smith/schwartz/landau
Yes, I’ve used the same kind of argument. If, in a two-candidate democratic election, A has more votes than B, should A be the winner? I would argue yes.
If, in a 99-voter democratic election, A has 50 votes and B has 49, should A be the winner? I would argue yes.
If, in a 99-voter democratic election, A has 50 unenthusiastic votes and B has 49 wildly enthusiastic votes, should A be the winner? I would argue yes. There are others that argue no, that B has more social utility. I would say this is a difference of opinion that rests not on logic or voting criteria, but personal values. The two camps can respectfully disagree with each other. Call it the “Majority” versus “Utility” disagreement. I also think there are election types (private organizations, clubs, whatever) where the “Utility” direction might be more appropriate than the “Majority” direction. That’s fine.
But, for those elections where we believe that A should be the winner in that scenario -- the “Majority” believers -- that is what leads us to the Condorcet camp, as opposed to Borda, score, range, etc.
And expanding to multiple candidates, if Candidate A would beat all other candidates head to head, then A should be the winner. A is the Condorcet Winner, just the same as if A is the Condorcet Winner if he has more votes in a two-candidate election.
(In your final paragraphs, I am not sure if you are talking about a candidate other than the Condorcet Winner, or, a candidate from a multi-candidate Smith Set that would (in the case of a cycle) by definition have another candidate that is preferred over it.)
But yes, I definitely agree that there should be a bright line between methods that
A: “elect a Condorcet Winner if one exists”
and methods that might
B: “elect a winner other than the Condorcet Winner”.
For us “Majority” believers, we are in violent agreement that group A is superior to group B.
But I also believe that there should be a bright line between methods that
C: identify a “candidate or candidates that would defeat all other candidates head to head”
and methods that might
D: “elect a single winner that is not a Condorcet Winner if a CW does not exist”.
Group C stops with the identification of the Condorcet Winner, or the Smith Set if the CW does not exist. (Or, Group C might stop with the identification of the Weak Condorcet Winner, or the Schwartz Set if the WCW does not exist, if beats-or-ties is deemed allowable.)
Group D contains ranked-pairs, beatpaths, etc.
The reason I believe in the distinction is because D fails criteria that C does not. And if C and D are conflated, it does a disservice to C. When in large elections with a limited number of candidates, a CW is much more probable than a cycle. It does Condorcet proponents no favors to have Condorcet Methods described as “flawed” in the way group D is.
Group D is “decisive” where Group C is not. In these cases I would argue decisiveness is overvalued.
What do you believe the Smith Set signifies? Is it meaningless to you other than something from which a winner should be algorithmically selected?
Thank you for the exchange,
Curt
On Mar 24, 2018, at 2:10 AM, robert bristow-johnson rbj@audioimagination.com wrote:
---------------------------- Original Message ----------------------------
Subject: Re: [EM] smith/schwartz/landau
From: "Curt" <accounts@museworld.com mailto:accounts@museworld.com>
Date: Sat, March 24, 2018 12:20 am
To: "election-methods@lists.electorama.com mailto:election-methods@lists.electorama.com" <election-methods@lists.electorama.com mailto:election-methods@lists.electorama.com>
On Mar 23, 2018, at 6:36 PM, robert bristow-johnson rbj@audioimagination.com wrote:
---------------------------- Original Message ----------------------------
From: "Curt" accounts@museworld.com
https://github.com/tunesmith/condorcet-counter https://github.com/tunesmith/condorcet-counter
I opined a bit in the README but that’s not really the point of the project. I just wanted an easy way to identify Smith and Schwartz sets for myself.
to wit: "It's this author's view that a method should only be called a Condorcet if it is limited to identifying the Smith Set,"
seems to me that your view is that the current definition of "Condorcet-compliant-method" should be changed. so is Tideman Ranked-Pairs or Schulze Beat-Path methods not "Condorcet methods"?
Yes, that is my view. They should not be called “Condorcet Methods”, because they are not guaranteed to select the candidate(s) that would defeat all other candidates.
There is a clear difference between a “Condorcet Method” that finds a Condorcet Winner or Smith Set, and a “tiebreaking" method that tries to pick a single winner from a multi-candidate Smith Set. The latter fails criteria that the former does not. I don’t know what we should call these tiebreaking algorithms - perhaps they are not quite “tiebreaking” methods since a cycle is not exactly a tie. But it isn’t appropriate to call them “Completion” methods either as that implies something that it isn’t.
