Condorcet tie-breaking (was Re: Multiple Same Choices)

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Condorcet tie-breaking (was Re: Multiple Same Choices)

Craig Carey-2
Mike O. wrote:
>Your suggestion to solve circular ties by a 2nd balloting is ok,
>and I wouldn't object to it. But no one likes a method that requires
>a 2nd balloting.

Here's another proposal for breaking the circular tie:

Calculate which two candidates (A and B) were "least beat".
If A pairwise-beat B then A is the winner;
else hold a runoff between the two.

This way, a runoff wouldn't always be necessary and the electorate
will probably be satisfied with the results.

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Pairwise winner of the 2 least-beaten

Craig Carey-2
That wouldn't work out, picking the pairwise winner of the two
least-beaten candidates. Say Clinton is Condorcet winner in a
Buchanan, Clinton, Nader race. And say the Buchanan voters are so
devious that they rank Nader over Clinton, to create a circular tie,
hoping that Buchanan will win the circular tie. The Buchanan voters
know that Buchanan beats Nader, and so they make Nader beat Clinton
real big. So big that Buchanan & Nader are the least beaten candidates.
Since the Buchanan voters know that Buchanan beats Nader, they know that
their candidate will win the circular tie, when it's solved in that
way.

There's nothing the Clinton voters can do to defend against that
offensive strategy. The only defense would be for the Nader voters
to vote Clinton in 1st place, and not vote Nader in 1st place.

But with Condorcet's method, the Clinton voters can make that offensive
strategy impossible by simply not voting a 2nd choice. Then, Buchanan,
who has a majority against him, since the Nader+Clinton majority ranks
Clinton over him, has no way to beat Nader with a majority, since the
Buchanan voters aren't a majority (if they were, Buchanan would be
Condorcet winner).

So then, Condorcet's method has an easy defensive strategy for Clinton
voters to thwart that offensive strategy by the Buchanan voters.

***

So, in that situation, the Clinton + Nader majority can easily
prevent Buchanan from being the least beaten, and from winning. Not
so if we pick the pairwise winner of the two least beaten candidates.

***

Another thing: Say, again, Clinton is middle Condorcet winner, and
Buchanan beats Nader. This time the Buchanan voters don't use
order-reversal, but some of them, on principle, just can't
bring themselves to vote for Clinton. Or maybe some of them just
don't bother, or don't believe in rank-voting, or are in a hurry
to an appointment on voting day, etc. So some of the Buchanan
votrs, for innocent reasons, don't rank Clinton.

What happens with Condorcet's method? Buchanan again has a majority
against him (Clinton + Nader voters). Nader has the Buchanan voters
against him. Clinton, whom the Buchanan voters have allowed to be
beaten by Nader, has the Nader voters against him. Of these sets
of beating-voters, the smallest set is the Nader voters, and so
Clinton is the least beaten & wins. The innocently-intended bullet-
voting of the Buchanan voters hasn't kept the Condorcet winner from
winning.

You might say, why is that important? If Buchanan voters don't vote
for Clinton, doesn't that mean they deserve Nader? No, because
they didn't intentionally try to sabotage Clinton. Sure, if Nader
might beat Buchanan, then the Buchanan voters can't be saved from
the consequences of their bullet-voting--a Nader victory. No method
could save them in that case. But it isn't necessary to have a method
that penalizes short rankings beyond that. That penalizes short rankings
by Buchanan voters even if Buchanan beats Nader.

Besides, who says all the Buchanan voters deserve that? I said that
_some_ of them didn't vote for Clinton. The ones who did vote for
Clinton in 2nd place would feel that it isn't entirely fair
what happened to the Buchanan voters due to the mistake made by
some of them. And what about the Clinton voters? The unnecessary
defeat of the Condorcet winner, Clinton, hurts the interest of
a lot of Buchanan & Clinton voters.

In a rank-balloting election, I don't want to have a short ranking
backfire against me when it doesn't have to. Even if it's my short
ranking, but especially if it's someone else's.

