Copeland Strategy

[Mike Ossipoff]

But before I get to Copeland, I just want to add something about
Coombs, something that I inadvertently left out when replying
to Don about divided votes. The whole benefit of Coombs is
that, as I said, it eliminates from the extremes, because
, if there's a 1-dimensional political spectrum, everone's last
choice is at one of the very extremes of the spectrum. But if
you neglect to rank a few of your last choices, and Don divides
that last choice between them, instead of honestly counting them
as your the last choices expressed on your ballot, and
if some others do the same, then those candidates won't be
getting the last choice count that they'd otherwise get,
and Coombs no longer is sure to leave the Condorct winner
un-eliminated. And it no longer meets LO2E-2. Or, to put
it differently, it won't work. People won't be satisfied
with its results. But I shouldn't be advising Don about
his proposal. I should let him do it as he wants, even
if it doesn't work. Coombs, after all, though it's better
than most (if done right), isn't really my recommendation.

***

Now, about Copeland:

I want to say a few more things, just to thorougly lay Copeland
to rest, by pre-emptively answering things that someone might
say later.

Even if someone challenges the strategic aspects of the scenariois
that we've given for the Rich Parties problem (and I'll get
to such challenges later), that doesn't change the fact that
it makes no sense at all for the winning party to depend on how
many candidates the various parties run, or how many people
of each persuasion run. 

I've previously worded this in terms of a situation where we're
going to vote on what movie to go to on a particular evening,
and there are Westerns, adventure movies & crime dramas.
Because we tend to like some genres more than othrs,
all the Westerns beat all the adventure movies, all the
adventure movies beat all the crime dramas & all the crime
dramas beat all the Westerns. There only are a few crime
dramas playing, though they're all excellent, and have lots
of advocates in our group. There are lots of adventure movies
playing. So of course Copeland picks a Western for no reason
other than that there aren't many crime dramas playing. 
Excuse me, but that's a ridiculous reason to pick something.
Copeland is nonsense.

And even if we grant (which I'm sure we don't) that the
number of movies movies, of a particular genre, that are
playing has some kind of relevance for the choice of a genre,
and thereby disqualify the crime dramas, that would suggest
choosing an adventure movie instead of a Western, since 
there are more adventure moving playing than any other
genre. No, we pick a Western because there are few
crime dramas playing. Nonsense.

***

In the example that I posted the other day, with 3 parties
& 5 candidates, someone could object: "If the C voters prefer
B to the A candidates, then the C party would un-co-operate with
the A party, by only running 1 candidate. That way, B would
n longer have fewer candidates than any other party,
and it would be a Copeland tie between A1 & B. In Regular
Champion, A1 would win--and Regular Champion has been Bruce's
main proposal, as I've understood him. But in 
Fishburn//Copeland//Condorcet, or just Copeland//Condorcet,
B would win, sinc Condorcet is the tie-breaker. Of course it
would be better to just use Condorcet instead, if we can
only save Copeland by Condorcet :-)  That way no party
]would have to strategize when it picks candidates in
order to foil the A strategy & elect the Condorcet winner.

***

At this point, it would be good to put Condorcet strategy in
a simpler way than last time, without the algebra. There's
a briefer way of demonstrating the same thing:

Say there are 3 parties in a circular tie where all the A candidates
beat all the B candidates beat all the C candidates beat all the
A candidates (Yes, I know this order is different from my
example, but it doesn't matter). And say that, in each party, there's
a candidate who beats each of that party's other candidates.

Now, say we add a candidate to a certain party (A). That adds one
Copeland point to the Copeland score of that party's strongest
candidate, and adds a point to the score of the party that beats
A. And it adds a negative point to the party that A beats.

The overall effect of this, then, is to give a point to each
party except the one that A beats, and to take a point from
the party that A beats. This is really the same as just giving
2 negative points to the party that A beats. Now, let's change
the meaning of "point" by saying that this gives a negative
point to the party that A beats. A "point" now means 2 Condorcet
points.

So adding a candidate to a party gives a negative point to the
party that it beats.

>From that it follows that the winning party will be the one
that is beaten by the party with fewest candidates. Just
as I showed last time.

***

So here's another defensive strategy: party B, if we ignore the
fact that campaigns cost money, could run 2 candidates instead
of 1. The 2nd one could be a frank duplicate of the other, 
specifically promising to do exactly what the other would
do. A duplicate candidate for purely strategic purposes.

Well let's go back to my old B beats A beats C beats B example,
where B is the middle Condorcet winner. Party C knows that the
A voters might truncate, either strategically or innocently, and
wants to make sure that this won't give the election to A1. They
know that party C won't win, so they protect B by only running
1 candidate. This is known before the election, and party
A would likely run 2 candidates also. But as long as B runs
2, & C runs 1, A can't possibly win. So A could advise its
people to not truncate. But knowing that a lot of people do
anyway, A at least ensures that it's B that wins, by A running
2 candidates.

This means that party B has a sound & dilemma-free winning strategy
in Copeland, when there are just 3 parties. Lots of methods are
problem-free in a 3-candidate election, including Condorcet,
Bucklin, Stepwise-Plurality.

But note that, even in the 3-candidate election, Copeland
requires Duplicate candidate strategy on the part of B, and
requires party C to have the organization needed to make sure
that either no other C candidates run, or that its voters won't
vote for them if they do. And that's even with just truncation.
Condorcet doesn't require any strategy against truncation. 
Condorcet doesn't require any defensive strategy at all 
unless order-reversal is likely. That sets Condorcet apart
from every other method.

And that 3-party Copeland strategy doesn't work anymore if there
are more parties, & it isn't known which has the Condorcet winner,
which party would beat each of the others in 2-party elections.

***

The point is just that someone could later say that party C
wouldn't run 2 candidates; but Copeland still has more strategyk
problems. Condorcet's properties that I've talked about applyk
no matter how many parties or candidates there are. Copeland
doesn't have those properties, and that goes for Regular Champion,
Fishburn//Copeland//Condorcet, & any other Copeland version
that Bruce or anyone comes up with.

As I said, a method that chooses a category according to how
many alternatives are in the category that beats it is
nonsense. Copeland is nonsense.

***

Mike









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