[EM] More rank-method proposals and comments on new proposals

[Michael Ossipoff]

I didn't name this proposal:

1. Determine defeats a la Symmetrical ICT

2. Discard defeats that are in cycles

3. If exactly one candidate is unbeaten, s/he wins

4. If all or no candidates are unbeaten, elect the most top-ranked

5. If some, but not all, candidates are unbeaten, elect the most
top-ranked unbeaten candidate.
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I'll call it NC Symmetrical ICT

(NC stands for "no cycles")

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It reminds me of something that I proposed a long time ago, which I
called the "subcycle rule": Others have independently later proposed
it. It seems to me that it turned out to have some problem that made
it not a good idea.

Whatever the method is, to "replace a cycle" means to apply the method
to the members of that cycle, and replace the cycle with the winner.

Replace every cycle that doesn't contain,as an element, a smaller
cycle. Repeat till there are no cycles.

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Every rank method that I've proposed after Symmetrical ICT is proposed
tentatively.

Let me tentatively propose this:

CR Symmetrical ICT.

Determine defeats according to Symmetrical ICT.

Do cycle replacement, as defined above, with Symmetrical ICT as the method.

Apply Symmetrical ICT to the remaining candidates..

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I don't know which, if any, of Symmetrical IC-Schwartz-Top, NC
Symmetrical ICT, CR Symmetrical ICT, Symmetrical iC-Beatpath(lv), or
Symmetrical IC-Rankded-Pairs(lv) are any good. My favorite of those is
Symmetrical IC-Schwartz-Top, but I'm not sure.

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For polling, the Condorcet Criterion might be desirable.

If it's desired to do the best toward finding the CW, by encouraging
complete sincere rankings, then ordinary ICT would be better than
Symmetrical ICT, though no rank method really would encourage sincere
rankings, for reasons that differ between methods.

But if there are lots of candidates, and people wouldn't want to rank
them all, and it's desired to not discourage voting, then Symmetrical
ICT would be better, with an assurance that there's no need to rank
unacceptable candidates.
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But suppose that people insisted on a ranked-method for official
public elections?

Maybe someday people will be interested in doing the very laborious
handcounts needed by the rank methods, and dedicated enough to
democracy to be willing to do that work. Maybe rank-method
handcounting will be regarded as a good, socially productive source of
lots of employment.

In official public elections, it would be best to be able to assure
people that they needn't rank unacceptables,and so Symmetrical ICT
would be better than ICT.

MMC would be desirable, whether for official elections or for polling.
Methods such as Symmetrical IC-Schwartz-Top (if they don't have a
problem that I don't know of) would gain it at the cost of trading FBC
for 0-info non-top FBC (Weak FBC).

AOCBucklin would get it by trading the Condorcet Criterion for it.
Because I don't consider CC important in public elections, compared to
the other criteria that I advocate, then that could be a good trade.
But in order to get MMC, while keeping full FBC, comes at the cost of
having defection-resistance that isn't quite as good as that of the
ICT methods.

An advantage of AOCBucklin for public elections is that it can be
offered as an option in an Approval election. An option would be
easier to propose and enact than a new method. There's something
appealing about giving people a choice, in an election, between
methods as diverse (though related) as Approval and AOCBucklin.

A disadvantage of AOCBucklin is that the AOC part of it can't really
be defined without a computer program. And the program-section that
gives it the delay that confers MMC compliance greatly increases the
length and complexity of its computer program--not that the count
would be done by computer, because computer counting will probably
never be fraud-secure.

I don't know which of those methods' criterion and properties
combinations would be best. It would depend on the desirability of FBC
vs Weak FBC, compared to the desirability of ICT's better
defection-resistance vs that of AOCBucklin, and the desirability of
MMC vs Condorcet. As for the latter, MMC is almost surely more
desirable in official public elections, as compared to CC.

But, other than ICT, Symmetrical ICT and AOCBucklin, I don't know if
any of these rank methods that I've been proposing would have some
prohibitive problem that I don't know about, or if they really meet
the criteria that they seem to meet.

If there's some reason why merely disregarding defeats that are in
cycles, as opposed to choosing from the Schwartz set, wouldn't achieve
MMC for ICT, then I don't know why not. But I'm not saying that there
isn't. As for Clone-Independence, I realize that ICT's top-count
spoils that.

Isn't the possibility of cycles among the majority-preferred set of
candidates the only reason why ICT doesn't meet MMC?

Mike Ossipoff













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