I'm not saying that this short-ranking aspect of it is all that
crucial to fairness, but it's desirable to elect the Condorcet
winner as reliably as possible. Condorcet's method does.
It's best to elect the Condorcet winner, the candidate who'd beat
each of the others in separate 2-way elections.

What happens if we pick the pairwise winner of the two least-beaten
candidates? Well Buchanan has a majority against him, and Clinton
doesn't, and Nader doesn't unless the Clinton voters contribute to
one, which they might not do. In that case, Clinton & Nader are the
2 who are in that final 2-way comparison, and, of those 2, Nader
beats Clinton, since the bullet-voting Bucnanan voters have allowed
him to. So Nader wins instead of Condorcet winner Clinton.

The earlier example, the order-reversal one, is important, not because
order-reversal on a significant scale is plausible in a public election,
but because Condorcet's method is ready for it if it did happen. If the
order-reversal succeeded in that example, that would mean that the
majority (Nader + Clinton) who ranked Clinton over Buchanan, in order
to keep Buchanan from winning, wouldn't get what they all want. That
is the failure that we want to avoid with single-winner reform. Condorcet
doesn't need strategy to enforce that majority's wishes unless order-reversal
is attempted, and, even then, it doesn't require a defensive strategy
that includes not voting one's favorite in 1st place.


Mike Ossipoff
 



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Re: Pairwise winner of the 2 least-beaten

Craig Carey-2
Mike O. wrote:
>That wouldn't work out, picking the pairwise winner of the two
>least-beaten candidates. Say Clinton is Condorcet winner in a
>Buchanan, Clinton, Nader race. And say the Buchanan voters are so
>devious that they rank Nader over Clinton, to create a circular tie,
>hoping that Buchanan will win the circular tie.

To what did your message reply?  You changed the subject line and
didn't quote anything from the original.

>The Buchanan voters know that Buchanan beats Nader, and so they
>make Nader beat Clinton real big.  So big that Buchanan & Nader are
>the least beaten candidates.

How does Buchanan beat Nader if a majority rank Buchanan last?

I tried playing with some numbers but didn't get them to come out
meeting all your conditions, then got tired.  <grumble>  Could you
post some vote numbers to make your examples (now and in the future)
easier to follow?  They'll make good test cases that all the
algorithms can be judged on.

--Steve

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Re: Pairwise winner of the 2 least-beaten

Craig Carey-2
Steve Eppley writes:

>
> Mike O. wrote:
> >That wouldn't work out, picking the pairwise winner of the two
> >least-beaten candidates. Say Clinton is Condorcet winner in a
> >Buchanan, Clinton, Nader race. And say the Buchanan voters are so
> >devious that they rank Nader over Clinton, to create a circular tie,
> >hoping that Buchanan will win the circular tie.
>
> To what did your message reply?  You changed the subject line and
> didn't quote anything from the original.


I'm going to start making more use of copies in my replies.

You suggested that circular ties be solved by determining which 2
candidates are the 2 least-beaten ones, and choosing, as the winner,
the one of those two who beats the other in a pairwise comparison. It's
to that proposal that that letter is a reply.

>
> >The Buchanan voters know that Buchanan beats Nader, and so they
> >make Nader beat Clinton real big.  So big that Buchanan & Nader are
> >the least beaten candidates.
>
> How does Buchanan beat Nader if a majority rank Buchanan last?

No majority ranks Buchanan last. A majority ranks Clinton over Buchanan.
Buchanan beats Nader because either he has more 1st choice voters,
or he has help from the Clinton voters, or both.
If Buchanan has more 1st choice voters than Nader, then he of course
beats him unless the Clinton voters favor Nader sufficiently.

>
> I tried playing with some numbers but didn't get them to come out
> meeting all your conditions, then got tired.  <grumble>  Could you
> post some vote numbers to make your examples (now and in the future)
> easier to follow?  They'll make good test cases that all the
> algorithms can be judged on.