The actual objection I have is that when both are described as “Condorcet Methods”, then it’s too easy in the literature (and the blogs, and the wikipedia articles, particularly from Condorcet detractors) to paint with a broad brush and argue that all Condorcet Methods are flawed in some manner, same as how all other methods are “unfair” in some way, which ultimately does a disservice to the Condorcet Method. An election that has a Condorcet Winner is not unfair in those ways, compared to something like IRV or Plurality or Top-Two.
It might worth a survey of what a Smith Set actually means. I believe it signifies something valuable about the electorate, beyond just an indication that the election is “incomplete” and that we should apply some algorithm to divine a single winner from it.
well, arguing about the semantics is one thing, arguing about theory or ideals is another, and arguing about practice is yet another.
so whether you call it "Condorcet-compliant" or call it a turnip, there are ranked-ballot tabulation procedures that are 1. Decisive (they will elect someone) and 2. If a Condorcet Winner exists, the procedure will elect the CW. we gotta call that something and "Condorcet-compliant method" is more descriptive than "turnip". And it serves a purpose. It separates both practice and "theory and ideals" of these aforementioned procedures from other ranked-ballot systems such as IRV, Borda, or Bucklin.
both Ranked-Pairs and Schulze are fundamentally not defined as some post algorithm to divine a single winner from a Smith set that is larger than 1. They are well-defined procedures, in their own right, that happen to elect the CW if a CW exists. IRV may elect the CW if one exists, but of course we know that hasn't always been the case in practice. They are not "tiebreaking" a Smith set. they are not a procedure to be applied after it is discovered no single CW exists. they are procedures that will elect a candidate by the same rules whether a CW exists or not. But the candidate elected will be the CW if one exists. So the only practical difference between these turnips is what their outcome might be if there was a Smith set greater than 3 and some weird voting alignment.
So we need a term to draw the line between Ranked-Pairs or Schulze or BTR-IRV on one side and Bucklin, Borda, or IRV on the other. What semantic would you suggest?
the salient difference is simply what happened in my town 9 years ago: A candidate for mayor was elected to office when the voters in the city unambiguously marked their ballots that they preferred a different specific candidate. that is the problem with any non-turnip method. it's the converse of who a CW is. if everyone's vote carries the same weight (this is the "one-person-one-vote" principle), if Candidate A is preferred by more voters than Candidate B, what possible reason in the world should the less-preferred candidate be tapped to serve than the more-preferred candidate? especially when no other candidate is preferred over the more-preferred candidate?
When at all possible (because it isn't always, at least in theory), if more voters mark their ballots preferring Candidate A over Candidate B than the number of voters marking their ballots to the contrary, then Candidate B is not elected. What semantic should be used for the previous sentence?
--
r b-j rbj@audioimagination.com mailto:rbj@audioimagination.com
"Imagination is more important than knowledge."
Election-Methods mailing list - see http://electorama.com/em http://electorama.com/em for list info
---------------------------- Original Message ----------------------------
Subject: Re: [EM] smith/schwartz/landau
From: "Curt" accounts@museworld.com
Date: Sat, March 24, 2018 11:30 pm
To: "election-methods@lists.electorama.com" election-methods@lists.electorama.com
Yes, I’ve used the same kind of argument. If, in a two-candidate democratic election, A has more votes than B, should A be the winner? I would argue yes.
If, in a 99-voter democratic election, A has 50 votes and B has 49, should A be the winner? I would argue yes.
If, in a 99-voter democratic election, A has 50 unenthusiastic votes and B has 49 wildly enthusiastic votes, should A be the winner? I would argue yes. There are others that argue no, that B has more social utility. I would say this is a difference of opinion that rests not on logic or voting
criteria, but personal values. The two camps can respectfully disagree with each other. Call it the “Majority” versus “Utility” disagreement. I also think there are election types (private organizations, clubs, whatever) where the “Utility” direction might be more
appropriate than the “Majority” direction. That’s fine.
But, for those elections where we believe that A should be the winner in that scenario -- the “Majority” believers -- that is what leads us to the Condorcet camp, as opposed to Borda, score, range, etc.
And expanding to multiple candidates, if Candidate A would beat all other candidates head to head, then A should be the winner. A is the Condorcet Winner, just the same as if A is the Condorcet Winner if he has more votes in a two-candidate election.
(In your final paragraphs, I am not sure if you are talking about a candidate other than the Condorcet Winner, or, a candidate from a multi-candidate Smith Set that would (in the case of a cycle) by definition have another candidate that is preferred over it.)
