Another comment on the turkey-raising criticism of conditionality-by-mutuality:
Sure, if several rival candidates' supporters all give a conditional vote to
the same loser, in order to get a mutual vote thereby, then that loser will
get more votes in those transactions than any one of the rivals, and could
thereby win.
1. This requires that only one loser is getting those conditional
turkey-raising votes. Or at least that their number is significantly less than
that of the
rivals. In reality, if you're going to insincerely vote one loser over your
rivals for that reason, you'd also vote the whole set of losers similarly.
2. This consequence of turkey-raising could also be referred to as backfiring
burial. You know that when burial backfires in Beatpath, that's considered
a virtue, a deterrent. Then it's a virtue and a deterrent in the
mutually-conditional methods too. Voters attempting burial strategy are asking
for it. Don't
expect the method to protect voters practicing burial.
Voting options:
I recently said that MTAOC, MCAOC and AOCBucklin don't really make sense as
options in an Approval election (though certainly AOC does). I said
that because Approval's count rule says nothing about majority. I felt that
Middle-When-Needed and Stepwise-When-Needed would be more in the
option-using-voter's interest, and for that reason MTAOC, etc., as options
didn't make sense. But that was before I found out that Middle-When-Needed
and Stepwise-When-Needed almost surely violate FBC.
It seems to me that it's certain that the voting options of MTAOC, MCAOC and
AOCBucklin wouldn't violate FBC. That's because, for instance, an Approval
election
with some ballots using the AOCBucklin voting option is just like an ordinary
AOCBucklin count, but with some voters voting only at 1st rank. (those are the
voters
who are just voting an Approval ballot instead of using the AOCBucklin voting
option).
An MCA ballot is just an ABucklin ballot that only uses the 1st two rank
positions. So it's clear that MCA voting and ABucklin voting are entirely
compatible as options in the same Approval election.
The difference between the MCA option and the MTA option is just that, if there
are two or more candidates with a majority (MTA and MCA ballots haven't yet
given
votes to their middle-rated candidates), the MTA ballots will give a vote to
their middle-rated majority candidates, and the MCA ballots won't. Of course
there's no
reason why some voters couldn't opt to manage their votes in the MTA way, while
others opt to manage their votes in the MCA way.
And, if the MCA vote-management option doesn't cause an FBC failure, and the
MTA vote-management option doesn't cause an FBC failure, then it seems to me
that there's no reason to expect an FBC violation when both options are
available.
I can't say that the above statements are _certain_. But they seem convincingly
supported.
A more uncertain question is: As a vote management option in an Approval
election, is there a different option, other than the MTAOC, MCAOC and
AOCBucklin options, that is more in the option-user's interest--without causing
an FBC violation?
I don't like to leave uncertainties or open questions when I leave this mailing
list, but those uncertainties will remain when I (soon) quit the list, unless
someone else
has answered them by that time.
MJ majority protections:
Yes, a majority who rate x,y and z over a, b and c still does so even if it
rates x, y and z differently, as is the case in ABucklin.
But the fact remains that if you rate them all fairly closely, then there's a
good chance that you're rating them all over where their
medians would otherwise be, and, therefore, are not raising x,y and z's medians
any more than you're raising a, b and c's medians.
So sure, it's like Bucklin in one respect, but there's a (sometimes good)
chance that you aren't helping one candidate over the other at all.
MJ is like Approval in which you have the option of only uncertainly (maybe and
maybe not) raising a candidate's final count score
against that of another candidate. ...and/or of only uncertainly raising a
candidate's final count score at all, instead of lowering it.
In RV, too, if you rate a candidate below hir mean rating, you lower hir mean
rating. And, additionally, the less extreme your rating,
the less effect it has.
But, as I said, I'd be glad for the enaction of MJ or RV, (instead of
Plurality, IRV, or any FBC-failing method) because they both essentially
are Approval with the above options. You don't have to use those options.
And they both meet FBC. RV also has Forest's solution to the ABE problem.
Approval has it too, implemented probabilistically.
So I stand by my ranking of:
1. Approval
2. RV
3. MJ
--among the methods in Ruderman's poll.
A more complete merit ranking:
1. MMPO2
2. MDDTR
3. optionally-conditional methods
4. automatically-conditional methods
5. ICT
(Approval and Bucklin versions below are ordinary, don't have conditionality)
6. ABucklin
7. Approval, MTA and MCA
8. RV
9. MJ
Among the optionally or automatically conditional
methods, I'd rank their Approval, MTA, MCA and ABucklin
versions in the same order as ordinary Approval, MTA, MCA and
ABucklin are ranked.
For public proposals, though, I'd say that ordinary Approval is at the top,
with AOC next.
Though AOC is better, brings big improvement to Approval, it's also true that
ordinary Approval already
had at least 3 other ways to deal with co-operation/defection:
1. Public declaration of principled refusal to accept a compromise or
co-operate with a faction (Maybe under
specified conditions)
2. The consequences, in subsequent elections, of defection
3. Forest's solution (probabilistically-implemented in Approval)
Regarding #2, a good strategy for a defected-against faction would be to refuse
to help the defectors
in the next election. Then give them another chance to co-operate in the
election after that. Factions should make
it clear that that will be their strategy.
In the co-operation/defection tournament for computer programs, described in
Scientific American some time ago,
the winner was a program called "Tit-For-Tat". I believe that the strategy that
I described in the above paragraph
is the Tit-For-Tat strategy: Vote the same strategy that the other faction did
in the previous election.
But SciAm later described another strategy that worked even better than
Tit-For-Tat. I don't remember what it was,
but it was nearly as simple as Tit-For-Tat.
The point is that there are good deterrent strategies for
co-operation/defection.
The broader point is that, even without AOC's conditionality, ordinary Approval
can deal very well with the
co-operation/defection problem. So ordinary Approval has merit, as will as
winnability, as a first proposal.
Mike Ossipoff
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