[EM] Stepwise AERLO option

[MIKE OSSIPOFF]

Stepwise AERLO (SA) option:

If any voters choose this option, then repeated AERLO trials are done. Each 
AERLO trial consists of two counts, an initial count and a final (promotion) 
count. In the 1st AERLO trial, each voter's AERLO line is where s/he put it.

In each subsequent AERLO application, the AERLO line of each voter who chose 
the SA option is moved one candidate down his/her ranking, unless someone 
above his/her AERLO line already has won. And a voter's AERLO line is never 
moved to below a candidate who has already won. If someone who has chosen 
the SA option doesn't mark an AERLO line, its position is assumed to be 
under hir favorite.

The repetition of the AERLO trials stops when every voter's ranking stops 
moving its AERLO line downward, for one of the reasons specified in the 
paragraph before this one. The current winner at that time then becomes the 
final winner.

[end of SA definition]

SA(PC) uses SA with PC:

In my usual 40,25,35 example, this completely gets rid of the need for 
defensive strategy, even when order-reversal is tried:

Sincere rankings:

40: AB
25: BA
35: CB

The A voters use offensive order-reversal:

40: AB
25: BA
35: CB

A wins.

But say the B & C voters have chosen the SA option:

In the 1st AERLO trial, the B & C voters automatically have an AERLO line 
placed under their favorite.
So, in the 1st AERLO trial, A wins in the 1st count and also in the 2nd 
count.

Then the C voters' ranking moves its AERLO line down one candidate, to below 
B. The B voters don't move their AERLO line down, since that would be moving 
it to below someone who has already won.

Now, in the 2nd AERLO trial, A again wins in the 1st count. But in the 2nd 
count, the C voters' ranking promotes B to 1st place, and B wins.

No rankings will move their AERLO line any lower, for the reasons specified 
in SA's definition, and so B is the final winner.

Of course it doesn't work so perfectly when there are more than 3 
candidates. Then, the B voters could move their AERLO line to below a 4th 
candidate, a nonwinner who could win instead of CW B.

It's then similar to Bucklin, except that Bucklin always has that situation, 
and it only happens here if there's offensive order-reversal. And it's also 
like the fact that in wv, when defensive truncation is considered, it's the 
B voters who must protect B. The difference is that now when they do so, by 
not using the SA option, it elects B instead of C, as it would in defensive 
truncation in ordinary wv.

Also, maybe  the SA(wv) &/or SA(ERBucklin) strategy situation could be 
improved some by having some added provisiion to try to prevent the SA 
option from going into action for rankings that are going to benefit later 
from SA. I realize that that would be imperfect and would lead to 
complications, which could be dealt with. How much benefit it could bring, I 
don't know.

It would be nice if something like SA, with suitable improvements, could 
make it possible for a majority to always protect a CW's win without using 
any strategy at all. Or to always be able to keep the win in the sincere 
Smith set without using any strategy at all.

That doesn't violate Gibbard-Satterthwaite, it seems to me, because 
Gibbard-Satterthwaite merely says that every method should be able to have 
_some_ kind of stratgegy incentive, under _some_ special conditions, not 
that a majorilty should need strategy to protect a CW.

So the question of how good a method can be is still open, unless someone 
can prove that it's impossible for a method to guarantee that a majority can 
always protect the win of a CW while voting sincerely.

I'm not saying that SA can guarantee that, even with the help of 
complicating rules. But that goal was my reason for checking out SA. Can 
anyone find a method that guarantees that a majority can protect a CW's win, 
or at least prevent a particular candidate from stealing that win, without 
doing other than voting sincerely? SFC-complying methods guarantee that 
under SFC's reasonable premise conditions. Can any method guarantee that 
unconditionally? Can anyone prove that there's no such method?

Mike Ossipoff

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