Re: [EM] Poll on voting-systems, to inform voters in upcoming enactment-elections
On 2024-04-13 07:54, Michael Ossipoff wrote:
On Fri, Apr 12, 2024 at 16:05 Kristofer Munsterhjelm :
I would prefer that the merit question for the poll stays the same:
"which voting methods do you prefer to which others?", i.e. ranking
them
in preference.
Then it would be up to the individual voter to consider what aspects of
the method are most important
:-D. “…stays the same”? You’re trying to completely reverse the
express-purpose & entire fundamental nature of the poll that I proposed.
It was for informing voters about the EM membership’s social-ranking of
proposals for public political elections.
What this shows is that the purpose of the poll wasn't made clear
enough. See also Joseph Malkevitch' post, sfs
Kristofer—
Sorry about the language. I’m not an Internet attack-person, & I don’t want
to sound like one.
I departed from decorum, though I don’t want to, & usually don’t, when you
proposed to cancel the poll that I’d asked for (generating a collective EM
social-ranking of methods’ merit for public political elections), in
which we’ve been participating.
On Fri, Apr 12, 2024 at 22:54 Michael Ossipoff email9648742@gmail.com
wrote:
On Fri, Apr 12, 2024 at 16:05 Kristofer Munsterhjelm :
I would prefer that the merit question for the poll stays the same:
"which voting methods do you prefer to which others?", i.e. ranking them
in preference.
Then it would be up to the individual voter to consider what aspects of
the method are most important
:-D. “…stays the same”? You’re trying to completely reverse the
express-purpose & entire fundamental nature of the poll that I proposed. It
was for informing voters about the EM membership’s social-ranking of
proposals for public political elections.
and anyone who wants to use it to guide
reform can just screen away the unproposable methods.
Sure, anyone need only find all of the ones that are
public-election-suitable & also simple enough to be proposable. … by
searching through a ton of chaff.
But it would still, of course be completely meaningless & useless, because
people have no way of knowing for what purpose or by what standard the EM
members were rating those methods…& the members, by your system of course
would all be evaluating & ranking based on all different standards &
purposes.
You proposal is nonsense. What it amounts to is a proposal to cancel the
poll that people have been participating, & replace it with a new entirely
different one, of your idiosyncratic choosing… one so vague in its question
as to be completely meaningless, & useless for any purpose.
It’s late, & this this time of night isn’t the time to start a long reply.
I just wanted to post these brief preliminary comments. More about this
tomorrow maybe.
Definitely more either on this, or replies to other posts, + maybe some of
the electioneering we spoke of.
After all, we have to do that anyway, because it's pretty much
impossible to collapse disparate concerns into a single order without
making some assumptions about which concerns are most important. Would I
recommend Benham ahead of Schulze? Well, that depends on whether there's
tons of strategy in the place in question and whether they (and I) can
accept the nonmonotonicity.
In the absence of any such situational information, any order will be
imperfect. In any case, if the poll's output ranking ends up being like
Extrinsic Borda-Weighted Landau Intersection > Iterative Refinement
Keener + Sinkhorn (mean) > Schulze > RP > Approval > IRV,
then it's a simple matter for reformers to just discard everything above
Schulze (or RP) for a public proposal. In practice, I doubt the exotic
methods will rank that high anyway.
-km
Election-Methods mailing list - see https://electorama.com/em for list
info
On 2024-04-13 07:54, Michael Ossipoff wrote:
On Fri, Apr 12, 2024 at 16:05 Kristofer Munsterhjelm :
I would prefer that the merit question for the poll stays the same:
"which voting methods do you prefer to which others?", i.e. ranking
them
in preference.
Then it would be up to the individual voter to consider what aspects of
the method are most important
:-D. “…stays the same”? You’re trying to completely reverse the
express-purpose & entire fundamental nature of the poll that I proposed.
It was for informing voters about the EM membership’s social-ranking of
proposals for public political elections.
(Ignore my last message; my computer had a hiccup.)
What this shows is that the purpose of the poll wasn't made clear
enough. See also Joseph Malkevitch' post, "Purpose of Poll 2".
