[EM] Re: Participation examples

[Kevin Venzke]

Chris,

 --- Chris Benham <chrisbenham at bigpond.com> a écrit : 
> Kevin,
> Regarding  the 3 methods I have  recently posted: "Approval Runoff" 
> (AERWE),  "Improved Generalised Bucklin" (featuring  "forwards-backwards 
> runoff"), and  Condorcet  completed  by reduced-rank Condorcet.
> I would be very interested in seeing any examples of Participation failure.

I've come up with one each.  You may want to check my IGB work.

Condorcet completed by utility-based compression:
40 b 100, c 80, a 0
35 c 100, a 25, b 0

B is the CW and wins.

Add in:
25 a 100, b 25, c 0

Now there's a cycle.  When the ballots are compressed to two-rank, C is the winner.


"AERWE" (Approval Runoff):

6 A>D>C | B  (The pipes are the approval cutoffs.)
5 B>D>C | A
A has a majority and wins.

Add in:
4 C>A | B>D
First B and then A are shunted, at which point D has a majority.


Improved Generalised Bucklin (IGB):

6 A>E>B>C>D
5 B>E>A>C>D
The final pairing is A vs. E, and A wins, clearly.

Add in:
4 C>D>A>B>E
Now the final pairing is E vs. himself, so E wins.


Please tell me if your results differ.


Kevin Venzke
stepjak at yahoo.fr


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