[EM] Re: equal rankings IRV

[Chris Benham]

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.

Judging by the example at Steve Eppley's site, it seems to meet his 
(similar) "Non-Drastic Defense" criterion. 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
unambiguusly 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>Left

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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