hybrids (Smith//Approval, Approval Sorted
Margins, Double Defeat Hare) as being part of the "anything else that's
cardinal" category? I would imagine so, but I want to be sure.

As for WSDC compliance, I'm not all that sure which methods pass, so
I'll ask the other members if they could let me know which of the
methods pass WDSC. If nobody answers, do you want to just equal-rank all
Smith methods equal, specify a more detailed ranking yourself, or
something else?

*I don't like approval cutoffs. I need at least 3-4 bins. The first one
is what I'd do if I wanted to provide the most information, the latter
is "what I'd actually accept". Use the first one, I guess.

Them's the breaks when it comes to Approval. But got it, I'll count
what's above the first cutoff.

-km

Election-Methods mailing list - see https://electorama.com/em for list
info

Yep, cardinal-Condorcet is included. On Tue, May 14, 2024 at 8:10 AM Kristofer Munsterhjelm <km_elmet@t-online.de> wrote: > On 2024-05-13 23:30, Closed Limelike Curves wrote: > > 1. STAR > > 2. Smith//Score > > 3. Score > > 4. Highest medians > > 5. Approval, anything else that's cardinal > > 6. Approval with runoff > > ---- Approval cutoff ---- > > 7. Ranked Pairs > > 8. Schulze > > 9. Any Smith-efficients that satisfy weak defensive strategy criterion > > ---- Second, bigger approval cutoff* ---- > > 10. Any other Smith-efficients > > 11. Any non-Smith Condorcet methods > > 12. RCIPE > > 13. IRV > > 14. Plurality > > Are you counting cardinal hybrids (Smith//Approval, Approval Sorted > Margins, Double Defeat Hare) as being part of the "anything else that's > cardinal" category? I would imagine so, but I want to be sure. > > As for WSDC compliance, I'm not all that sure which methods pass, so > I'll ask the other members if they could let me know which of the > methods pass WDSC. If nobody answers, do you want to just equal-rank all > Smith methods equal, specify a more detailed ranking yourself, or > something else? > > > *I don't like approval cutoffs. I need at least 3-4 bins. The first one > > is what I'd do if I wanted to provide the most information, the latter > > is "what I'd actually accept". Use the first one, I guess. > > Them's the breaks when it comes to Approval. But got it, I'll count > what's above the first cutoff. > > -km > ---- > Election-Methods mailing list - see https://electorama.com/em for list > info >
KM
Kristofer Munsterhjelm
Tue, May 14, 2024 4:56 PM

On 2024-05-14 17:13, Closed Limelike Curves wrote:

Yep, cardinal-Condorcet is included.

What do you want to do if nobody responds as to what methods pass WDSC?
Provide your own updated ballot or just equal-rank all other Smith methods?

-km

On 2024-05-14 17:13, Closed Limelike Curves wrote: > Yep, cardinal-Condorcet is included. What do you want to do if nobody responds as to what methods pass WDSC? Provide your own updated ballot or just equal-rank all other Smith methods? -km
MO
Michael Ossipoff
Tue, May 14, 2024 5:55 PM

It seems to me that the Weak Defensive Strategy Criterion was a
generalization of FBC:

One should never get a worse result because they didn’t vote something they
like less over something they like more.

Strictly-speaking, Condorcet methods fail, but wv Condorcet doesn’t fail
importantly. Most other Condorcet methods fail badly, because they fail FBC
badly.

I don’t expect Benham to either, though wv is all that I’ve tested.

On Tue, May 14, 2024 at 09:56 Kristofer Munsterhjelm km_elmet@t-online.de
wrote:

On 2024-05-14 17:13, Closed Limelike Curves wrote:

Yep, cardinal-Condorcet is included.

What do you want to do if nobody responds as to what methods pass WDSC?
Provide your own updated ballot or just equal-rank all other Smith methods?