But yes, I definitely agree that there should be a bright line between methods that
A: “elect a Condorcet Winner if one exists”
and methods that might
B: “elect a winner other than the Condorcet Winner”.
For us “Majority” believers, we are in violent agreement that group A is superior to group B.
But I also believe that there should be a bright line between methods that
C: identify a “candidate or candidates that would defeat all other candidates head to head”
and methods that might
D: “elect a single winner that is not a Condorcet Winner if a CW does not exist”.
Group C stops with the identification of the Condorcet Winner, or the Smith Set if the CW does not exist. (Or, Group C might stop with the identification of the Weak Condorcet Winner, or the Schwartz Set if the WCW does not exist, if beats-or-ties is deemed allowable.)
Group D contains ranked-pairs, beatpaths, etc.
The reason I believe in the distinction is because D fails criteria that C does not. And if C and D are conflated, it does a disservice to C. When in large elections with a limited number of candidates, a CW is much more probable than a cycle. It does Condorcet proponents no favors to have
Condorcet Methods described as “flawed” in the way group D is.
Group D is “decisive” where Group C is not. In these cases I would argue decisiveness is overvalued.
well, organizations and governments have to move on.� they need answers and elections are held to provide answers.
for a single-seat (usually executive) office, what would you suggest?� a runoff?
What do you believe the Smith Set signifies? Is it meaningless to you other than something from which a winner should be algorithmically selected?
�
it's not meaningless.� it just need not be a concept coded in election law.� remember (i am not sure you got this point), Ranked-Pairs and Schulze do not select a winner from the Smith set.� RP and Schulze select a winner from the entire field of candidates using a
consistent rule and, it turns out, that the winner selected by RP or Schulze is the CW if a CW exists.� that's in Group A.
"Group A" is a crappy term.� as bad as "turnip".� so here's a quite abridged taxonomy:
Mark-Only-One ballot:
� �1. FPTP� (plurality.� decisive)
� �2. FPTP runoff if no majority
Mark as many as you want:
� �3. Approval
Mark ballot scoring candidates:
� �4.� Score voting or Range voting
Ranked-choice ballot:
� �5. Bucklin
� �6. Borda
� �7. IRV
� �8. Ranked Pairs (let's say based on margins)
� �9. Schulze (margins)
�10. Min/Max
�11. IRV-BTR
then there are all of these esoteric methods that are promoted by some people in this group.
what should be the term that differentiates 8, 9, 10, 11 from 5, 6, 7?
r b-j� � � � � � � � � � � � �rbj@audioimagination.com
"Imagination is more important than knowledge."
�
�
�
�
---------------------------- Original Message ----------------------------
Subject: Re: [EM] smith/schwartz/landau
From: "Curt" accounts@museworld.com
Date: Sat, March 24, 2018 11:30 pm
To: "election-methods@lists.electorama.com" election-methods@lists.electorama.com
(In your final paragraphs, I am not sure if you are talking about a candidate other than the Condorcet Winner, or, a candidate from a multi-candidate Smith Set that would (in the case of a cycle) by definition have another candidate that is preferred over it.)
i was referring to the 2009 mayoral race in Burlington Vermont.� IRV was used, but the ballot data was publically available and we could re-tabulate the ballots according to other rules and we discovered that a CW existed and was not the IRV winner (which meant that the CW came in
"third" by IRV reckoning).
there was no cycle.� the Smith set was of size 1.
the CW was the more centrist Democrat
the IRV winner (and election winner) was Prog
the plurality winner (counting first-choice votes) was GOP
so three different candidates all having some claim of legitimacy for office.� but the law was IRV and the Prog won even though the CW beat him by about 5% in a head-to-head.
the next year, the city voters voted to repeal IRV and we have reverted back to Plurality with a runoff if 40%
cannot be obtained.
--
r b-j� � � � � � � � � � � � �rbj@audioimagination.com
"Imagination is more important than knowledge."
�
�
�
�
On Mar 24, 2018, at 9:21 PM, robert bristow-johnson rbj@audioimagination.com wrote:
---------------------------- Original Message ----------------------------
From: "Curt" <accounts@museworld.com mailto:accounts@museworld.com>
A: “elect a Condorcet Winner if one exists”
B: “elect a winner other than the Condorcet Winner”.
[within A: ]
C: identify a “candidate or candidates that would defeat all other candidates head to head”
D: “elect a single winner that is not a Condorcet Winner if a CW does not exist”.
