[EM] Re: equal rankings IRV

[Chris Benham]

James G-A,
In response to me writing  (Mon.Jun.14, originally):

Take this example of sincere preferences:
45:Right>CentreRight>Left
35:CentreRight>Right>Left
20:Left>CentreRight>Right

CentreRight is both the sincere CW and IRV winner.
IRV is vulnerable to the "Push-over" strategy. This from EMR:

push-over
The strategy of ranking a weak alternative higher than one's preferred 
alternative, which may be useful in a method that violates monotonicity 
<http://condorcet.org/emr/defn.shtml#monotonicity>.

In the above example, some (but not too many) of the Right supporters 
can use the Push-over strategy to make Right win:

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.
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.

You wrote (Fri.Jun.18):



>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.

CB: You are referring to sincere prefernces, whereas I meant pairwise win on the voted
rankings (in spite of the Right supporters feigning indifference between Right and Left.)

Earlier in your post, you wrote:


> 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...

CB: I assume you meant to agree  "that regular IRV makes strategising" MORE "risky for the Right
wing voters than ER-IRV(whole)."
My point in having ALL the Right supporters engage in the Pushover-like strategy, was to make the
contrast with plain IRV, where the would-be strategists always have to worry that there will be too
many of them.
Also, I had in mind a more polarised electorate than you seem to assume, in which the Right and Left
camps hate each other.Like in this example.

Sincere preferences:
40:FarRight>Right>>>FarLeft
35:Right>FarRight>>>FarLeft
25:FarLeft>>>Right>FarRight

Right is the sincere CW and IRV winner.

Ballots:
11:FarRight=FarLeft (strategising FarRight supporters)
29:FarRight>Right
26:Right>FarRight
09:Right
06:FarLeft>Right
19:FarLeft

First-preference tallies: FarRight40, Right35, FarLeft36.
Right is eliminated and then FarRight pairwise beats FarLeft 55-25.

I have given this more polarised example to make it plausible that the strategising FarRight
supporters can rely on the Right voters supporting their candidate in the runoff.
Also these numbers are meant to show that the strategists have a wide "margin of error".
The number of strategists was the smallest possible for the Pushover strategy to succeed. With
a smaller number the strategists do themselves no harm. If ALL the FarRight supporters had tried
the srtategy, then it still would have worked. FarRight would have squeaked home in the runoff
26-25. If fewer Right supporters had truncated, then this margin would have been greater.


Chris Benham