Scott Ritchie wrote:
On Mon, 2005-07-11 at 13:41 -0500, Dan Bishop wrote:
* Independence of Clones: FAIL.
Consider the example election (in which A and D won) with D replaced by
D1>D2>D3:
33 A>D1>D2>D3>B>C
33 B>D1>D2>D3>A>C
32 C>D1>D2>D3>A>B
2 D1>D2>D3>A>B>C
The elimination order is C, B, A, D3, D2, D1. The coalition {A, D1, D2,
D3} is entitled to 1 seat, and {A, B, D1, D2, D3} is entitled to 2
seats. The winners are D1 and D2, which gives the D clone set an extra
seat compared to the original election.
D is a condorcet winner here. D1 is a condorcet winner as well, but it
seems very interesting to note that even if we eliminate a quota's worth
of votes from the D supporters after declaring D1 elected, D2 would be a
condorcet winner. This seems meaningful, as it implies that both D1 and
D2 have distinct quotas worth of votes rating them as top preference
before eliminating any nonwinning candidates - that sounds like they
should win.
What if we clone someone outside of this set, ie other than D1, D2, and
D3? Can teaming occur then?
It does not.
If A is replaced by A1>A2>A3, {A1, D} wins.
If B is replaced by B1>B2>B3, {A, D} wins.
If C is replaces by C1>C2>C3, {A, D} wins.
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