[…]
Group D is “decisive” where Group C is not. In these cases I would argue decisiveness is overvalued.
well, organizations and governments have to move on. they need answers and elections are held to provide answers.
for a single-seat (usually executive) office, what would you suggest? a runoff?
Appropriate remedies might be a runoff after another period of consideration, or a power-sharing agreement. But this ties into what it means to have a multi-candidate Smith Set.
What do you believe the Smith Set signifies? Is it meaningless to you other than something from which a winner should be algorithmically selected?
it's not meaningless. it just need not be a concept coded in election law.
But I'm honestly curious what you believe the multi-candidate Smith Set signifies or means.
remember (i am not sure you got this point), Ranked-Pairs and Schulze do not select a winner from the Smith set.
Is this a semantic argument, or are you saying that ranked-pairs and schulze can elect single winners that are not in the Smith Set? Can you produce an example ballot set? I’m currently under the impression that is incorrect, as Wikipedia says both are Smith-compliant. I would love to be corrected if Wikipedia is wrong. I would not regard a method as Condorcet-compliant if it is not Smith-compliant.
At any rate, I am not here to lobby for a particular term for the methods in Group D. Only to argue that a distinction between groups C and D should exist, and without it, we do a disservice to Condorcet Methods by allowing them to be describe as “flawed” in ways that only group D is. I am open to suggestions.
On 25 Mar 2018, at 06:30, Curt accounts@museworld.com wrote:
What do you believe the Smith Set signifies? Is it meaningless to you other than something from which a winner should be algorithmically selected?
To me Smith Set is a criterion that in some sense and at first sight looks natural, but on second thought does not cover all possible scenarios well. I mean that if there is a group of candidates that are a unified group, and they beat all others, then yes, one of them should at least in most cases win. This is related to clones. If all the Smith Set candidates can be considered to be clones, then nominating only one of them would probably lead to electing that candidate as a Condorcet Winner.
What are the problems then? One problem is that those Condorcet methods that are based on rankings only, and possibly a pairwise matrix only, can carry only limited information on what the preferences of the voters are. There can be multiple explanations to what the voter preferences might have been. There are scenarios where electing from the Smith Set may not be natural.
Another problem of the Smith Set is that it may look more natural than it is, when one draws the end results (in paper or in one's mind) so that all the Smith Set candidates are at top, and all others below. This drawing technique to some extent hides the defeats within the Smith Set from the eye.
The best I can do to demonstrate these problems is to give you one particular (old) example scenario where selecting the winner outside of the Smith Set seems quite natural. In some extreme situations Smith Set may thus not be the right choice.
17: A > B > d > C
16: A > d > B > C
17: B > C > d > A
16: B > d > C > A
17: C > A > d > B
16: C > d > A > B
This example is a classic strong cycle of A, B and C, with one more candidate (d) added. Candidates A, B and C are not clones since they are not next to each others in the ballots. Candidate d is not in the Smith Set, but is very close to being a Condorcet Winner (2 votes short). Candidates A, B and C are very far from being Condorcet Winners.
BR, Juho
Hi Juho, thank you for this example ballot set. I have added it to the codebase as a test case with some documentation. (Both Smith and Schwartz should identify A, B, and C.)
A, B, and C all defeat each other 66:33. And they each defeat d 50:49. I understand the urge to award d the win, given those numbers. But I believe that that urge ascribes “intensity of preference” to A, B, and C - when for Condorcet, which is purely ordinal, we have no idea. If I imagine those voters as voting stoically, dispassionately, poker-face, then I have no idea whether they passionately prefer A to B, or if, for instance, they are completely torn but have some consistent but trivial reason to pick one over the other. So in the absence of intensity-of-preference data, we really don’t have enough data to conclude that d should be the winner - for all we know, there actually is more passion in those 50:49 splits.
So I am having trouble seeing it as a flaw with the Smith Set concept itself. I do agree that it points to some sort of flaw, but I think the proper identification of the flaw’s home requires zooming out and looking at the framework.
Each time we step close to determining an election winner, we make a choice to lose fidelity in some fashion.
-
We have a need to collectively decide something, and so we voice that need by identifying a question to answer. But in identifying or voicing that question, we risk losing some essential part of the real question. In other words, we risk a failure of specification. But, we need to move forward, so we accept that risk, and move forward with the question as asked.
-
In asking the question, we identify options for a solution - the candidates in an election. But in doing so, we risk omitting some of the proper solution spectrum. The collected candidates may still be insufficient in some way. But, we have to draw the line somewhere, so voters are restricted to choosing between a potentially imperfect slate of candidates.
