[EM] Mixing IRV and Condorcet
Stephane Rouillon
stephane.rouillon at sympatico.ca
Mon Apr 7 15:19:01 PDT 2003
...in order to make it acceptable to most voters.
Please let me show how I think Condorcet can be made acceptable to
usual voters, even in the cases described by James.
> The situation I was concerned about looks more like this (first preferences only,
> rest as before):
> 10 FR
> 38 R
> 3 C
> 39 L
> 10 FL
>
> or even
> 48 R
> 3 C
> 49 L
>
> C is still the Condorcet winner, but in very different circumstances.
> I know it makes sense, but that doesn't make it acceptable to the electorate at
> large.
>
> James
>
Starting from Chris example:
> The example I referred to at the top:
> 10: FR > R > C > L > FL
> 10: R > FR > C > L > FL
> 15: R > C > FR > L > FL
> 16: C > R > L > FR > FL
> 15: C > L > R > FL > FR
> 13: L > C > FL > R > FR
> 11: L > FL > C > R > FR
> 10: FL > L > C > R > FR
>
Suppose I use ranked pairs (relative margins) to build my
ranked results from these ballots:
10: FR>R 90: R>FR => R>FR (80%)
20: FR>C 80: C>FR => C>FR (60%)
35: FR>L 65: L>FR => L>FR (30%)
51: FR>FL 49: FL>FR => FR>FL (2%)
35: R>C 65: C>R => C>R (30%)
51: R>L 49: L>R => R>L (2%)
66: R>FL 34: FL>R => R>FL (32%)
66: C>L 34: L>C => C>L (32%)
79: C>FL 21: FL>C => C>FL (58%)
90: L>FL 10: FL>L => L>FL (80%)
First let me say that a realistic example would contain a greater mix
because politicians cannot usually be placed on a left-right axis or at
least the electorate
has other considerations to take in account...
Lock R>FR (80%), L>FL (80%), C>FR (60%), C>FL (58%),
R>FL (32%), C>L (32%), L>FR (30%), C>R (30%), FR>FL (2%),
R>L (2%).... There is no cycle the result is C>R>L>FR>FL.
Now how could justify the fact that C is the winner using a IRV
approach.
One interesting fact is that removing a candidate does not affect the
ordering between the others (when there is no cycle). When there is some
cycles, I think that at least, removing the last does not affect the
order of the others.
Let's use IRV iterative elimination process, but keeping the Condorcet
order
to select the looser that is eliminated:
1st round:
result C>R>L>FR>FL => FL eliminated.
Ballots for 2nd round:
10: FR > R > C > L
10: R > FR > C > L
15: R > C > FR > L
16: C > R > L > FR
15: C > L > R > FR
34: L > C > R > FR
2nd round:
result C>R>L>FR => FR eliminated.
Ballots for 3rd round:
35: R > C > L
16: C > R > L
15: C > L > R
34: L > C > R
3rd round:
result C>R>L => L eliminated.
Ballots for 4th round:
35: R > C
65: C > R
4th round:
result C>R => R eliminated.
Using IRVists vocabulary, C wins with a 65% majority over R.
A generalized version of this method using truncated ballots for a fully
proportional multiple-winners method is available among several other
models at
http://groups.yahoo.com/group/Electoral_systems_designers
Comments as new members are welcome...
S. Rouillon
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