Could you give a link to the post where you first proposed the subject
of the poll, before the voting itself started? I'd be happy to just
continue with that subject, as long as we stick with it instead of
changing it after the voting period has started.
In other words, I'm not trying to sneakily change anything, but I would
prefer it to stay consistent with what was first proposed.
-km
Check out my initial poll-proposal. How could it be mis-construed? What
several different meanings could it have?
What remained in doubt?
What about what Mallkevich said? He didn’t really say anything specific.
On Sat, Apr 13, 2024 at 02:03 Kristofer Munsterhjelm km_elmet@t-online.de
wrote:
On 2024-04-13 07:54, Michael Ossipoff wrote:
On Fri, Apr 12, 2024 at 16:05 Kristofer Munsterhjelm :
I would prefer that the merit question for the poll stays the same:
"which voting methods do you prefer to which others?", i.e. ranking
them
in preference.
Then it would be up to the individual voter to consider what aspects
of
the method are most important
:-D. “…stays the same”? You’re trying to completely reverse the
express-purpose & entire fundamental nature of the poll that I proposed.
It was for informing voters about the EM membership’s social-ranking of
proposals for public political elections.
What this shows is that the purpose of the poll wasn't made clear
enough. See also Joseph Malkevitch' post, sfs
I like to put my replies at the top, where they’re more easily found.
It’s late at night here now, but I’ll post a link tomorrow, as early as
possible.
I’d be the last person to want to change the poll’s purpose. That purpose
was my reason for starting the poll.
Yes, the subject of purpose should be discussed more. I really didn’t know
that.
I’d specified that it be about merit-in-use, & I specifically excluded
complexity & proposability. …big mistake.
When I saw the complexity & unproposability nominations, I said, “Oh shit,
I muffed that specification. What’s the point of complicating it with
unproposable methods?”
But I didn’t want to say anything, because I’d already defined the poll.
But today or yesterday (depending on where you live), two people expressed
exactly my misgivings. “What are unproposable methods doing in the poll?”
Though I’d just wanted it to be about how well the methods would work in
use, it’s also true that that’s irrelevant if the method can’t even be
proposed !!
That was something that I missed when I specified the poll.
So I expressed my agreement with those people. …& I asked if we can change
it to:
“Rank in order of suitability for public-proposal, which includes
proposability.”
Yes it’s a change, but it’s a change in the spirit of the poll’s
initially-expressed intent. …like a typo-correction, it would only change a
clause that’s obviously contrary to my expressed purpose.
Two people expressed that it didn’t make sense to include unproposable
methods, because it’s contrary to the expressed purpose.
As I said, they’re right.
I didn’t try to decree a change. I merely asked if we can make that change.
Can we?
Most motions & issues can be dealt with by discussion for consensus…”Does
anyone object to this proposal?”.
I was the 3rd person to comment that it doesn’t make any sense to include
unproposable methods.
Now I ask if there’s objection, opposition or disagreement with my
proposal/motion.
On Sat, Apr 13, 2024 at 02:09 Kristofer Munsterhjelm km_elmet@t-online.de
wrote:
On 2024-04-13 07:54, Michael Ossipoff wrote:
On Fri, Apr 12, 2024 at 16:05 Kristofer Munsterhjelm :
I would prefer that the merit question for the poll stays the same:
"which voting methods do you prefer to which others?", i.e. ranking
them
in preference.
Then it would be up to the individual voter to consider what
aspects of
the method are most important
:-D. “…stays the same”? You’re trying to completely reverse the
express-purpose & entire fundamental nature of the poll that I proposed.
It was for informing voters about the EM membership’s social-ranking of
proposals for public political elections.
(Ignore my last message; my computer had a hiccup.)
What this shows is that the purpose of the poll wasn't made clear
enough. See also Joseph Malkevitch' post, "Purpose of Poll 2".
Could you give a link to the post where you first proposed the subject
of the poll, before the voting itself started? I'd be happy to just
continue with that subject, as long as we stick with it instead of
changing it after the voting period has started.
In other words, I'm not trying to sneakily change anything, but I would
prefer it to stay consistent with what was first proposed.
