[EM] Approval-Condorcet hybrid encouraging truncation

[Kevin Venzke]

Forest Simmons wrote:
>I must be missing something. Could you give an 
>example in which the approval winner is not the 
>winner of the method?

I don't think it's itself a method.  It's a "family of
voting methods" of them, like he said.  The two rules
specify what the ballot must look like, and who cannot
win.  There is a lot of freedom permitted as to who
actually wins.

To give an example for your question, it would be
permissible for a method in the family to elect a
candidate who beats pairwise the approval winner.

Steve Eppley wrote:
>2. For all pairs of candidates, say x & y, y is 
>socially ordered over x if the number of votes that 
>rank "y over x" exceeds the number of votes that 
>rank "x over y" and the number of votes that rank "y 
>over the dividing line over x" exceeds the number of 
>votes that rank "x over the dividing line over y." 

Isn't it superfluous to say "y over the dividing line
over x" and vice versa?  Won't you get the same
results if you say "y over the dividing line" and vice
versa?

>Assuming only one winner is to be elected, it's 
>always possible to satisfy condition 2 (or the 
>revised wording) since the subset of pairings that 
>meet condition 2 is acyclic. (I have a proof of 
>acyclicity, but it's tedious so I won't post it 
>without a request.) 

I think this is intuitive.  Isn't it just a
consequence of it being impossible to have a cycle
with an approval ballot?

>I'm concerned that some voters wouldn't use the 
>dividing line strategically as intended, and instead 
>treat it as some sort of "sincere approval" dividing 
>line. In that case, the dividing line may 

I believe the method I most recently proposed
satisfies your 2nd rule (about who can't win) but not
the 1st (about the ballot).  That is, it is not
possible for a candidate to win if he's beaten by a
single candidate on both matrices (Condorcet and
Approval).

I also think my method could alleviate some of your
concern about the voters using the divider
efficiently.  This is because the voter cannot order
among candidates whom they don't approve.  Thus if
they want to put the "dividing line" (which exists
only effectively) right after their first preference,
they cannot name compromises.

It's debatable whether it would be better to do
something other than add the two matrices.

>So even though many voting methods could be tweaked 
>to be in the family that satisfies Sincere Defense, 
>only the best methods should be considered.

I wonder what you think would approach a "best
method."  Do you think tinkering with the ballot
format is completely out?

Kevin Venzke
stepjak at yahoo.fr


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