[EM] Correct Weak FBC definition. Method comparison under various conditions. AOCBucklin definition.

[Michael Ossipoff]

Weak FBC:

If the winner is a candidate top-voted on a certain ballot, then
raising an additional candidate to top on that ballot shouldn't cause
the winner to be someone not then top-voted on that ballot, by letting
that candidate beat an already top-voted candidate. If the election is
0-info, then moving that additional candidate to top shouldn't
decrease the probability that a candidate top-voted on that ballot
wins.

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Weak FBC could be called Non-Top 0-info FBC.

It's intended to describe the degree of FBC protection afforded by
method like Symmetrical IC-Schwartz-Top.

Such a method wouldn't let the raised candidate beat an already
top-voted one, and could fail FBC only by affecting a beatpath defeat
in a way that caused violation of Weak FBC.
Even if the election isn't 0-info, that beatpath-related failure is
unlikely to be predictable. The information available wouldn't be
sufficient to know whether raising a new candidate to top would help
or harm the top-rated candidates--as if it were a 0-info election.

Voters therefore wouldn't have predictive beliefs about such a
beatpath-involved FBC failure, unless the media claimed to have such
information, and the public believed the media as they do now.

Actually, though Symmetrical IC-Schwartz-Top fails ordinary FBC, I
don't know how NC Symmetrical ICT could fail it. But maybe it could. I
don't know. Maybe NC Symmetrical ICT passes MMC and full (as opposed
to weak) FBC--I don't know why it wouldn't.

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I won't add anything to what i said about methods for polling in my
previous post. But, regarding official public elections, if people
insisted on using rank-balloting for them:

I'll compare 3 methods:

Symmetrical ICT

Symmetrical IC-Schwartz-Top or NC Symmetrical ICT

AOCBucklin


1. If voters believe the Democrat-disinformation:

Then, full (as opposed to weak) FBC is necessary, because the media
could claim to know that ranking a non-Republocat in 1st place would
cause the favorite-defeat that is permitted by Weak-FBC compliance.

Weak FBC won't do, and so Symmetrical IC-Schwartz-Top won't do. Maybe
NC Symmetrical ICT would be ok.

Comparing the above-listed methods by pairs:

Symmetrical ICT vs NC Symmetrical ICT

If NC Symmetrical ICT passes full FBC, then it would be the better of
those two, if it also passes MMC. I don't know of it failing either
criterion.

NC Symmetrical ICT vs AOCBucklin:

If NC Symmetrical ICT meets MMC and full FBC, then both methods meet
nearly the same criteria.

AOCBucklin meets LNHe instead of just 0-info LNHe, but there's little
if any important difference between those 2 criterion compliances.

NC Symmetrical ICT's defection-resistance is somewhat more powerful.
That would make it a little better in that comparison, if it meets the
criteria that it seems to.

If NC Symmetrical ICT only meets Weak FBC, then that would disqualify
it from consideration, under the above-stipulated conditions. If it
fails MMC, then AOCBucklin would be clearly better of the two.

Conclusion: If NC Symmetrical ICT doesn't have criterion failures that
I haven't noticed, then it's a little better than AOCBucklin.
Otherwise, AOCBucklin is distinctly better.

2. If voters don't believe the Democrat-disinformation:

If we'd just elected the Greens into the presidency and most of
Congress, then there'd be no reason to be concerned that our
electorate would believe that the winner must always be a Democrat or
a Republican. Then, a form of the Democrat-disinformation claiming
that moving some particular candidate up to 1st place would affect a
beatpath in a way that would make all the 1st ranked candidates lose,
would be unlikely to be believed.

Then Weak FBC would be good enough, and Symmetrical IC-Schwartz-Top would be ok.

Under these conditions, AOCBucklin doesn't offer anything that the
MMC-complying ICT methods don't offer. And they have somewhat better
defection-resistance.

AOCBucklin would be better than Symmetrical ICT, because MMC is more
important than slightly better defection-resistance. The main value of
defection-resistance is that it lets voters benefit from MMC. Only
Machiavellian voters would do the ridiculously insincere voting that
could exploit AOCBucklin's less perfect defection-resistance. But,
though unlikely, Symmetrical or ordinary ICT's MMC failure can happen
accidentally, by itself. (if there's a cycle that includes all of the
majority-preferred set of candidates).