-
We set a time to choose. But in doing so, we risk the deadline being too soon for some voters, in that they might not be finished with their decision process. So we lose some fidelity there in measuring voter preference exactly.
-
We want to protect against bullying, intimidation, and some people being convinced to make their vote count “less” than someone else’s, and so we decide to protect the ideal of “one person, one vote” where every person’s vote counts the same. But there we lose some fidelity in measuring intensity of preference among voters.
So I’m inclined to think that the example below is more about the costs associated with something like #4 above. In fact, the scenario seems very similar to me, to the one I sketched out earlier - if, in a two-candidate election, A defeats B 50:49, but A’s support is lukewarm and B’s is passionate, should B win? I think you can defend that if you value “social utility” and “intensity of preference” more than “one-person-one-vote” or "majority", but I wouldn’t count that as a flaw with the Condorcet method in particular, since it’s a majority-type of voting method.
Regards,
Curt
On Mar 25, 2018, at 7:05 AM, Juho Laatu juho.laatu@gmail.com wrote:
On 25 Mar 2018, at 06:30, Curt accounts@museworld.com wrote:
What do you believe the Smith Set signifies? Is it meaningless to you other than something from which a winner should be algorithmically selected?
To me Smith Set is a criterion that in some sense and at first sight looks natural, but on second thought does not cover all possible scenarios well. I mean that if there is a group of candidates that are a unified group, and they beat all others, then yes, one of them should at least in most cases win. This is related to clones. If all the Smith Set candidates can be considered to be clones, then nominating only one of them would probably lead to electing that candidate as a Condorcet Winner.
What are the problems then? One problem is that those Condorcet methods that are based on rankings only, and possibly a pairwise matrix only, can carry only limited information on what the preferences of the voters are. There can be multiple explanations to what the voter preferences might have been. There are scenarios where electing from the Smith Set may not be natural.
Another problem of the Smith Set is that it may look more natural than it is, when one draws the end results (in paper or in one's mind) so that all the Smith Set candidates are at top, and all others below. This drawing technique to some extent hides the defeats within the Smith Set from the eye.
The best I can do to demonstrate these problems is to give you one particular (old) example scenario where selecting the winner outside of the Smith Set seems quite natural. In some extreme situations Smith Set may thus not be the right choice.
17: A > B > d > C
16: A > d > B > C
17: B > C > d > A
16: B > d > C > A
17: C > A > d > B
16: C > d > A > B
This example is a classic strong cycle of A, B and C, with one more candidate (d) added. Candidates A, B and C are not clones since they are not next to each others in the ballots. Candidate d is not in the Smith Set, but is very close to being a Condorcet Winner (2 votes short). Candidates A, B and C are very far from being Condorcet Winners.
BR, Juho
Election-Methods mailing list - see http://electorama.com/em for list info
---------------------------- Original Message ----------------------------
Subject: Re: [EM] smith/schwartz/landau
From: "Curt" accounts@museworld.com
Date: Sun, March 25, 2018 2:12 am
To: "election-methods@lists.electorama.com" election-methods@lists.electorama.com
On Mar 24, 2018, at 9:21 PM, robert bristow-johnson rbj@audioimagination.com wrote:
---------------------------- Original Message ----------------------------
From: "Curt" <accounts@museworld.com mailto:accounts@museworld.com>
A: “elect a Condorcet Winner if one exists”
B: “elect a winner other than the Condorcet Winner”.
[within A: ]
C: identify a “candidate or candidates that would defeat all other candidates head to head”
D: “elect a single winner that is not a Condorcet Winner if a CW does not exist”.
[…]
Group D is “decisive” where Group C is not. In these cases I would argue decisiveness is overvalued.
well, organizations and governments have to move on. they need answers and elections are held to provide answers.
for a single-seat (usually executive) office, what would you suggest? a runoff?
Appropriate remedies might be a runoff after another period of consideration, or a power-sharing agreement. But this ties into what it means to have a multi-candidate Smith Set.
What do you believe the Smith Set signifies? Is it meaningless to you other than something from which a winner should be algorithmically selected?
it's not meaningless. it just need not be a concept coded in election law.
But I'm honestly curious what you believe the multi-candidate Smith Set signifies or means.
well, what i think about the Smith Set, whether it be single or multi-candidate set in a single-winner race, is that there is no compelling reason that any candidate in the complement of the Smith
set should be elected.� because the electorate is clear that there are other, more preferred, candidates in any scenario.� but it doesn't have to be encoded into law.
remember (i am not sure you got this point), Ranked-Pairs and Schulze do not select a winner from the Smith set.
