[EM] Re: equal rankings IRV

[Chris Benham]

Dear  Marcus,

You wrote (Tues.Jun.15):

"This is Steve Eppley's "Non-Drastic Defense" criterion:

> Non-Drastic Defense:  Each voter must be allowed to vote
> as many alternatives tied for top as she wishes, and for
> all x e A, x must not be elected if there exists y e A
> such that that more than half of the voters vote y over x
> and no worse than tied for top.

Here is an example where ER-IRV(fractional) violates
Steve Eppley's "Non-Drastic Defense" criterion:

   20 A=B=C>E>...
   20 A=B=D>E>...
   20 A=C=D>E>...

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

   38 E>...

   A majority of the voters strictly prefers candidate A
   to candidate E and ranks candidate A tied for top.
   Nevertheless, candidate E is the winner."

CB: Thanks for your interest and good example. Maybe somwhat 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.) 

CB: 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).

Chris Benham


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