AOCBucklin has the further advantage that its reciprocity requirement
is optional, making it more flexible.

And its usability as an option in an Approval election could count in
its favor. I've spoken of an initiative or referendum, in a Green
government, regarding what voting system to adopt. In such an
election, AOCBucklin could be a compromise that Approvalists would
support, while also being a compromise that IRVists would use against
TUC, due to its compliance with LNHe and CD.

So:

Favoring AOCBucklin: The flexibility of an _optional_
reciprocity-requirement; Usability as an option in an Approval
election.

Favoring Symmetrical IC-Schwartz and NC Symmetrical ICT: Somewhat
better defection-resistance.

Maybe the latter advantage has more practical importance, favoring
those ICT methods.

Though I've defined AOCBucklin on EM, I should probably define it again here:

ln Bucklin, in each round, each ranking gives a vote to its
next-lower-ranked candidate to which it hasn't yet given a vote.

The winner is the first candidate to get a vote total greater than
half the number of voters. If that doesn't happen, then the winner is
the candidate with the most votes when every ballot has given votes to
all of its ranked candidates.

ER-Bucklin allows more than one candidate at any rank position. As
usually defined, each candidate at a rank position receives a whole
vote, when the ballot gives to that rank-level.

As defined in the electowiki, and as I define it, ER-Bucklin has a
delay that confers MMC compliance:

If there are N candidates who have received votes at a rank position,
then, before that ballot gives to its next rank position, that
vote-giving is delayed by an extra N-1 rounds.

When a ballot gives votes to a next lower rank position, it
simultaneously gives a vote to each candidate at that next rank
position.

I often call ER-Bucklin "ABucklin", because it's easier to write. The
"A" stands for "Approval".

The "OC" stands for optional conditional.

In the Bucklin context, an "approval" is a vote given to a candidate
ranked below 1st place.

The voter can indicate that s/he wants any vote to any candiidate to
be conditional upon reciprocity on the part of the faction who rank
that candidate in 1st place. Up to the number specifying that
reciprocity requirement, your faction's approval to their candidate is
conditional upon their giving equal favor to your faction's top-ranked
candidates, at that rank-level or higher.

That's a brief, and necessarily incomplete, vague and unclear, verbal
description of the conditionality. Some time ago, I posted to EM the
pseudocode for a computer program to implement optional
conditionality. As I've said, it can't really be defined, or clearly
and completely specified, other than by the computer program.

(but I don't suggest that an official election count be done by computer)

Optional conditionality could also be available in Approval. I call
that AOC. AOC and AOCBucklin could both be offered as options in the
same Approval election.

I'd expect that conditionality would often be welcomed and used by
voters in Approval or Bucklin. I would expect Approvalists to like the
availability of those two options (AOC and AOCBucklin) , and to
support that proposal in an election to decide the voting system.

Any option regarding how a voter will use hir own vote doesn't and
can't in any way violate the rights of other voters, including voters
who don't choose the option.

In Summary, there are several methods that I'd suggest and like, if
people insisted on rank-balloting in official public elections, and if
there weren't any count-fraud problem (maybe, as I said, people are
dedicated enough to do labor-intensive handcounts, and maybe that work
is regarded as socially-productive jobs provided by govt.

They include:

ICT or (especially) Symmetrical ICT
AOCBucklin

(the below-listed methods might or might not work as intended)

NC Symmetrical ICT
CR Symmetrical ICT
Symmetrical IC-Schwartz-Top
Symmetrical IC-Beatpath(lv)
Symmetrical IC-Ranked-Pairs(lv)

If voters don't believe the Democrat-disinformation:

Of those, AOCBucklin would probably be the best

...but maybe NC Symmetrical ICT

...or maybe Symmetrical IC-Schwartz-Top.

If voters believe the Democrat-disinformation:

Whether AOCBucklin or NC Symmetrical ICT is better depends on whether
NC Symmetrical ICT meets both of the criteria MMC and full FBC. I
don't know of a way it could fail either, but I don't guarantee it.

Mike Ossipoff










Mike Ossipoff













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