Is this a semantic argument, or are you saying that ranked-pairs and schulze can elect single winners that are not in the Smith Set? Can you produce an example ballot set?
we're having a semantic difference.� RP and Schulze elect a candidate drawing from the entire pool of
candidates.� they do not identify a Smith set and then proceed to select from the Smith set.
so it's just an election procedure say like IRV is or Bucklin is.� same ballots, different way of looking at the ballots. and if a CW exists, the RP winner and Schulze winner will be the CW. (and it turns out that RP and Schulze will elect the same candidate in the case of a Smith set of 3,
and i am convinced a bigger Smith set is highly unlikely to occur in a real governmental election.� RP is simpler to explain to legislators and the public than is Schulze, in my opinion.� so it really just matters whether or not we consider the RP winner to be the best indication of the
least disapproved candidate.)
I’m currently under the impression that is incorrect, as Wikipedia says both are Smith-compliant. I would love to be corrected if Wikipedia is wrong. I would not regard a method as Condorcet-compliant if it is not Smith-compliant.
i am not taking an issue with that.� i
understand why, in RP at least, why the winner is in the Smith set.� but it's not the same as a method that acts in one way to get the CW, and then, if no CW is forthcoming, does a secondary algorithm to pick the winner.� RP and Schulze do what they do on the entire pool of
candidates.
At any rate, I am not here to lobby for a particular term for the methods in Group D. Only to argue that a distinction between groups C and D should exist, and without it, we do a disservice to Condorcet Methods by allowing them to be describe as “flawed” in ways
that only group D is. I am open to suggestions.
i just wanna know what we wanna call a ranked-ballot election method that elects the Condocet Winner when such exists.� what should such a class of methods be called?
r b-j� � � � � � � � � � � � �rbj@audioimagination.com
"Imagination is more important than knowledge."
�
�
�
�
On 03/23/2018 09:33 PM, Curt wrote:
Thanks to Kristofer for explaining my “beats” vs “beats or ties” confusion.
For anyone interested, here is the software package of me using scala to
compute Smith and Schwartz sets. It’s not super-advanced, but it at
least avoids mutable variables. In the future I may try to use more
expressive FP concepts, and pull in one of the faster Schwartz
algorithms. I don’t entirely understand the graph algorithms yet.
https://github.com/tunesmith/condorcet-counter
I opined a bit in the README but that’s not really the point of the
project. I just wanted an easy way to identify Smith and Schwartz sets
for myself.
As Kevin pointed out, the Schwartz set is actually the union of all
minimal such sets, because (unlike for Smith) that's not the same thing
as just one such minimal set.
At https://wiki.electorama.com/wiki/Beatpath_example_12 there is an
example where the Schwartz set has two components ({A,B,C,D} and {E}).
Could you test your software on it?
-km
Hi Kristofer,
Thank you for the test case, I’ve added it locally.
I had deja vu on this example because I came across it once before and it looked wrong to me at first. Here, I input the ballots and I got {E} as the single-member Smith and Schwartz set.
But then I realized the example has an alternate ballot style where
1:A>B
is supposed to be interpreted as
1:A>B>C=D=E=F=G=H=I=J=K=L
My default ballot counter does not do that, it assumes no opinion over the rest. I now have a todo to supply a flag to support both ballot styles. :)
I adjusted the ballot input to manually specify the ties, and I got a Schwartz Set of {A, B, C, D, E}. (And then {F, G}, and then {H}, and then {I, J, K, L}).
It identifies the Smith Set as all candidates.
My Schwartz implementation is based off the Floyd-Warshall algorithm here: https://wiki.electorama.com/wiki/Maximal_elements_algorithms
My implementation:
https://github.com/tunesmith/condorcet-counter/blob/master/src/main/scala/com/keenworks/vote/condorcet/set/SchwartzService.scala
It looks like that pseudocode doesn’t try to identify components within the Schwartz Set. But looking at the tally I see how E is the Weak Condorcet Winner. Is there pseudocode that identifies these minimal sets separately?
I will have to update my mental definition of Schwartz Set and update y docs; I would have thought E would be the Schwartz Set, although I see looking at the tally how that isn’t true. But I wish my code to identify the WCW(s) from the Schwartz Set, just like it identifies any CW from the Smith Set.
