[EM] ER-Bucklin fails monotonicity

[James J Faran]

It seems to me that ER-Bucklin(whole) does not satisfy FBC since Bucklin
does not.

Example: 3 candidates, 10 voters

Preferences:
2:A>B>C
1:A>C>B
3:C>A>B
4:B>C>A

1st round scores are 3:4:3 for A,B,C: No majority. 2nd round scores are
6:6:8. C has the largest majority and so wins.

What is a poor A>B>C voter to do? Well, he can elect B by burying his
favorite, casting his vote as B>A>C.

Preferences Cast:
1:A>B>C
1:A>C>B
3:C>A>B
4:B>C>A
1:B>A>C

1st round scores are 2:5:3 and B has a majority and wins.

Does this provide a counterexample to FBC or have I misunderstood FBC?

I suspect any multiple step method to be susceptible to this sort of
behavior: make the first round close for the voter's second choice, make
the second round choose the voter's third choice. (Of course, for
elimination methods, e.g. runoffs or Toombs, the thing to do is to
change who gets eliminated in round one.)

If 50% does not constitute majority vote victory but 50%+1 does, this
example can be modified to give a similar example.

I don't know how AERLO might affect this, nor do I have a good enough
understanding of Ossipoff's suggestion re modified Bucklin (something to
do with fraction of the extra vote needed to get a majority) to see how
that might affect this.

Jim Faran
 
On Thu, 2005-06-30 at 21:29, James Green-Armytage wrote:
> Kevin, you wrote:
> >This seems like a new interpretation. I believe both this interpretation
> >and
> >ERB(fractional) satisfy monotonicity, since in neither method can raising
> >a candidate cause any other candidate to get their votes earlier.
> 
> Does my interpretation of ER-Bucklin(whole) satisfy FBC? (And, in my
> terminology, ZCRIC?) My guess is that it does. Here's a reference for the
> my ER-Bucklin(whole)definition:
> http://wiki.electorama.com/wiki/ER-Bucklin
> 
> James
> 
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