[EM] equal rankings IRV

[Chris Benham]

Marcus,
You wrote (Wed.Jun.16):

Dear Chris Benham,

you wrote (15 June 2004):
> According to Mike, it meets his "Weak Defensive Strategy
> Criterion" (WDSC): 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.

You wrote (16 June 2004):
> Thanks for your interest and good example. Maybe somewhat
> confusingly, Steve Eppley gives two versions of this
> criterion (same name and author, but slightly different
> definitions).
>
> Here is the other one:
> > non-drastic defense: If more than half of the voters
> > prefer alternative y over alternative x, then that
> > majority must have some way of voting that ensures x
> > will not be elected and does not require any of them
> > to rank y over any more-preferred alternatives. (This
> > is promoted by Mike Ossipoff under the name Weak
> > Defensive Strategy Criterion. Non-satisfaction means
> > some members of the majority may need to misrepresent
> > their preferences by voting a compromise alternative
> > over favored alternatives if they want to ensure the
> > defeat of less-preferred alternatives.)
>
> In your example, y is A and  x is E. The top three groups
> of voters, who all ranked A equal first with two other
> candidates, can ensure that E is not elected by ranking A
> alone in first place.  There is no candidate that they
> prefer to A, so  ER-IRV(fractional) seems to meet this
> version (as Mike Ossipoff in effect claimed).

What do you think about this example?:

   10 B>C>A>E>...
   10 B>D>A>E>...
   10 C>B>A>E>...
   10 C>D>A>E>...
   10 D>B>A>E>...
   10 D>C>A>E>...

   7 B>E>...
   7 C>E>...
   7 D>E>...

   38 E>...

A majority of the voters strictly prefers candidate A
to candidate E. In my opinion, this example demonstrates
that ER-IRV(fractional) violates Mike Ossipoff's WDSC and
Steve Eppley's "non-drastic defense" criterion. What do
you think?

Markus Schulze

CB:I agree with you. With the votes as they are above, A has no first preferences and so is the
first to be eliminated. The best that the majority who prefer A to E can do for A without ranking
A above any candidate they prefer (to A)is for sixty of them (the top six groups of ten in your
example) to rank A equal-first with two other candidates.
This will result in these first-preference tallies: A20, BCD each 20.3333, E38.
A still has the lowest tally, and so is eliminated.


Chris Benham


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