-km
Election-Methods mailing list - see https://electorama.com/em for list
info
I'm glad Michael has now decided he's not an "Internet attack-person". However, actions speak louder than words, so if he decides to unblock me and back down over his comments he's made to and about me, I might be inclined to believe him. Maybe he'd want to read my clarification post on Sainte-Laguë/Webster v Huntington-Hill first - I don't know. http://lists.electorama.com/pipermail/election-methods-electorama.com/2024-April/005685.html
Toby
On Saturday, 13 April 2024 at 10:08:32 BST, Michael Ossipoff <email9648742@gmail.com> wrote:
Kristofer—
Sorry about the language. I’m not an Internet attack-person, & I don’t want to sound like one.
I departed from decorum, though I don’t want to, & usually don’t, when you proposed to cancel the poll that I’d asked for (generating a collective EM social-ranking of methods’ merit for public political elections), in which we’ve been participating.
Is there actually a problem though? Here's how you described it on 4/6 and how I've been building my rankings:
Good point. I was meaning to clarify that. This poll is intended to be
about merit-in-use. ...disregarding winnability & proposability. ...but
taking into account strategy-problems,, expense of implementation, expense
& difficulty of administration, complexity & consequent insecurity of
count, & consequent count-fraud vulnerability. So, it's about
merit-in-use, in all its aspects.
Of course we don't rate those various merit-in-use considerations in the
same order.
That explicitly includes complexity and multiple aspects highly correlated with proposability.
On 4/13/24 05:42, Michael Ossipoff wrote:
I like to put my replies at the top, where they’re more easily found.
It’s late at night here now, but I’ll post a link tomorrow, as early as
possible.
I’d be the last person to want to change the poll’s purpose. That purpose
was my reason for starting the poll.
Yes, the subject of purpose should be discussed more. I really didn’t know
that.
I’d specified that it be about merit-in-use, & I specifically excluded
complexity & proposability. …big mistake.
When I saw the complexity & unproposability nominations, I said, “Oh shit,
I muffed that specification. What’s the point of complicating it with
unproposable methods?”
But I didn’t want to say anything, because I’d already defined the poll.
But today or yesterday (depending on where you live), two people expressed
exactly my misgivings. “What are unproposable methods doing in the poll?”
Though I’d just wanted it to be about how well the methods would work in
use, it’s also true that that’s irrelevant if the method can’t even be
proposed !!
That was something that I missed when I specified the poll.
So I expressed my agreement with those people. …& I asked if we can change
it to:
“Rank in order of suitability for public-proposal, which includes
proposability.”
Yes it’s a change, but it’s a change in the spirit of the poll’s
initially-expressed intent. …like a typo-correction, it would only change a
clause that’s obviously contrary to my expressed purpose.
Two people expressed that it didn’t make sense to include unproposable
methods, because it’s contrary to the expressed purpose.
As I said, they’re right.
I didn’t try to decree a change. I merely asked if we can make that change.
Can we?
Most motions & issues can be dealt with by discussion for consensus…”Does
anyone object to this proposal?”.
I was the 3rd person to comment that it doesn’t make any sense to include
unproposable methods.
Now I ask if there’s objection, opposition or disagreement with my
proposal/motion.
There's also...
https://electowiki.org/wiki/Approval_Sorted_Margins
I'm assuming this is the same as "Margins-Sorted Approval" in the poll. To me, it sounds very similar to the Margins-Sorted Minimum Losing Votes method discussed here a few days ago (and also one of the nominated methods), except the initial ordering is seeded by approval and not minmax. That difference looks like it fixes MSMLV's cloneproofness failures.
By my reckoning, that just leaves the following methods unexplained. Hopefully the folks who put them forward will provide at least a brief explanation soon.
Double Defeat, Hare
Max Strength Transitive Beatpath
Gross Loser Elimination
On 4/12/24 12:19, Kristofer Munsterhjelm wrote:
On 2024-04-11 23:52, Richard, the VoteFair guy wrote:
I suggest creating a list of links to the associated Wikipedia or Electowiki articles, one for each method. One person supplying all the links will save time for the rest of us. Personally I'm going to need to read about some of these methods.
Good idea. Here are some links and brief descriptions. I've tried to be neutral; I may post later with my thoughts about the methods, and what notable criteria they pass and fail that I know of.