-km

Election-Methods mailing list - see https://electorama.com/em for list
info

It seems to me that the Weak Defensive Strategy Criterion was a generalization of FBC: One should never get a worse result because they didn’t vote something they like less over something they like more. Strictly-speaking, Condorcet methods fail, but wv Condorcet doesn’t fail importantly. Most other Condorcet methods fail badly, because they fail FBC badly. I don’t expect Benham to either, though wv is all that I’ve tested. On Tue, May 14, 2024 at 09:56 Kristofer Munsterhjelm <km_elmet@t-online.de> wrote: > On 2024-05-14 17:13, Closed Limelike Curves wrote: > > Yep, cardinal-Condorcet is included. > > What do you want to do if nobody responds as to what methods pass WDSC? > Provide your own updated ballot or just equal-rank all other Smith methods? > > -km > ---- > Election-Methods mailing list - see https://electorama.com/em for list > info >
KM
Kristofer Munsterhjelm
Tue, May 14, 2024 6:36 PM

On 2024-05-14 19:55, Michael Ossipoff wrote:

It seems to me that the Weak Defensive Strategy Criterion was a
generalization of FBC:

One should never get a worse result because they didn’t vote something
they like less over something they like more.

Strictly-speaking, Condorcet methods fail, but wv Condorcet doesn’t fail
importantly. Most other Condorcet methods fail badly, because they fail
FBC badly.

I don’t expect Benham to either, though wv is all that I’ve tested.

If a majority prefers one particular candidate to another, then they
should have a way of voting that will ensure that the other cannot win,
without any member of that majority reversing a preference for one
candidate over another.

which would indicate that the majority can bar a particular candidate
from winning by voting in some given way that does not involve order
reversal, only truncation.

If there's a sincere CW, then it's the same as your criterion, but if
not, then there may be one majority who prefers A to B and another that
prefers A to C, but no majority preferring A to both B and C. Then the
majority preferring A to B should have a way to stop B from winning...

I think? It's not my criterion.

-km

On 2024-05-14 19:55, Michael Ossipoff wrote: > It seems to me that the Weak Defensive Strategy Criterion was a > generalization of FBC: > > One should never get a worse result because they didn’t vote something > they like less over something they like more. > > Strictly-speaking, Condorcet methods fail, but wv Condorcet doesn’t fail > importantly. Most other Condorcet methods fail badly, because they fail > FBC badly. > > I don’t expect Benham to either, though wv is all that I’ve tested. https://electowiki.org/wiki/Weak_Defensive_Strategy_criterion says that Schulze passes. So does http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-April/102004.html. It also seems to define the criterion a bit differently: >> If a majority prefers one particular candidate to another, then they >> should have a way of voting that will ensure that the other cannot win, >> without any member of that majority reversing a preference for one >> candidate over another. which would indicate that the majority can bar a particular candidate from winning by voting in some given way that does not involve order reversal, only truncation. If there's a sincere CW, then it's the same as your criterion, but if not, then there may be one majority who prefers A to B and another that prefers A to C, but no majority preferring A to both B and C. Then the majority preferring A to B should have a way to stop B from winning... I think? It's not my criterion. -km
CL
Closed Limelike Curves
Tue, May 14, 2024 6:47 PM

which would indicate that the majority can bar a particular candidate
from winning by voting in some given way that does not involve order
reversal, only truncation.

Only exaggeration, more precisely—basically, you can elect the Condorcet
winner by voting approval-style and bunching up the candidates at the top
and bottom. (Possibly with some intermediate ranks for "unsure").

On Tue, May 14, 2024 at 11:36 AM Kristofer Munsterhjelm <
km_elmet@t-online.de> wrote:

On 2024-05-14 19:55, Michael Ossipoff wrote:

It seems to me that the Weak Defensive Strategy Criterion was a
generalization of FBC:

One should never get a worse result because they didn’t vote something
they like less over something they like more.

Strictly-speaking, Condorcet methods fail, but wv Condorcet doesn’t fail
importantly. Most other Condorcet methods fail badly, because they fail
FBC badly.

I don’t expect Benham to either, though wv is all that I’ve tested.

If a majority prefers one particular candidate to another, then they
should have a way of voting that will ensure that the other cannot win,
without any member of that majority reversing a preference for one
candidate over another.

which would indicate that the majority can bar a particular candidate
from winning by voting in some given way that does not involve order
reversal, only truncation.

If there's a sincere CW, then it's the same as your criterion, but if
not, then there may be one majority who prefers A to B and another that
prefers A to C, but no majority preferring A to both B and C. Then the
majority preferring A to B should have a way to stop B from winning...

