iterated Condorcet checks out

[Mike Ossipoff]

The Iterated Condorcet method recently proposed by Steve seems to
go quite a long way to make successful offensive strategy even
less feasible than it would be in ordinary Condorcet. In other words,
it seems to work well.

My examples here have nearly all used just 3 candidates, for the
sake of simplicity, and because MPV (Hare, Instant-Runoff, Alternatiave
Vote, Elimination) & Runoff & Borda & Copeland (including Regular
Champion) will all gladly & co-operatively screw up for us in
a 3-candidate example.

But, to make Condorcet even have the possibility of a conceivable
problem, it's necessary to have at least 4 candidates, and an
uncertainty about which of at least 2 is a middle Condorcet winner.

But I needed at least 5 candidates to find a possibility of
making offensive strategy work, with Iterated Condorcet. 
5 candidates, and an uncertainty about which of at least 3
candidates is middle condorcet winner.

And, more than that, successful offensive strategy would
require _much_ more sophistication, in Iterated Condorcet.

I don't consider it a problem in regular Condorcet, but in
Iterated Condorcet it becomes very much more demanding
of an elaborate plan, a 2-stage strategy, like when someone
plans several moves ahead in chess, hoping that the other player
will co-operate & fall into an elaborately laid-out trap.

In this letter, I'm not giving an example of successful offensive
strategy in Iterated Condorcet, because I don't have one yet. I'm
just going to send a rough description of the kind of thing
that an offensive strategist might try for. Whether it would
even really be possible, I don't know. The fact that none of us,
who are interested in this topic, have written an example of
successful offensive strategy in that method yet underlines
the un-likeliness that a typical voter would find & attempt
such a strategy, or that it could even be easily explained to
him how to do it. And if even if it's possible to do, it would
require so much publicity, to reach a sufficient number of
voters, that surely its intended victims would be tipped off.
And offensive strategy in Condorcet, with tipped-off victims,
is a losing proposition. Though I've said that about regular
Condorcet, it's true to a much greater degree with Iterated
Condorcet, due to the complexity of the strategy.

Before outlining the cheat-possibility, I should add that
someone might say that offensive strategy is virtually impossible
in MPV. Sure, but MPV doesn't need offensive strategy on the part
of voters, because the MPV method itself will often cheat the
Condorcet winner out of his win, necessitating defensive strategy
on the part of voters, even without any offensive strategy by other
voters.

***

Say it's a 5-candidate election, and the candidates are A, B, C,
D, & E. There's a 1-dimensional political spectrum, and the 
candidates' order of positions on that spectrum are as written.
I other words, A is at 1 extreme, E is at the other extreme,
and C is in the middle, with 2 candidates to each side in the
political spectrum, though not necessarily really halfway between
A & E.

D is the Condorcet winner, but the D & E voters don't know that,
and so they extend their rankings farther. For all they know,
A might win if they don't give support to B over A. In fact, they
feel that they need to protect at least C with the option to move
him up to 1st choice if someone worse wins.

The A, B, & C voters are much more sophisticated than the D & E
voters, and have it all planned out. They create a circular tie
that B will win--possible only because the D & E suckers believe
they need to vote B over A.

So far it's like regular Condorcet. But when B wins the 1st count,
the D & E voters, or at least the D voters, move C up to 1st place,
to prevent B from keeping its order-reversal win (this of course
happens automatically, because the D & E voters have selected that
option on their ballots).

So the D voters now have C ranked equal to D on their ballots.

Because D is Condorcet winner, C initially had a majority against
him, from the D & E side. But not anymore. Now that the D voters 
have moved C up to 1st place, C might no longer have a majority
against him. In fact, in the circular tie, C might now have
the fewests votes against him in a defeat.

***

So that's how successful offensive strategy _might_ be able
to happen in Iterated Condorcet. As I said, I haven't written
an example yet, and so I don't know if one can be written.
Any strategy that the members of this list have trouble with
isn't very feasible in a public election!

***

If one wanted to make it even harder to succeed with offensive
strategy, then it would probably take the kind of options
that I hinted at, based on order-reversal indicators that
the election computer could test for, and act on, on a voter's
behalf, if he/she chose that option.

But it hardly seems necessary to further thwart order-reversal,
beyond the degree to which Iterated Condorcet does so.

In fact, it seems to me that large scale order-reversal would
be so unlikely in a public election that the ordinary Condorcet
versions that we've already discussed would be perfectly sufficient.
Sure, it's good to have perfecting refinements available as a backup,
in case they're needed, but the ordinary Smith//Condorcet &
plain Condorcet methods are perfectly adequate for public sw
reform proposals. At leasts for a 1st public proposal. I'd add
perfecting refinements, like the iteration, if & when an order-
reversal problem actually materialized.

Of course, on the other hand, Iterated Condorcet isn't appreciably
more complicated. Its iteration rule isn't complicated. So I'm
certainly not saying that I oppose Smith//Iterated-Condorcet
as a public proposal.


Mike








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