I've only done the methods that have a wiki page. At the bottom is a list of those methods that don't. Their proposers have already described them, but they might need a more clear description; in any case, I'll leave that to them :-)
Smith//Score:
This is a composite method. https://electowiki.org/wiki/Composite_methods
It takes rated ballots.
It first eliminates every candidate not in the Smith set, and then does Range voting (Score voting) on the remaining candidates. No normalization is done after the elimination, so a vote A: 10, B: 7, C: 0 still gives B 7 points and C 0 even if A isn't in the Smith set.
In Daniel Carrera's words: "The ballot would look like a Score ballot. To process the ballots, the scores are converted into rankings (equal rankings allowed), and the highest scoring candidate inside the Smith set is elected." See also Toby's last post.
Approval with manual runoff:
First do a round of Approval voting. Determine the top two candidates, then hold a later second round to determine who of the two wins. This is like STAR, but spacing the rounds apart makes it possible to hold debates, discuss the differences between the finalists, and so on. On the other hand, it's more expensive.
Smith//Approval (explicit - specified approval cutoff):
This is a composite method. It takes a ranked ballot with an approval cutoff marked.
Every voter approves of (gives a point to) every candidate ranked above his approval cutoff. The Smith set member with the most points wins.
Smith//Approval (implicit):
Like Smith//Approval, except the voter can't specify an approval cutoff. Instead, every candidate ranked is counted as approved, and every candidate not ranked as not approved. The intent is to deter burial.
Woodall:
https://electowiki.org/wiki/Woodall%27s_method
This method takes ranked ballots. First make a note of the initial Smith set. Then keep doing IRV until only one candidate of the initial Smith set remains. Elect that candidate. Note: This is not Benham - the initial Smith set never changes.
Schwartz-Woodall:
The same as Woodall, but with the Schwartz set. The Schwartz set is slightly less prone to ties.
Copeland//Borda:
https://electowiki.org/wiki/Ranked_Robin
This method takes ranked ballots.
First eliminate every candidate not in the Copeland set. Then calculate the Borda scores of the remaining candidates and elect its winner. This can be done by using the Condorcet matrix alone.
Minmax(wv):
https://electowiki.org/wiki/Minimax_Condorcet_method
This method takes ranked ballots.
Based on the ballots, consider each one-on-one matchups between candidates. Elect the candidate who has the most comfortable lead against the candidate who does best against him, one on one.
Plurality:
You know this one. Choose-one ballots, equal rank not allowed, most first preferences wins.
Majority Judgement (category):
https://en.wikipedia.org/wiki/Majority_judgment
Various tiebreakers exist, e.g.
https://en.wikipedia.org/wiki/Highest_median_voting_rules#Tiebreaking_procedures
This takes graded ballots. The candidates give each candidate a grade, usually one of Excellent, Very Good, Good, Acceptable, Poor, or Reject. For each candidate, calculate the highest grade so that a majority gives that candidate at least that grade. The candidate with the highest such majority grade wins.
The method is often indecisive, which means a tiebreaker has to be used. There are many, but they all try to preserve the dynamics of MJ.
IRV:
https://en.wikipedia.org/wiki/Instant-runoff_voting
This should also be familiar to everybody here. It takes ranked ballots. Repeatedly eliminate the Plurality loser until a candidate obtains a majority of the non-exhausted first preferences.
STAR:
https://en.wikipedia.org/wiki/STAR_voting
This takes rated ballots. The ballot typically has six ratings (zero to five inclusive), but the method could work with any number. The method counts the total number of points for each candidate. The pairwise winner of the two candidates with the most points wins.
Schulze:
https://electowiki.org/wiki/Schulze_method
This takes ranked ballots. The method is complex but basically amounts to a cloneproof Smith generalization of Minmax.
Let a beatpath from a candidate A to another candidate Z be a series of pairwise defeats A beats B beats C beats... beats Y beats Z. The strength of the path is measured by the strength of its weakest individual pairwise contest. Let "the" beatpath from A to Z be the beatpath of strongest strength.
The Schulze winner is the candidate whose beatpath to anybody else is at least as strong as their beatpath back to him.