I think? It's not my criterion.

-km

Election-Methods mailing list - see https://electorama.com/em for list
info

> > which would indicate that the majority can bar a particular candidate > from winning by voting in some given way that does not involve order > reversal, only truncation. > Only exaggeration, more precisely—basically, you can elect the Condorcet winner by voting approval-style and bunching up the candidates at the top and bottom. (Possibly with some intermediate ranks for "unsure"). On Tue, May 14, 2024 at 11:36 AM Kristofer Munsterhjelm < km_elmet@t-online.de> wrote: > On 2024-05-14 19:55, Michael Ossipoff wrote: > > It seems to me that the Weak Defensive Strategy Criterion was a > > generalization of FBC: > > > > One should never get a worse result because they didn’t vote something > > they like less over something they like more. > > > > Strictly-speaking, Condorcet methods fail, but wv Condorcet doesn’t fail > > importantly. Most other Condorcet methods fail badly, because they fail > > FBC badly. > > > > I don’t expect Benham to either, though wv is all that I’ve tested. > > https://electowiki.org/wiki/Weak_Defensive_Strategy_criterion says that > Schulze passes. > > So does > > http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-April/102004.html > . > > It also seems to define the criterion a bit differently: > > >> If a majority prefers one particular candidate to another, then they > >> should have a way of voting that will ensure that the other cannot win, > >> without any member of that majority reversing a preference for one > >> candidate over another. > > which would indicate that the majority can bar a particular candidate > from winning by voting in some given way that does not involve order > reversal, only truncation. > > If there's a sincere CW, then it's the same as your criterion, but if > not, then there may be one majority who prefers A to B and another that > prefers A to C, but no majority preferring A to both B and C. Then the > majority preferring A to B should have a way to stop B from winning... > > I think? It's not my criterion. > > -km > ---- > Election-Methods mailing list - see https://electorama.com/em for list > info >
MO
Michael Ossipoff
Tue, May 14, 2024 7:26 PM

Oh, okay, I just misremembered it. Approval passes it too.

It sounds similar to Minimal-Defense.

Maybe my mistaken version describes something useful too, but it’s harder
for rank-methods strictly pass.  ...but Approval passes.

It was a long time ago when we discussed those criteria before, & so I
can’t be sure of much about them.

On Tue, May 14, 2024 at 11:36 Kristofer Munsterhjelm km_elmet@t-online.de
wrote:

On 2024-05-14 19:55, Michael Ossipoff wrote:

It seems to me that the Weak Defensive Strategy Criterion was a
generalization of FBC:

One should never get a worse result because they didn’t vote something
they like less over something they like more.

Strictly-speaking, Condorcet methods fail, but wv Condorcet doesn’t fail
importantly. Most other Condorcet methods fail badly, because they fail
FBC badly.

I don’t expect Benham to either, though wv is all that I’ve tested.

If a majority prefers one particular candidate to another, then they
should have a way of voting that will ensure that the other cannot win,
without any member of that majority reversing a preference for one
candidate over another.

which would indicate that the majority can bar a particular candidate
from winning by voting in some given way that does not involve order
reversal, only truncation.

If there's a sincere CW, then it's the same as your criterion, but if
not, then there may be one majority who prefers A to B and another that
prefers A to C, but no majority preferring A to both B and C. Then the
majority preferring A to B should have a way to stop B from winning...

I think? It's not my criterion.

