[EM] Re:"Runoff without Elimination", Condorcet efficiency

[Chris Benham]

Kevin,
Previously I wrote:

CB:I recently considered this method (and similar non-elimination versions of IRV), but
> rejected it because it fails this example:
> 
> 51:A>B>C
> 50:B>A>C
> 100:C
> 52:D>E>C
> 49:E>D>C 
> 302 votes. 
> 
> The CW (and Plurality winner) is C. IRV elects E. "RWE" elects the Bucklin winner,D.

To which you responded:

"By my calculations, RWE (as I meant it above) and Bucklin both pick C.
I'm very curious about how you get D as the Bucklin winner.  C is the only candidate
who can ever achieve a majority.  Are you perhaps eliminating voters?"

CB:Oops! Yes, I blundered. I trimmed the original example so that all the voters truncated
just under the CW, wrongly thinking that that in this case it made no difference. The big 
difference was that in the original, the 100 C supporters gave their second preferences to 
D. I did work it out again, but for some reason still transferred C's preferences to D.
I have no idea how I got E as the IRV winner. (I wrote it down some time ago).
The original:
51:A>B>C>D>E
50:B>A>C>D>E
100:C>D>B>E
52:D>E>C>B>A
49:E>D>C>B>A 
302 votes.
C is CW, and Plurality and Borda winner. IRV,Bucklin and RWE elect D.

Chris Benham





  


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