Baldwin:
https://electowiki.org/wiki/Baldwin%27s_method
This takes ranked ballots.
Baldwin is the Borda analog of IRV. In each round, the candidate with the lowest Borda count is eliminated. The last man standing wins. Also called Total Vote Runoff by Foley and Maskin.
Black:
https://electowiki.org/wiki/Black%27s_method
This takes ranked ballots.
If there is a Condorcet winner, elect that CW. Otherwise elect the Borda winner.
Approval:
https://electowiki.org/wiki/Approval_voting
This takes an Approval ballot: vote for one or more. The candidate with the most marks wins.
Benham:
https://electowiki.org/wiki/Benham%27s_method
This method takes ranked ballots. Repeatedly eliminate the Plurality loser until there's a Condorcet winner among the remaining candidates. Elect the Condorcet winner when that happens.
Smith//DAC:
This is a composite method. https://electowiki.org/wiki/Composite_methods
https://electowiki.org/wiki/Descending_Acquiescing_Coalitions
It takes ranked ballots.
First eliminate every candidate not in the Smith set. Then perform the DAC algorithm to determine the winner.
The DAC algorithm is complex, with the result being a cloneproof method otherwise close to Plurality.
Essentially, the DAC algorithm works like this: For each ballot, for each set of candidates a voter acquiesces to, increase that set's count by one. Then sort the sets in order of count, descending. Starting at the top with the current viable set being every candidate, eliminate from the viable set every candidate who is not in the set at the list's current position, unless that would eliminate everybody. The candidate/s remaining once you've traversed the whole list is/are the winner/s.
A voter acquiesces to a set if he doesn't rank any candidate outside the set strictly above a candidate within the set.
RCIPE:
https://electowiki.org/wiki/Ranked_Choice_Including_Pairwise_Elimination
This takes ranked ballots.
Modify IRV to, instead of eliminating the Plurality loser, eliminate the current Condorcet loser among the remaining (uneliminated) candidates. Only eliminate the Plurality loser if there is no Plurality loser. Once a candidate has a majority of the non-exhausted first preference votes, elect that candidate.
RP(wv):
https://electowiki.org/wiki/Ranked_Pairs
This takes ranked ballots.
First count the pairwise matrix. Create a sorted list of every pairwise victory, sorted by its strength. Break ties by random ballot.
Proceed from the top down the list, locking in a pairwise relation unless it would create a cycle.
At the end, the locked-in contests give an order of candidates. This is the election order: the candidate on top is the winner.
Strictly speaking, the tiebreaking is by random voter hierarchy, but I've skipped the details about how that is constructed.
I think that should be correct, but if I forgot something or described them incorrectly, let me know.
The methods not described are:
Margins-Sorted Approval
Double Defeat, Hare
Margins-Sorted Minimum Losing Votes (equal-rated whole)
Gross Loser Elimination
Max Strength Transitive Beatpath
-km
Election-Methods mailing list - see https://electorama.com/em for list info
I'm going to try to restate this to see if I follow. Ignore computational complexity for the moment. I'm going to use margins as the basis just to keep it clear.
Take all N! potential orderings, and for each consider the margins for the N(N-1)/2 resulting pairwise comparisons (e.g., A>B>C gives A over B, A over C, and B over C). If you're upholding a pairwise defeat, the margin is positive; if you're reversing a pairwise defeat it's negative; and pairwise ties are always zero. Pick the ordering whose weakest comparison is best. Break ties by looking at the second weakest, then third weakest, etc.
That is, if you sort each ordering's comparison strengths in ascending order, you want the one that is lexicographically best.
Am I right in this?
On 4/9/24 22:58, Forest Simmons wrote:
I would like to nominate ...
Max Strength Transitive Beeatpath:
Elect the head of the strongest transitive beatpath.
A transitive beatpath is a list of candidates in which each candidate is
pairbeaten by every candidate listed ahead of it.
A transitive beatpath P implies a defeat W>L if W precedes L in the path P.
The stronger of two different beatpaths is the one that implies the
strongest defeat that is not implied by the other.
