[EM] Dual Dropping method and "Preference Approval" ballot ideas

[matt at tidalwave.net]

On 9 Sep 2002 at 22:31, Adam Tarr wrote:

> This seems like a slick idea, and very in line with the whole motivation 
> behind both resolution methods.  The only drawback I can think of is that 
> the difference between the two is so small that using one or the other is 
> just about as good (and a lot easier to explain).

If the difference being small constitutes a "drawback" then how is advantage 
measured?  The difference is big enough in elections where RP and SSD generate 
different winners.  Explanation in two sentences: Dropping cost is the total strength 
of defeat of the dropped candidate pairs.  DD says that if RP and SSD don't select 
the same winning candidate then the winning candidate is taken from the method 
that had the smallest dropping cost.

> Can anyone come up with a relatively simple example where RP and SSD 
> differ, but RP ends up overturning less winning votes (or winning margins, 
> if you like)?  It's pretty hard to come up with a reasonable example where 
> the two differ, period.  Here's the simplest I can come up with, and it 
> doesn't correspond nicely to any political spectrum I can come up with:

7:A>B>C>D
5:B>D>C>A
4:D>C>A>B
4:C>D>A>G
1:D>B>C>A

The defeats (from strongest to weakest) are:
A>B 15-6
C>A and D>A 14-7
B>C 13-8
B>D 12-9
C>D 11-10

Ranked Pairs throws out the B>C defeat and declares C the winner.  SSD throws 
out the C>D and B>D defeats and declares D the winner.  SSD has overturned 33 
votes and RP only 13.  SSD overturned more votes.  Its easy to see why.  When the 
two bottom pairs form different cycles SSD drops them.  RP only needs to drop a 
single higher ranked pair.  But the two bottom pairs have more votes than the single 
higher ranked pair.

I verified this with the Condorcet_DD.pl (version 2.0) script, which computes RP, 
SSD and DD. http://sfads.osdn.com/7.html?topic=condorcet-dd,perl-foundry,234

> If anyone can come up with an example that shows the opposite, i.e. SSD 
> overturning more votes, it would be nice to see.  As it stands, all this 
> analysis has led me to is the thought that SSD tends to be a little better 
> than RP when they differ.

Intuitively, SSD is a little more discriminating in choosing candidate pairs to drop.  
So I am inclined to agree that SSD may have a small overall advantage.  But you 
are wrong if you don't think RP sometimes has lower dropping cost than SSD.  I 
created the simple example above from scratch today with paper and pencil.  It was 
a good puzzle, not too easy and too hard.
 
> What you are proposing is basically a Condorcet voting system where we ask 
> the voters "kindly only vote for candidates you approve of".  Obviously 
> this can't really be enforced, so it has pretty limited value.  Other 
> people have proposed allowing voters to put an "approval cutoff" on the 
> ballot, and using the approval counts as a tie-breaker in the case of a 
> cyclic ambiguity.  The problem with this is that it can introduce a lot of 
> strategy.

I am inclined to agree with you.  However, I think there is already a lot of strategy 
opportunity with the Condorcet methods (including my own DD) using ordinary 
preference ballots.  Approval (plain approval, not mixed with preference) has an 
advantage here, not because it doesn't also invite strategy, but because it reduces 
the overall impact.  I suggest placing an approval cutoff in the preference ballots 
also, but not as a tie-breaker.  Instead, I think that the approval cut-off should be 
used to complete the ballot by placing the unvoted candidates between the 
approved and unapproved candidates.  Although this is imperfect, it seems to me 
that this is probably an improvement over leaving the ballots incomplete or 
completing them by just appending the unvoted candidates as lowest ranked.

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