[EM] Re: equal rankings IRV

[James Green-Armytage]

Chris Benham wrote:
>Take this example of sincere preferences:
>45:Right>CentreRight>Left
>35:CentreRight>Right>Left
>20:Left>CentreRight>Right
[strategy using regular IRV:]
>25:Right>CentreRight>Left
>20:Left>Right>CentreRight  (these are Push-over strategising  Right
>supporters)
>35:CentreRight>Right>Left
>20:Left>CentreRight>Right
>Now CentreRight has the lowest first-preference tally, and then Right
>wins. The strategists had to be sure that Right had a pairwise
>win against Left, and that Right wouldn't be eliminated. It could be
>difficult or risky to coordinate, because obviously if too many  Right
>supporters vote that way, then Left will win .
>But look what happens when the method is ER-IRV(whole)!  Now the Right
>supporters have a vastly improved Pushover-like
>opportunity.
>45:Right=Left>CentreRight
>35:CentreRight>Right>Left
>20:Left>CentreRight>Right
>First-preference tallies
>Right:45       CentreRight:35      Left:65
>CentreRight has the lowest tally, and so is eliminated then Right wins. 

	James here. Chris, this is a really interesting example. This is one of
the beautiful things about the EM list. I probably wouldn't have thought
up an example like this on my own, but you did and you were able to share
it with me in response to my question. I think that I might agree with you
that in this particular example, regular IRV makes strategizing less risky
for the Right wing voters than ER-IRV(whole). However, I'm not sure that
such a situation is very likely to occur...

>This time no coordination was needed. As long as the Right suporters knew
>that Right had more first-prefernces than CentreRight, and a
>pairwise win against Left, then each individual Right supporter got an
>increased expectation by insincerely upranking Left from last to
>equal-first  with no risk.

	Hmm, no, here I disagree. The fact that Right has a pairwise win against
Left does *not* guarantee that Right will win once CenterRight is
eliminated, if indeed so many Right voters are voting left equal in first
place. For example, if a fair number of the CenterRight voters preferred
Left over Right, and if all the Right voters strategically ranked Left
equal in first place, Left would be likely to beat Right once CenterRight
was eliminated. To put it to numbers:

sincere:
45: Right>CentreRight>Left
25: CentreRight>Right>Left
10: CentreRight>Left>Right
20: Left>CentreRight>Right
>
>
strategic:
45: Right=Left>CentreRight (the sinister devious ones)
25: CentreRight>Right>Left
10: CentreRight>Left>Right
20: Left>CentreRight>Right
>

ER-IRV tally
Left		CentreRight		Right
65		35			45
+10		-35			+25
75		0			70

	So here, Left wins as a result of the Right voters' miscalculated
strategy. So, the voters in your example need to know that Right will beat
Left sheerly by virtue of the votes transferred from CentreRight before
they can safely commit to all voting Right=Left>CentreRight.
	But anyway, getting back to your example specifically, I notice that the
Right and CenterRight have a stunning 80-20 mutual majority. Which sort of
makes me think that the Left voters will not have too much hope for their
candidate. Hence, if they have reason to think that CentreRight will be
eliminated first, especially as a result of some evil Right wing order
reversal scheme, I think that they would not be too unlikely to protect
CentreRight by voting Left=CentreRight>Right. If all of them vote this
way, and the CentreRight voters vote sincerely, then I think that there is
not a damn thing that the Right voters can do about it. And again, this
sort of protection strategy would be harder in plain IRV, because it would
involve order reversal, and, in Mike's terms, favorite betrayal.
	Still, I like your line of questioning a lot. These are really good and
interesting examples. Let me know if you come up with any more, or if you
find my counter-argument here unconvincing. 

best,
James