[EM] Condorcet Ties

[MIKE OSSIPOFF]

It was asked:

> > >What are the most acceptable forms of tie breaking
> > >other than random, that might be used before random
> > >in the case of Condorcet Voting.
> >
> > >
> > >I mean actual ties in voting preferences
> > >and not merely failure to have a Condorcet approved
> > >candidate.
> >

I reply:

> > So you're not talking about circular tie solutions, but rather about
> > actual pairwise ties, or equal defeats, right?
> >
> > SSD has a version that I've called Cloneproof SSD, or Small Committee 
>SSD.
> > It's equivalent to what Markus Schulze proposes for small committee 
>votes.
> > Norman Petry prefers it too.
> >
> > You've been to the electionmethods website, and so I don't need to
> > define SSD here.
> >
> > Cloneproof SSD is SSD with a different stopping rule. Instead of
> > declaring a winner as soon as there's an unbeaten candidate, Cloneproof 
>SSD
> > stops & declares a winner when there are no cycles in the current
> > Schwartz set. Whoever is unbeaten at that time wins.
> >
> > Now, about the ties you asked about:
> >
> > Sometimes, in a small committee, there will be several defeats that
> > are equally the weakest defeats in the current Schwartz set.
> > We've defined the weakest defeat as the one with least support.
> > In other words, if A beats B, then the defeat's support is the number
> > of people ranking A over B. But if there are 2 or more defeats that
> > are equally the weakest in the current Schwartz set, as measured in
> > that way, then drop the one that has the most opposition. The opposition
> > to A's defeat of B is the number of people ranking B over A. If there
> > are more than one defeat in the current Schwartz set that have the
> > same support and the same opposition, then drop all of those 
>simultaneously.
> >
> > Above, I said "Whoever is unbeaten at that time wins." But what if
> > more than one candidate wins? Then delete from the rankings every
> > candidate other than those unbeaten ones, and repeat the count, from
> > the start, with those reduced rankings. Repeat until doing so fails
> > to reduce the number of winners.
> >
> > When that happens, choose among the winners by Random Ballot, or
> > Chairman Ballot (decide in advance which it will be).
> >
> > Random ballot means that you choose a ballot from the election at
> > random, and whichever of the winners is highest ranked on that ballot
> > wins the election. Of course if the winners are all ranked equal on
> > that ballot, then you pick another random ballot, till you get one
> > that solves the tie.
> >
> > Chairman Ballot is the same as Random Ballot, except that the chairman's
> > ballot is always used to solve those ties. Of course if the chairman's
> > ballot ranks the winners equally, then use Random Ballot.
> >
> > The above method is agreed by several people on EM to be the best
> > way to count ranked ballots for a single-winner choice, in small 
>committees
> > where ties are likely. (In public elections, where ties
> > are quite rare, it doesn't matter how they're solved. If there's
> > a tiebreaker already on the books, the reform legislation could just
> > say to use it, where I here said to use Random Ballot or Chairman 
>Ballot.
> >
> > As has been pointed out, and as I demonstrated here, Cloneproof SSD
> > is equivalent to BeatpathWinner. I claim that Cloneproof SSD's 
>definition
> > is more naturally & obviously motivated & justified, but BeatpathWinner
> > makes for a briefer computer program, and a somewhat faster-running
> > program. That shouldn't ordinarily be important, and I consider
> > Cloneproof SSD's better plausibility more important. But you might
> > want to use BeatpathWinner to implement Cloneproof SSD, if brevity of
> > the computer program, and minimum running time are important. Of course
> > it would be quite rare for there to be so many candidates & voters for
> > running time to be significant.
> >
> > >
> > >ps.
> > >Also, I notice that the EM webpage does not list
> > >Condorcet as a voting system, but rather lists Minmax as
> > >the name of the system..
> >
> > Blake Cretney calls his website the EM resource website. Blake's
> > website isn't officially authorized as that, unless I'm mistaken.
> >
> > "Minmax" is vague, as exemplified by Blake defining it in a way
> > different from how it's usually used here.
> >
> > Blake's website is really just Blake's website. Unless I'm mistaken,
> > Rob hasn't designated it the official EM resource website. But
> > Rob, tell me if I'm mistaken on that.
> >
> > Blake's website contains some criteria definitions that act contrary
> > to how people expect those criteria to act. Additionally, there may
> > be one or more vaguely-defined criteria there too.
> >
> > Blake's advocacy, at his website, of margins, as opposed to 
>defeat-support,
> > is _not_ representative of opinion at this website.
> >
> > >but with a different type of counting
> > >(Minmax as described there goes for a minimum score
> > >rather than for a maximum score as described at
> > >http://electionmethods.org/)
> > >
> > >Is there another name for Condorcet voting
> >
> > Some call PC "Minmax". I prefer PC, because "Minmax" can mean too
> > many different things.
> >
> > Cloneproof SSD, Small Committee SSD, and BeatpathWinner are 3
> > names for the same Condorcet version.
> >
> > Sometimes pairwise-count methods in general are called Condorcet's
> > method, but that isn't really correct. Condorcet specified some
> > particular methods, with particular circular tie solutions, and those
> > are rightfully Condorcet's method. He proposed at least 2 circular
> > tie solutions, a top down one and a bottom up one. Tideman's method,
> > aka Tideman's Ranked Pairs Rule, is the best interpretation of 
>Condorcet's
> > top down rule. PC, Smith//PC, & SSD (which should include
> > Cloneproof SSD) are some interpretations of Condorcet's bottom-up
> > rule, which Condorcet didn't express in the detail that we might like,
> > hence the several interpretations. PC is the literal interpretation.
> > SSD is the most refined, best-working interpretation. BeatpathWinner
> > qualifies as Condorcet's method because of its equivalence with
> > Cloneproof SSD.
> > ,
> > >and is Condorcet voting currently considered the best option
> > >for a single winner race?
> >
> > It's the most popular method on EM for that purpose. An increasing 
>number
> > of people consider Condorcet's method to be the best single-winner
> > method.
> >
> > Mike Ossipoff
> >
> > Check these websites:
> >
> > http://www.electionmethods.org
> >
> > http://www.barnsdle.demon.co.uk/vote/sing.html
> >
> >
> >
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> >
>

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