Example:

40%: Buchanan, Nader, Clinton  (order-reversal cheating attempt)

25%: Clinton   (defensive truncation to thwart order-reversal)

35%: Nader, Clinton  (the side needing the compromise votes for him)

A 60% majority prefer Clinton to Buchanan. Buchanan beats Nader
40 to 35.

***

What happens in this scenario, using the 2 circular tie solutions,
Condorcet's method & the one that picks the pairwise winner of the
2 least beaten candidates?

Circular tie: Nader beats Clinton beats Buchanan beats Nader.

First, by Condorcet's method, the Buchanan cheaters can't do anything
about the fact that Buchanan has a majority against him--a 60%
majority (Clinton + Nader) have voted Clinton over him. Nor do they,
on their own, have the power to make anyone else be beaten with a majority
against him. By ranking Nader over Clinton they, with the Clinton voters'
help, cause Clinton to be beaten with 75% against him. That makes Clinton,
by far, the most beaten candidate. But, not having the help of the Clinton
voters, the Buchanan voters, who don't constitute a majority, have no
way of making Nader be beaten with a majority against him. So Nader only
has 40% against him. Therefore Nader, with only 40% against him, is the
the winner by Condorcet's method.

The defensive truncation strategy by the Clinton voters has made it
impossible for the Buchanan voters to gain by order-reversal, and has,]
in fact soundly punished them for trying it. The mere knowledge that
the Clinton voters expect order-reversal, and (especially since they
have no real reason to vote for a 2nd choice) are going to truncate,
will deter order-reversal.

***

Now, what about the count rule that says to find the 2 least beaten
candidates, and pick as the winner the one who beats the other in a
pairwise comparison?

As I said, Clinton is, by far, the most beaten candidate, meaning that
Buchanan & Nader are the 2 least beaten ones. Of those 2, Buchanan
beats Nader, and therefore wins by that rule.

That means that the offensive strategy of the Buchanan voters, the
order-reversal cheating, has succeeded. The  mere fact that they
can beat Nader means that they can win in this way if they add their
votes to those of the Nader voters in order to make Clinton be
_badly_ beaten.

***

So my point was that the offensive strategy of order-reversal cheating
isn't rewarded in Condorcet's method, when a simple defensive strategy
is used. Since Clinton voters really have no reason to vote a 2nd choice,
no one would really order-reverse in this 3-way election, using Condorcet's
method, though they could get away with it much more easily in other methods.

***

Mike

>
> --Steve
> .-
>


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Re: Pairwise winner of the 2 least-beaten

Craig Carey-2
In reply to this post by Craig Carey-2
Mike O. wrote:
>You suggested that circular ties be solved by determining which 2
>candidates are the 2 least-beaten ones, and choosing, as the winner,
>the one of those two who beats the other in a pairwise comparison. It's
>to that proposal that that letter is a reply.

No, I suggested:
If the least beat also pairwise-beat the 2nd least beat,
then the least beat wins.  
Else a runoff between the two.

Mike's example:
>40%: Buchanan, Nader, Clinton  (order-reversal cheating attempt)
>25%: Clinton   (defensive truncation to thwart order-reversal)
>35%: Nader, Clinton  (the side needing the compromise votes for him)

Tie-break summary:
Nader    -40%
Buchanan -60%
Clinton  -75%

Since Nader (the winner in plain Condorcet) is least beat but
Buchanan beat him, we get a runoff between Nader and Buchanan.  This
gives the Clinton voters a chance to vote for Nader, so Nader wins
runoff.  

The runoff costs time and money, but it squelches the claims of the
Buchanan crowd that they were robbed by a weird voting system.  This
was the point of my proposal.

Thanks for the example numbers.  They make it so much easier for me
to understand.  I hope we make this a universal practice.