-km

Oh, okay, I just misremembered it. Approval passes it too. It sounds similar to Minimal-Defense. Maybe my mistaken version describes something useful too, but it’s harder for rank-methods strictly pass. ...but Approval passes. It was a long time ago when we discussed those criteria before, & so I can’t be sure of much about them. On Tue, May 14, 2024 at 11:36 Kristofer Munsterhjelm <km_elmet@t-online.de> wrote: > On 2024-05-14 19:55, Michael Ossipoff wrote: > > It seems to me that the Weak Defensive Strategy Criterion was a > > generalization of FBC: > > > > One should never get a worse result because they didn’t vote something > > they like less over something they like more. > > > > Strictly-speaking, Condorcet methods fail, but wv Condorcet doesn’t fail > > importantly. Most other Condorcet methods fail badly, because they fail > > FBC badly. > > > > I don’t expect Benham to either, though wv is all that I’ve tested. > > https://electowiki.org/wiki/Weak_Defensive_Strategy_criterion says that > Schulze passes. > > So does > > http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-April/102004.html > . > > It also seems to define the criterion a bit differently: > > >> If a majority prefers one particular candidate to another, then they > >> should have a way of voting that will ensure that the other cannot win, > >> without any member of that majority reversing a preference for one > >> candidate over another. > > which would indicate that the majority can bar a particular candidate > from winning by voting in some given way that does not involve order > reversal, only truncation. > > If there's a sincere CW, then it's the same as your criterion, but if > not, then there may be one majority who prefers A to B and another that > prefers A to C, but no majority preferring A to both B and C. Then the > majority preferring A to B should have a way to stop B from winning... > > I think? It's not my criterion. > > -km >
MO
Michael Ossipoff
Tue, May 14, 2024 7:43 PM

Okay, the WDSC definition that you posted shows its difference from
Minimal-Defense, which is met by wv Condorcet, but not by Approval. (…or by
most non-wv Condorcet.)

…& of course different from my guess about WDSC, which is met by Approval,
& effectively but not strictly by wv Condorcet. …& seriously failed by most
non-wv Condorcet.

On Tue, May 14, 2024 at 11:36 Kristofer Munsterhjelm km_elmet@t-online.de
wrote:

On 2024-05-14 19:55, Michael Ossipoff wrote:

It seems to me that the Weak Defensive Strategy Criterion was a
generalization of FBC:

One should never get a worse result because they didn’t vote something
they like less over something they like more.

Strictly-speaking, Condorcet methods fail, but wv Condorcet doesn’t fail
importantly. Most other Condorcet methods fail badly, because they fail
FBC badly.

I don’t expect Benham to either, though wv is all that I’ve tested.

If a majority prefers one particular candidate to another, then they
should have a way of voting that will ensure that the other cannot win,
without any member of that majority reversing a preference for one
candidate over another.

which would indicate that the majority can bar a particular candidate
from winning by voting in some given way that does not involve order
reversal, only truncation.

If there's a sincere CW, then it's the same as your criterion, but if
not, then there may be one majority who prefers A to B and another that
prefers A to C, but no majority preferring A to both B and C. Then the
majority preferring A to B should have a way to stop B from winning...

I think? It's not my criterion.

-km

Okay, the WDSC definition that you posted shows its difference from Minimal-Defense, which is met by wv Condorcet, but not by Approval. (…or by most non-wv Condorcet.) …& of course different from my guess about WDSC, which is met by Approval, & effectively but not strictly by wv Condorcet. …& seriously failed by most non-wv Condorcet. On Tue, May 14, 2024 at 11:36 Kristofer Munsterhjelm <km_elmet@t-online.de> wrote: > On 2024-05-14 19:55, Michael Ossipoff wrote: > > It seems to me that the Weak Defensive Strategy Criterion was a > > generalization of FBC: > > > > One should never get a worse result because they didn’t vote something > > they like less over something they like more. > > > > Strictly-speaking, Condorcet methods fail, but wv Condorcet doesn’t fail > > importantly. Most other Condorcet methods fail badly, because they fail > > FBC badly. > > > > I don’t expect Benham to either, though wv is all that I’ve tested. > > https://electowiki.org/wiki/Weak_Defensive_Strategy_criterion says that > Schulze passes. > > So does > > http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-April/102004.html > . > > It also seems to define the criterion a bit differently: > > >> If a majority prefers one particular candidate to another, then they > >> should have a way of voting that will ensure that the other cannot win, > >> without any member of that majority reversing a preference for one > >> candidate over another. > > which would indicate that the majority can bar a particular candidate > from winning by voting in some given way that does not involve order > reversal, only truncation. > > If there's a sincere CW, then it's the same as your criterion, but if > not, then there may be one majority who prefers A to B and another that > prefers A to C, but no majority preferring A to both B and C. Then the > majority preferring A to B should have a way to stop B from winning... > > I think? It's not my criterion. > > -km >