Election-Methods mailing list - see https://electorama.com/em for list info
Here is my ballot. There are a couple of methods I'm still not sure exactly how they work, and many I'm undecided between. There are also several methods that would probably give good results but seem far too complex to me (e.g. Schulze) so don't meet my approval criteria. I feel inclined to simply tie all these methods rather than spend too much time working out an exact ranking.
-
Approval2. Smith//Score3. Margins-Sorted Approval4. Smith//Approval (explicit - specified approval cutoff)5. RP(wv)6. Benham7. Minmax(wv)8. STAR
Approval cut-off point here
The rest except:
Last: Plurality
TobyOn Friday, 12 April 2024 at 17:20:53 BST, Kristofer Munsterhjelm km_elmet@t-online.de wrote:
On 2024-04-11 23:52, Richard, the VoteFair guy wrote:
I suggest creating a list of links to the associated Wikipedia or
Electowiki articles, one for each method. One person supplying all the
links will save time for the rest of us. Personally I'm going to need
to read about some of these methods.
Good idea. Here are some links and brief descriptions. I've tried to be
neutral; I may post later with my thoughts about the methods, and what
notable criteria they pass and fail that I know of.
I've only done the methods that have a wiki page. At the bottom is a
list of those methods that don't. Their proposers have already described
them, but they might need a more clear description; in any case, I'll
leave that to them :-)
Smith//Score:
This is a composite method. https://electowiki.org/wiki/Composite_methods
It takes rated ballots.
It first eliminates every candidate not in the Smith set, and then does
Range voting (Score voting) on the remaining candidates. No
normalization is done after the elimination, so a vote A: 10, B: 7, C: 0
still gives B 7 points and C 0 even if A isn't in the Smith set.
In Daniel Carrera's words: "The ballot would look like a Score ballot.
To process the ballots, the scores are converted into rankings (equal
rankings allowed), and the highest scoring candidate inside the Smith
set is elected." See also Toby's last post.
Approval with manual runoff:
First do a round of Approval voting. Determine the top two candidates,
then hold a later second round to determine who of the two wins. This is
like STAR, but spacing the rounds apart makes it possible to hold
debates, discuss the differences between the finalists, and so on. On
the other hand, it's more expensive.
Smith//Approval (explicit - specified approval cutoff):
This is a composite method. It takes a ranked ballot with an approval
cutoff marked.
Every voter approves of (gives a point to) every candidate ranked above
his approval cutoff. The Smith set member with the most points wins.
Smith//Approval (implicit):
Like Smith//Approval, except the voter can't specify an approval
cutoff. Instead, every candidate ranked is counted as approved, and
every candidate not ranked as not approved. The intent is to deter burial.
Woodall:
https://electowiki.org/wiki/Woodall%27s_method
This method takes ranked ballots. First make a note of the initial
Smith set. Then keep doing IRV until only one candidate of the initial
Smith set remains. Elect that candidate. Note: This is not Benham - the
initial Smith set never changes.
Schwartz-Woodall:
The same as Woodall, but with the Schwartz set. The Schwartz set is
slightly less prone to ties.
Copeland//Borda:
https://electowiki.org/wiki/Ranked_Robin
This method takes ranked ballots.
First eliminate every candidate not in the Copeland set. Then calculate
the Borda scores of the remaining candidates and elect its winner. This
can be done by using the Condorcet matrix alone.
Minmax(wv):
https://electowiki.org/wiki/Minimax_Condorcet_method
This method takes ranked ballots.
Based on the ballots, consider each one-on-one matchups between
candidates. Elect the candidate who has the most comfortable lead
against the candidate who does best against him, one on one.
Plurality:
You know this one. Choose-one ballots, equal rank not allowed, most
first preferences wins.
Majority Judgement (category):
https://en.wikipedia.org/wiki/Majority_judgment
Various tiebreakers exist, e.g.
https://en.wikipedia.org/wiki/Highest_median_voting_rules#Tiebreaking_procedures
This takes graded ballots. The candidates give each candidate a grade,
usually one of Excellent, Very Good, Good, Acceptable, Poor, or Reject.
For each candidate, calculate the highest grade so that a majority gives
that candidate at least that grade. The candidate with the highest such
majority grade wins.