Curt
On Mar 26, 2018, at 1:00 AM, Kristofer Munsterhjelm km_elmet@t-online.de wrote:
On 03/23/2018 09:33 PM, Curt wrote:
Thanks to Kristofer for explaining my “beats” vs “beats or ties” confusion.
For anyone interested, here is the software package of me using scala to compute Smith and Schwartz sets. It’s not super-advanced, but it at least avoids mutable variables. In the future I may try to use more expressive FP concepts, and pull in one of the faster Schwartz algorithms. I don’t entirely understand the graph algorithms yet.
https://github.com/tunesmith/condorcet-counter
I opined a bit in the README but that’s not really the point of the project. I just wanted an easy way to identify Smith and Schwartz sets for myself.
As Kevin pointed out, the Schwartz set is actually the union of all minimal such sets, because (unlike for Smith) that's not the same thing as just one such minimal set.
At https://wiki.electorama.com/wiki/Beatpath_example_12 there is an example where the Schwartz set has two components ({A,B,C,D} and {E}). Could you test your software on it?
-km
On 26 Mar 2018, at 01:36, Curt accounts@museworld.com wrote:
Hi Juho, thank you for this example ballot set. I have added it to the codebase as a test case with some documentation. (Both Smith and Schwartz should identify A, B, and C.)
A, B, and C all defeat each other 66:33. And they each defeat d 50:49. I understand the urge to award d the win, given those numbers. But I believe that that urge ascribes “intensity of preference” to A, B, and C - when for Condorcet, which is purely ordinal, we have no idea. If I imagine those voters as voting stoically, dispassionately, poker-face, then I have no idea whether they passionately prefer A to B, or if, for instance, they are completely torn but have some consistent but trivial reason to pick one over the other. So in the absence of intensity-of-preference data, we really don’t have enough data to conclude that d should be the winner - for all we know, there actually is more passion in those 50:49 splits.
We don't know the strengths of preferences (strength), but we know the number of voters (count) on each side in every pairwise preference. A, B and C are preferred over d weakly (count). A is preferred over B strongly (count). In the following examples preferences vary a lot if we study the strengths of preferences (strength).
In the following example d is weak (strength). (only ">>>" added to the original example)
17: A > B >>> d > C
16: A >>> d > B > C
17: B > C >>> d > A
16: B >>> d > C > A
17: C > A >>> d > B
16: C >>> d > A > B
In the following example d is strong (strength). (only ">>>" added)
17: A > B > d >>> C
16: A > d >>> B > C
17: B > C > d >>> A
16: B > d >>> C > A
17: C > A > d >>> B
16: C > d >>> A > B
Votes in the original example are almost symmetric in the sense that A, B and C are about as often below and above d, and the votes are about symmetric whether you read them from left to right or from right to left. This makes the ABC group and d about equal when thinking in terms of having them listed "on the right" or "on the left". The Smith Set candidates are in the ballots only marginally more "on the left" than candidate d. Therefore also their preference strengths (strength) are with good probability (under some randomness assumptions) about the same.
In summary, I don't see how to make any conclusions on the relative preferences (strength) of the ABC group and d. Just like Condorcet Winners could be popular or not (strength), also Smith Set members and non Smith Set members could be popular or not (strength). The example shows a situation where preferences can be whatever or about the same (strength), or in favour of d (count). There are three candidates that beat d, but that should not carry much weight since number of pairwise victories is known to be a poor criterion (because of clone problems).
So I am having trouble seeing it as a flaw with the Smith Set concept itself. I do agree that it points to some sort of flaw, but I think the proper identification of the flaw’s home requires zooming out and looking at the framework.
I think the interesting question is if electing from the Smith Set makes sense as often as electing a Condorcet Winner. Many people on this list think that in many elections it would make sense to always elect the CW (knowing that the strengths of preferences (strength) are not well known). People who think that way should ask themselves if they require the winner to come from the SS in the given example, of if d would be a better choice. If d is ok (again assuming no knowledge of the strengths of preferences (strength)), then SS should not be seen as a requirement (although 99.9% of the elections would still elect from the SS, since the situation given in the example is very rare).
To me that example tells that sometimes candidates outside the Smith Set can indeed be almost ideal (2 votes short of being a Condorcet Winner), and candidates in the Smith Set can sometimes be quite poor (creating a strong unified opposition with interest to change winner A to C). This kind of ballot sets are however very unusual. Practical Condorcet methods should therefore elect almost always from the Smith Set. But as far as I'm concerned, not necessarily as a requirement, because of special cases like this.
