[EM] ICT definition. Presumed Kemeny definition.

[Michael Ossipoff]

ICT:

Kevin Venzke proposed ICA. Improved-Condorcet-Approval.

ICA  passes FBC. The part of ICA that ICT uses is the Improved Condorcet
part. But instead of completing IC with
Approval, it completes it by electing the IC winner ranked top on the most
ballots.

ICT was introduced by Chris Benham. He gave it a longer name with longer
abbreviation-initials. I'm calling it ICT,
consistent with Keven Venzke's naming of ICA.

ICT definition:

(as described by Chris Benham, unless I've made an error)

Iff the number of voters ranking X over Y, plus the number of voters
equal-top-rating X and Y, is greater than the
number of voters ranking Y over X, then X "beats" Y.

Of course that's a very weak meaning for "beat", and it's possible for X
and Y to both beat eachother in that sense. Of course, when
I say "beat" (with or without the quotes), I mean it in the above-defined
sense.

If there's exactly one beats-all candidate (candidate who beats all of the
others), then s/he wins.

If not, then the winner is the beats-all candidatate who is ranked in 1st
place on the most ballots.

[end of ICT definition]

As I said, ICT meets FBC, and is defection resistant. Maybe so
defection-resistant as to be called defection-proof.

If Kevin &/or Chis are listening right now, I have a question:

What if, instead of defining "beat" as above, I said:

X is unbeaten by Y iff the number of voters ranking X over Y, plus the
number of voters equal-top-ranking X and Y, is at least equal
to the number of voters ranking Y over X.

If there is exactly one candidate not beaten by anyone, then s/he wins.

Otherwise, the winner is the unbeaten candidate who is ranked in 1st place
on the most ballots

[end of questioned alternative definition of ICT]

Would that still meet FBC and be defection-resistant? Would it lack some
other desirable property,
or acquire some undesirable property?

Kemeny:

I've read this definition of Kemeny:

The Kemeny ranking is the ranking of the candidates that most agrees with
the voters'
ordering of the candidates.

To elaborate a little:

The Kemeny ranking is the ranking of the candidates which, among all
possible rankings of
the candidates, has fewest disagreements with the voters' rankings
regarding candidate-pair-orderings.

To elaborate a little more:

Consider some particular ranking of all the candidates, which we'll call
the "comparison ranking":

Comparing the comparison ranking to some particular voter's ranking, count,
for every possible
pair of candidates, X and Y, the number of instances in which those two
rankings differ in the matter
of whether  X is ranked over Y, or vice versa. Each such instance counts as
a "disagreement"

(Presumably, if one of those 2 rankings ranks X and Y equal, that counts as
half of a disagreement)

The Kemeny ranking is the ranking of all the candidates that has the fewest
disagreements, counted over
all of the voters' rankings.

The winner is/are the candidate(s) at the top of the Kemeny ranking.

[end of presumed Kemeny definition]

Kemeny sounds democratic enough, but it's said that it requires much more
computation time than Condorcet.

I've heard it said that, with a lot of candidates, with modern computers,
counting an election might take more than
a reasonable amount of time. Vastly more time than Condorcet would take.

It's recently been said on EM that Kemeny's properties are like those of
Condorcet, except that it meets one
additional criterion, called the Reinforcement Criterion. I don't know what
that criterion says.

Kemeny fails FBC.

Unless someone can show otherwise, prudence dictates that we assume that
Kemeny is not defection-resistant.

According to the recent (maybe still ongoing) discussion about VoteFair and
Kemeny, VoteFair is quite similar
to Kemeny, and gives the same result under some, but not all,
circumstances. Kristofer says that, at least probably,
VoteFair doesn't meet both Condorcet's Criterion and Reinforcement--two
criteria met by Kemeny.

I don't consider Kemeny or Condorcet suitable proposals, because FBC
failure, and lack of defection-resistance.
I said more about that in my previous post.

Yes, Approval isn't defection-resistant either, but I expect more from a
rank method. To significantly improve on Approval
requires defection-resistance. No rank method should be considered unless
it is both FBC-complying and defection-resistant.

The reason why I'd probably prefer ICT to Approval is its defection
resistance. Its rank-balloting expressivity is, for me, only
a slight improvement over Approval. I'd probably use rankings between top
and bottom mostly only to use ICT's defection-resistance.

But also, with ICT and ABucklin, I'd might sometimes rank, below top and
above bottom, a few candidates merely because they'd very nearly
qualify to be approved in approval, or because they'd very barely qualify
to be approved in Approval. Those are the same candidates whom I'd
middle-rate
in MCA or MTA.

Mike Ossipoff






Mike Ossipoff
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