[EM] Chris: Approval vs IRV

[James Green-Armytage]

Adam Tarr wrote:
>In Approval, I can always vote for favorite, but the question is whether
>I 
>approve compromise as well.  It's a very similar dilemma, although I
>don't 
>have to actually sell out my favorite.
and:
>Now, despite the same amount of "favorite betrayal" as in the IRV
>example, 
>Favorite still wins.  So here we have a pretty good argument that
>approval 
>is MORE forgiving in this case than IRV.  In general, it takes twice as 
>much mistaken compromising to sink the stronger wing candidate in
>approval 
>versus IRV.

	Right, but using equal rankings IRV (whole votes), voters have more
leeway to support the compromise candidate without burying their favorite.
That is, as in approval, they can vote the compromise candidate equal to
their favorite.

Given your first example:
35% Worst
5% Worst>Compromise>Favorite
12% Compromise>Worst>Favorite
13% Compromise>Favorite>Worst
35% Favorite>Compromise>Worst

If 11/35 F>C>W voters vote F=C>W
35% Worst
5% Worst>Compromise>Favorite
12% Compromise>Worst>Favorite
13% Compromise>Favorite>Worst
11% Favorite=Compromise>Worst
24% Favorite>Compromise>Worst

IRV tally using whole votes
Worst	Compromise	Favorite
40		36			35
		+24			-35
40		60

	So, it takes 11 voters to compressing their rankings, or 6 voters
reversing their rankings, to elect Compromise in this example. In approval
voting, at least 16 F>C>W voters should have to vote FC in order to elect
compromise, and possibly more if any of the C>W>F voters happen to vote
CW. So from that point of view, it doesn't seem off-base to say that
ER-IRV(whole) handles this example at least as well as approval.
	Actually, as a side note, it's not clear to me how this example would
play out in approval. Would the Compromise voters approve their favorite
wing candidates? Would the wing candidates approve the Compromise
candidate? Or is it both?
	Anyway, I totally agree that Condorcet handles this example much better
than IRV, better than approval, and better than ER-IRV(whole). But I'm
just pointing out that ER-IRV(whole) does a better job than plain IRV. So
please keep that in mind.
	
best,
James