[EM] Pairwise winner of the 2 least-beaten

Mike Ossipoff dfb at bbs.cruzio.com
Sat Mar 2 17:01:49 PST 1996

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

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

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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