Coombs meets LO2E-2

[Mike Ossipoff]

Coombs' method, like Condorcet, Smith//Condorcet, Simpson-Kramer,
Bucklin, & Stepwise-Plurality, meets LO2E-2.

But, like Bucklin & Stepwise-Plurality, Coombs fails Condorcet's
Criterion, GMC, NPL, & NML. It of course, then, also doesn't
honor the basic democratic principles on which Condorcet's
Criterion & GMC are based.

Still, because Coombs, Bucklin & Stepwise-Plurality meet
LO2E-2, they're still pretty good, 2nd best after Condorcet,
Smith//Condorcet, & Simpson-Kramer.

***

If we were now voting among all of the methods proposed here,
or likely to be proposed for public elections, my ranking would
start out...

1. Condorcet & Smith//Condorcet
2. Simpson-Kramer
3. Coombs
4. Stepwise-Plurality
5. Bucklin

Of course no one has proposed Bucklin or Stepwise-Plurality
for EM recommendation, but someone has proposed Coombs, so it
would be in my ranking, right after Condorcet & Smith//Condorcet.
(No one has proposed Simpson-Kramer here either).

So, if another count were to be conducted for our EM vote,
I'd simply add Coombs right below Condorcet & Smith//Condorcet.
My only other change would be to list Condorcet & Smith//Condorcet
as 1st choices.

Of course any method that doesn't meet them already would be
improved if mitigated by requiring compliance with Condorcet's
criterion & GMC, or NPL & NML.

***

I've defined LO2E-2 in full here, but a brief way of putting
it could be: A method meets LO2E-2 iff a full majority who
rank A over B have a way of voting whereby they can ensure
that B won't win, and this doesn't require that they vote
a less-liked alternative equal to or over a more liked one.

That isn't my full & complete definition, which I've previously
posted on EM.

(Refusal to rank B doesn't count, here, as ranking a less-liked
alternative equal to a more-liked one, even though it does
treat B equally with things liked less than B, which are also
unranked).

***

In Bucklin, Stepwise-Plurality, & Coombs, the way to ensure
that B won't win is to refuse to rank it.

Not that that's always necessary. But it always works. Sometimes
Bucklin &, especially, Stepwise-PLurality will elect the Condorcet
winner even if no one observes that strategy. But when conducting
an election by either of those 2 methods, one should advise voters
to try to avoid extending their rankings farther than necessary,
to avoid ranking anything less-liked than what they consider
to be the likely necessary compromise.

I'd also suggest giving that advice in a Coombs election. But
in Coombs, you could also tell voters that if there's a 1-dimensional
political spectrum, and if a majority that you belong to can
agree on how the alternatives are ordered on the political
spectrum, then the method should work very well even if people
extend their rankings too far. It will still elect the Condorcet
winner then, instead of someone liked less by that majority.

To me, that's what makes Coombs better than Bucklin or Stepwise-
Plurality.

***

I've heard a few criticisms of Coombs' method:

1. "It isn't monotonic"

That means that voting someone lower can make him win, or
voting someone higher can make him lose. But I don't know of
a way that can happen in Coombs unless there's a split-vote
for last choice, and that's avoidable (by agreeing on
political spectrum ordering, or just voting rankings that
aren't unnecessarily long).

2. "It encourages people to insincerely rank a rival last"

But if that's just done by truncation, it doesn't accomplish
anything, at least in 3-candidate elections. In Condorcet
it doesn't accomplish anything in any elections, and that
may very well be true of Coombs also.

And if it's done as order-reversal, then it is thwarted, punished,
& deterred by defensive truncation, as a defensive strategy.
And, as we've discussed, order-reversal is unlikely in a public
election anyway.

If a majority rank something last (by not ranking it), that
majority also has the power to ensure that there's at least
1 other alternative that doesn't have that honor.

***

Mike 






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