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Re: Pairwise winner of the 2 least-beaten

Craig Carey-2
Steve Eppley writes:

>
> Mike O. wrote:
> >You suggested that circular ties be solved by determining which 2
> >candidates are the 2 least-beaten ones, and choosing, as the winner,
> >the one of those two who beats the other in a pairwise comparison. It's
> >to that proposal that that letter is a reply.
>
> No, I suggested:
> If the least beat also pairwise-beat the 2nd least beat,
> then the least beat wins.  
> Else a runoff between the two.
>
> Mike's example:
> >40%: Buchanan, Nader, Clinton  (order-reversal cheating attempt)
> >25%: Clinton   (defensive truncation to thwart order-reversal)
> >35%: Nader, Clinton  (the side needing the compromise votes for him)
>
> Tie-break summary:
> Nader    -40%
> Buchanan -60%
> Clinton  -75%
>
> Since Nader (the winner in plain Condorcet) is least beat but
> Buchanan beat him, we get a runoff between Nader and Buchanan.  This
> gives the Clinton voters a chance to vote for Nader, so Nader wins
> runoff.  
>
> The runoff costs time and money, but it squelches the claims of the
> Buchanan crowd that they were robbed by a weird voting system.  This
> was the point of my proposal.
>
> Thanks for the example numbers.  They make it so much easier for me
> to understand.  I hope we make this a universal practice.
> .-
>
There's no guarantee that all the Clinton voters will vote for Nader
over Buchanan. Even if most of them do, Buchanan can still win, since
he has so much more 1st choice support. If that happens, then the
Nader voters who thought they were safe voting Clinton in 2nd place,
because this would count toward Clinton winning instead of Buchanan,
if Nader can't win will wish that they'd abandoned their favorite &
voted for the un-liked "lesser-evil" Clinton in 1st place. That's what
we want to avoid.

Never only inlcude 2 candidates in a 2nd balloting. Whether, as in
Runoff, we hold a 2nd balloting whenever no one gets a 1st choice
majority, or whether we use a 2nd balloting to solve a circular tie,
the 2nd balloting has got to include all of the candidates (or at
least all of the candidates in the circular tie).

I have nothing against saying "If the least beaten candidate doesn't
beat the 2nd least beaten candidate, then hold a 2nd balloting between
all the candidates (or all the candidates in the circular tie). As
far as results are concerned, that's ok. But I warn that it's an added
rule that complicates the definition, and that if people accept the
importance of those 2 least beaten candidates, they'd just as well
be willing to just elect the least beaten one, and not do a 2nd
balloting.

***

Though Condorcet's method is my actual public proposal, I
non-publicly propose 2 other very good methods which sometimes
require a 2nd balloting:

Runoff-Pairwise (or BeatsAll-Approval):

In the event of a circular tie, hold a 2nd balloting between all the
candidates (or all the candidates in the circular tie), by Approval.


Condorcet-Approval:

Use Condorcet's method, but if every candidate (or every candidate
in the circular tie) is beaten with a full majority against him,
then hold a 2nd balloting between all the candidates (or all the
candidates in the circular tie).

My main purpose with these two 2-balloting methods would be for
devious electorates. Though order-reversal can create a circular
tie, it can't get you anywhere in that 2nd balloting. I'm not saying
these 2-balloting methods are _necessary_ for devious electorates, only
that they'd be a convenient simple way to eliminate even what small
amount of strategy dilemma Condorcet's method could have.

Of those two 2-balloting methods, Condorcet-Approval is the more
deluxe one, since it doesn't require a 2nd balloting nearly as often.
If order-reversal causes a circular tie that could otherwise make
the cheaters' candidate win, then Condorcet-Approval automatically
detects it & calls for a 2nd balloting, since such a circular tie will
be one in which everyone is beaten with a full majority against them.
Otherwise, rarely will everyone be that beaten, and so, with
Condorcet-Approval, Condorcet's count rule will ordinarily solve
circular ties without there being need for a 2nd balloting.

As I said, BeatsAll-Approval (Runoff-Pairwise) is good for groups
that agree on Pairwise-Count, but don't agree on how to solve
circular ties.

***

Mike



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