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

[Kevin Venzke]

Chris,

 --- Chris Benham <chrisbenham at bigpond.com> a écrit : 
> 1. The voter ranks candidates.  (As in Bucklin, voters should decide where to
> stop ranking.)
> 2. Initially count first-place rankings only.
> 3. While no one has votes from a majority (of ALL voters), AND non-eliminated candidates exist:
>    "Eliminate" the non-eliminated candidate with the fewest votes.
>    ("Eliminate" has no implied meaning besides what I'll say here.)
>    Recount the votes such that every voter approves their highest ranked
> non-eliminated candidate, as well as every eliminated candidate preferred to
> that non-eliminated candidate.  However, no one approves last-ranked (truncated)
> candidates.
> 4. Elect the candidate with the most votes.

> 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.

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?

I will run through my interpretation of RWE's handling of this election:
initially: 51 A, 50 B, 100 C, 52 D, 49 E.
E is eliminated.  D obtains 49 more votes for a total of 101.
now: 51 A, 50 B, 100 C, 101 D, 49 E*.  (* means eliminated.)
B is eliminated.  A obtains 50 more votes for a total of 101.
now: 101 A, 50 B*, 100 C, 101 D, 49 E*.
C is eliminated.  No one gains votes, so tallies remain the same.
Now, we must eliminate either A or D, who are tied.
However, no matter which we pick to eliminate, C will have a majority and win.

Kevin Venzke
stepjak at yahoo.fr


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