[EM] Re: equal rankings IRV

[Chris Benham]

Kevin,
In response to James G-A asking:

> 	So, I'd like to know if everyone agrees that the whole votes version of
> ER-IRV is better than the standard version of IRV where equal rankings are
> not allowed. If so, how much better is it? Does it have any new
> disadvantages that standard IRV doesn't have?

You wrote:

>It's much better in that I think there would not be so much nomination disincentive,
>or order-reversal incentive.
>
>It's going to be worse, from the perspective of people who think it's important
>to find majority-strength coalitions, because of all the compression incentive.
>It won't be possible to ensure that there is only one "majority winner."
>
CB: I  take it from this that you assume  that  ER-IRV(whole)  has a 
majority stopping rule, and so do not agree with what James G-A
wrote in response to me asking me if  the definition of  that method 
includes that rule.

>I would say not. Might as well just go on until only one candidate
>remains. Majority stopping rules in regular IRV are a false issue anyway,
>since the result is always equivalent to the result when you just keep
>going until you get to the last man standing.
>
>I realize that a majority stopping rule would be screwy with
>ER-IRV(whole). So I don't see any reason to mess with it.
>
CB: So I  just want to make it clear  that we are actually talking about 
one more method than some of us might be assuming, ie
standard IRV,  ER-IRV(fractional),  and  TWO versions of  ER-IRV(whole), 
with and without the majority stopping rule.
I  think I demonstrated in my last post that  ER-IRV(whole) with no 
stopping rule  is unacceptably vulnerable to simple theft of  the
election by  Push-over type strategising.
With the stopping rule, the method  has much more in common with 
Approval  than IRV. (It  could perhaps be called "Preferential
Approval" as I suggested in an earlier post.)  I  think the correct 
strategy in that method  would be very little different from just  giving
a [1] to all the candidates you would approve if the method was 
Approval, and then ranking the rest sincerely.

Chris Benham

PS: There were a couple of  small mistakes in my  Mon.Jun.14  post  in 
this thread, so here is the corrected version:

James,
I have always regarded equal-rankings allowed IRV(fractional) as a 
small, mostly irrelevant refinement of normal no equal-ranking
(except for truncation) allowed IRV which would never be implemented 
because it makes counting more difficult (especially if  
hand-counting paper ballots), and the demand for it from voters and 
parties would be very small.
So,like you, I was pleasantly surprised to see that this seemingly small 
refinement is a suffiiciently big improvement on standard IRV
for Mike Ossiopoff to rank it both above "Majority-Choice Approval" 
(MCA) and Approval. According to Mike, it meets his
"Weak Defensive Strategy Criterion" (WDSC).  From electionmethods.org:

If a majority prefers one particular candidate to another, then they 
should have a way of voting that will ensure that the other cannot win, 
without any member of that majority reversing a preference for one 
candidate over another.

 I can't see or imagine any possible theoretical disadvantage 
ER-IRV(fractional)  could have compared to standard IRV, so (in light of
the above) I rate it as unambiguosly better.

The same cannot be said of  ER-IRV(whole). Unlike standard IRV, it fails 
the Symetric Completion criterion and the "No Zero-Information
Strategy"  standard. The voter with no idea of how others vote, who has 
a sufficiently large gap in his/her ratings, now does better to
insincerely rank all those candidates above the gap in equal-first 
place.  But that is far from the worst of it!

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.
This example wouldn't work if there was a  "majority stopping rule" 
(because then Left would be declared the winner on the first round),
but if there was, then we would have an Approval-like method with lots 
of  insincere compression incentive, that  I am sure would fail
Clone Independence.
In the example, with ER-IRV(fractional)  the same strategy by the Right 
voters would also succeed, but the strategists had less margin
of error, and in general it is much easier and less risky with the whole 
votes version. But contradicting what I wrote earlier, maybe it is a
significant disadvantage of  ER-IRV(fractional) versus plain IRV that 
 Push-over strategising  is less risky and more tempting.
In conclusion, ER-IRV(whole) is worse than standard IRV. 
 ER-IRV(fractional) may be better than plain IRV, but I don't like its
chances of being introduced in practice. I would think that most voters 
wouln't see much point in it, and election officials would hate it.

Chris Benham





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