[EM] smith/schwartz/landau

Curt accounts at museworld.com
Sat Mar 24 20:30:32 PDT 2018


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 at audioimagination.com> wrote:
> 
> 
> 
> ---------------------------- Original Message ----------------------------
> Subject: Re: [EM] smith/schwartz/landau
> From: "Curt" <accounts at museworld.com <mailto:accounts at museworld.com>>
> Date: Sat, March 24, 2018 12:20 am
> To: "election-methods at lists.electorama.com <mailto:election-methods at lists.electorama.com>" <election-methods at lists.electorama.com <mailto:election-methods at lists.electorama.com>>
> --------------------------------------------------------------------------
> 
> >
> >> On Mar 23, 2018, at 6:36 PM, robert bristow-johnson <rbj at audioimagination.com> wrote:
> >> ---------------------------- Original Message ----------------------------
> >>
> From: "Curt" <accounts at 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 at audioimagination.com <mailto:rbj at audioimagination.com>
> 
> "Imagination is more important than knowledge."
>  
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