Each time we step close to determining an election winner, we make a choice to lose fidelity in some fashion.
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We have a need to collectively decide something, and so we voice that need by identifying a question to answer. But in identifying or voicing that question, we risk losing some essential part of the real question. In other words, we risk a failure of specification. But, we need to move forward, so we accept that risk, and move forward with the question as asked.
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In asking the question, we identify options for a solution - the candidates in an election. But in doing so, we risk omitting some of the proper solution spectrum. The collected candidates may still be insufficient in some way. But, we have to draw the line somewhere, so voters are restricted to choosing between a potentially imperfect slate of candidates.
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We set a time to choose. But in doing so, we risk the deadline being too soon for some voters, in that they might not be finished with their decision process. So we lose some fidelity there in measuring voter preference exactly.
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We want to protect against bullying, intimidation, and some people being convinced to make their vote count “less” than someone else’s, and so we decide to protect the ideal of “one person, one vote” where every person’s vote counts the same. But there we lose some fidelity in measuring intensity of preference among voters.
So I’m inclined to think that the example below is more about the costs associated with something like #4 above.
I don't see any strong connection to strength of preferences (strength). The example is intended to follow the "one person, one vote" and "majority" tradition of explaining how to design pure ranked (Condorcet) methods. To me the key question thus is, when measuring only pairwise preferences, are there situations where the best winner might come outside of the Smith Set. The given example is the most obvious and most extreme to me. And the key point there is that d is two votes short of being a Condorcet Winner. Let's assume that we all would like d to win if it was a CW. A, B and C on the other hand are far from being Condorcet winners. This can be seen as a question of having one major defeat (A, B, C) to some other candidate, or having three marginal defeats (d) to other candidates.
That's just my two cents. I'm just trying to encourage people to think if Smith Set should be seen as a requirement, or just as a the most common outcome when there is a top cycle.
BB, Juho
P.S. I note once more that the Smith Set should not be visualised as a group above d (although that is the way people always draw it). Cyclic preferences do not have any obvious geometric presentation on a 2D paper. An alternative drawing approach would be to draw all the candidates as far from the winner position as they have distance to being a Condorcet Winner. That's how I tend to see the given example. (There are however few alternative ways to count the distance of each candidate to becoming a Condorcet Winner.)
In fact, the scenario seems very similar to me, to the one I sketched out earlier - if, in a two-candidate election, A defeats B 50:49, but A’s support is lukewarm and B’s is passionate, should B win? I think you can defend that if you value “social utility” and “intensity of preference” more than “one-person-one-vote” or "majority", but I wouldn’t count that as a flaw with the Condorcet method in particular, since it’s a majority-type of voting method.
Regards,
Curt
On Mar 25, 2018, at 7:05 AM, Juho Laatu juho.laatu@gmail.com wrote:
On 25 Mar 2018, at 06:30, Curt accounts@museworld.com wrote:
What do you believe the Smith Set signifies? Is it meaningless to you other than something from which a winner should be algorithmically selected?
To me Smith Set is a criterion that in some sense and at first sight looks natural, but on second thought does not cover all possible scenarios well. I mean that if there is a group of candidates that are a unified group, and they beat all others, then yes, one of them should at least in most cases win. This is related to clones. If all the Smith Set candidates can be considered to be clones, then nominating only one of them would probably lead to electing that candidate as a Condorcet Winner.
What are the problems then? One problem is that those Condorcet methods that are based on rankings only, and possibly a pairwise matrix only, can carry only limited information on what the preferences of the voters are. There can be multiple explanations to what the voter preferences might have been. There are scenarios where electing from the Smith Set may not be natural.
Another problem of the Smith Set is that it may look more natural than it is, when one draws the end results (in paper or in one's mind) so that all the Smith Set candidates are at top, and all others below. This drawing technique to some extent hides the defeats within the Smith Set from the eye.
The best I can do to demonstrate these problems is to give you one particular (old) example scenario where selecting the winner outside of the Smith Set seems quite natural. In some extreme situations Smith Set may thus not be the right choice.
17: A > B > d > C
16: A > d > B > C
17: B > C > d > A
16: B > d > C > A
17: C > A > d > B
16: C > d > A > B
This example is a classic strong cycle of A, B and C, with one more candidate (d) added. Candidates A, B and C are not clones since they are not next to each others in the ballots. Candidate d is not in the Smith Set, but is very close to being a Condorcet Winner (2 votes short). Candidates A, B and C are very far from being Condorcet Winners.
BR, Juho
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