[EM] Dual Dropping method and "Preference Approval" ballotideas

[Elisabeth Varin/Stephane Rouillon]

> 7:A>D>C>B
> 5:C>B>D>A
> 3:B>D>C>A
> 3:A>B>D>C
> 3:B>A>C>D
> 1:D>C>B>A
>
> The defeats (from strongest to weakest) are:
>
> B>D and D>C; 14-8 each
> A>C and C>B; 13-9 each   ...and A>D; 13-9
> B>A; 12-10.
>
> Ranked Pairs throws out the C>B defeat and declares B the winner.  SSD
or
> beatpath throws out the B>A defeat and declares A the winner.
Obviously,
> one more voter was overturned by ranked pairs.  I used Rob LeGrand's
web
> site to check my work.

I do obtain the same results than you but not the same last conclusion:

Ranked pair: B>A>D>C
it overturns C>B (13-9)

SSD: A>D>C>B
it overturns B>A (12-10) ...but BD (14-8) too!
Correct me if I am wrong.
It is not fair to only count overturns related to the winner...

I am looking at Mr. Ossipoff and you last answers about relative
margins.
You say there is at most one Condorcet winner and it is important to use
a
method that would preserve it from truncation. I agree with the fact
that
truncation could destroy this information because once truncation
occurred
there is no way to find this Condorcet winner if it existed. For
example,
suppose we end up with ballots:
3: A
4: B>C>A
5: C>B>A
There is no more way to know who could have been the Condorcet winner.
3: A>B>C
4: B>C>A
5: C>B>A
B is the Condorcet winner.
Other case:
3: A>C>B
4: B>C>A
5: C>B>A
C is the Condorcet winner.
There might have been no Condorcet winner at all.
So preventing truncation is a good thing.
But where I differ, is that I believe there is already enough
incentive with relative margins to prevent truncation.
The decision to truncate its own ranked ballot is normally made
by a voter from its mathematical average gain (esperance).
Supposing there is a Condorcet winner and no voter have sincere
equally preferred candidates, using winning votes would garantee
the voter could only lose using truncation. Supposing the same with
relative margins or margins, the voter would already face a negative
esperance when evaluating truncation.

I will do this analysis in full detail for the previous example (12
voters)
and 3 candidates. You will see there is a lot more cases where
a voter harms himself (gets one of his/her lower ranked candidate
elected)
than cases where the voter enhance its result.
Now telling the voters not to truncate because they would generally
harm themself should be sufficient to not get truncation. If we cannot
expect a voter to protect his/her sincere preference we cannot expect a
voter to
even vote for his/her sincere preferences.

Analysis coming soon,
Steph.

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