[EM] Anti-reversal enhancements for Condorcet

MIKE OSSIPOFF nkklrp at hotmail.com
Sat Dec 27 00:01:01 PST 2003


You described an anti-reversal enhancement that involved a 2nd balloting. 
Sure, a 2nd balloting can further reduce wv's already tiny offensive 
strategy problem, assuming that it ever becomes a problem.

But it's not necessary to hold a 2nd balloting anytime there's a circular 
tie, though that's one solution.

If a CW's support isn't indifferent, s/he'll be ranked over the reversers' 
candidate by a majority, meaning that for the reversers' candidate to win, 
everyone else must have even bigger majority against them.

So the 2nd balloting should only be triggered if there's an 
all-majority-defeats circular tie.

Here's what I've propsed as a 2nd ballot solution:

If there's a circular tie all of whose members have another member ranked 
over them by a majorith, then a 2nd balloting is held.

Before the 2nd balloting, the pairwise defeats will have been published, and 
order-reversal, if it happened, can be noticed.

In the 2nd balloting, the reversal can be countered. It can be punished by 
defensive truncation. Or, as in your example, the C voters could rank B 
equal to C. Note that, with wv, they only need rank B equal to C. In margins 
they'd often have to rank B _over_ C. That's a lot more to ask.

But another possibilit for the 2nd balloting is an Approval balloting. That 
simpler method won't produce another cycle, and the defense against the 
reversers would consist of their victimes not voting for the reversers' 
candidate. In that case the defensive truncation elects the CW.

The 2nd balloting pretty much eliminates whatever amount of reversal problem 

Something similar can be used for committees. I'd suggest it for an EM poll, 
for instance.

To a poll, I'd add the rule that, after the result is announced, there's 
about a week or half-week period during which anyone can truncate their 
ranking if they choose to, or can uprank an alternative to 1st place.

(I prefer open polls in which voters post their ballots. That's the way to 
have proven security.
But, as these ballots come in, reversal opportunities could be obvious to 
those who haven't voted yet. The defdensive strategy option avoids that 
reversal problem).

Either of those 2 enhanhancements, or something similar, could be used for 

Tom Roiund and Steve Eppley separately independently proposed the 
candidate-withdrawal option:

After an election result, any candidate can declare that he withdraws, and 
call for another count of the same ballots with his name deleted from them.

That also thwarts offensive order-reversal.

I notice that candidate-withdrawal is part of your proposal.

For 1-balloting elections, the voter could have the option of drawing a line 
in his ranking, to indicate that, in the event of an all-majority-beaten 
circular tie involving candidates above and below that line, he wants to 
drop the candidates below the line. Then the same ballots, with the 
candiddates dropped, would be recounted. That would be a powerful deterrent 
to offensive order-reversal.

I don't claim to have covered all the possible anti-reversal enhancements. 
We've discussed a few other ones.

For instance, a tentative possible solution involves giving the voter the 
option to indicate that, if there's an all-majority-beaten circular tie, and 
if groups of voters sharing the same 1st  choices have certain patterns of 
unanimity and non-unanimity within those groups, in their subsequent 
choices, that voter wants do delete certain candidates. That may catch be 
able to catch some offensive order-reversals. Obviously that isn't a 
complete detailed proposal.

Methods more fancy and complicated than Condorcet are discussed. Though all 
methods have strategy, there's always the possibility that one of those 
fancier methods will get rid of defensive strategy need, as I've defined it 
here. Or at least let defensive truncation elect the CW, without the use of 
a 2nd ballotiong.

Mike Ossipoff

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