The method is often indecisive, which means a tiebreaker has to be
used. There are many, but they all try to preserve the dynamics of MJ.
IRV:
https://en.wikipedia.org/wiki/Instant-runoff_voting
This should also be familiar to everybody here. It takes ranked
ballots. Repeatedly eliminate the Plurality loser until a candidate
obtains a majority of the non-exhausted first preferences.
STAR:
https://en.wikipedia.org/wiki/STAR_voting
This takes rated ballots. The ballot typically has six ratings (zero to
five inclusive), but the method could work with any number. The method
counts the total number of points for each candidate. The pairwise
winner of the two candidates with the most points wins.
Schulze:
https://electowiki.org/wiki/Schulze_method
This takes ranked ballots. The method is complex but basically amounts
to a cloneproof Smith generalization of Minmax.
Let a beatpath from a candidate A to another candidate Z be a series of
pairwise defeats A beats B beats C beats... beats Y beats Z. The
strength of the path is measured by the strength of its weakest
individual pairwise contest. Let "the" beatpath from A to Z be the
beatpath of strongest strength.
The Schulze winner is the candidate whose beatpath to anybody else is
at least as strong as their beatpath back to him.
Baldwin:
https://electowiki.org/wiki/Baldwin%27s_method
This takes ranked ballots.
Baldwin is the Borda analog of IRV. In each round, the candidate with
the lowest Borda count is eliminated. The last man standing wins. Also
called Total Vote Runoff by Foley and Maskin.
Black:
https://electowiki.org/wiki/Black%27s_method
This takes ranked ballots.
If there is a Condorcet winner, elect that CW. Otherwise elect the
Borda winner.
Approval:
https://electowiki.org/wiki/Approval_voting
This takes an Approval ballot: vote for one or more. The candidate with
the most marks wins.
Benham:
https://electowiki.org/wiki/Benham%27s_method
This method takes ranked ballots. Repeatedly eliminate the Plurality
loser until there's a Condorcet winner among the remaining candidates.
Elect the Condorcet winner when that happens.
Smith//DAC:
This is a composite method. https://electowiki.org/wiki/Composite_methods
https://electowiki.org/wiki/Descending_Acquiescing_Coalitions
It takes ranked ballots.
First eliminate every candidate not in the Smith set. Then perform the
DAC algorithm to determine the winner.
The DAC algorithm is complex, with the result being a cloneproof method
otherwise close to Plurality.
Essentially, the DAC algorithm works like this: For each ballot, for
each set of candidates a voter acquiesces to, increase that set's count
by one. Then sort the sets in order of count, descending. Starting at
the top with the current viable set being every candidate, eliminate
from the viable set every candidate who is not in the set at the list's
current position, unless that would eliminate everybody. The candidate/s
remaining once you've traversed the whole list is/are the winner/s.
A voter acquiesces to a set if he doesn't rank any candidate outside
the set strictly above a candidate within the set.
RCIPE:
https://electowiki.org/wiki/Ranked_Choice_Including_Pairwise_Elimination
This takes ranked ballots.
Modify IRV to, instead of eliminating the Plurality loser, eliminate
the current Condorcet loser among the remaining (uneliminated)
candidates. Only eliminate the Plurality loser if there is no Plurality
loser. Once a candidate has a majority of the non-exhausted first
preference votes, elect that candidate.
RP(wv):
https://electowiki.org/wiki/Ranked_Pairs
This takes ranked ballots.
First count the pairwise matrix. Create a sorted list of every pairwise
victory, sorted by its strength. Break ties by random ballot.
Proceed from the top down the list, locking in a pairwise relation
unless it would create a cycle.
At the end, the locked-in contests give an order of candidates. This is
the election order: the candidate on top is the winner.
Strictly speaking, the tiebreaking is by random voter hierarchy, but
I've skipped the details about how that is constructed.
I think that should be correct, but if I forgot something or described
them incorrectly, let me know.
The methods not described are:
Margins-Sorted Approval
Double Defeat, Hare
Margins-Sorted Minimum Losing Votes (equal-rated whole)
Gross Loser Elimination
Max Strength Transitive Beatpath
-km
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