<HTML><FONT FACE=arial,helvetica><HTML><FONT SIZE=2 PTSIZE=10 FAMILY="SANSSERIF" FACE="Arial" LANG="0">I wrote:<BR>
<BR>
>>What I'm interested in at the moment is going beyond IRV, Condorcet and<BR>
>>Approval towards a single winner system that gives high utility,<BR>
>>generally preferred winners.<BR>
<BR>
James Armytage-Green replied:<BR>
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>Sounds interesting. What do you have in mind specifically?<BR>
<BR>
<BR>
<B><U>Ranked Approval</U><BR>
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</B><U>How you vote</U><BR>
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Voters may approve as few or as many candidates as they wish.<BR>
<BR>
Voters then rank the candidates they have approved (equal ranking allowed). You can only rank candidates who you approve.<BR>
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<U>How you decide the winner:</U><BR>
<BR>
If no candidate is approved on a majority of ballots the most approved candidate wins.<BR>
<BR>
If one candidate is approved on a majority of ballots then that candidate wins.<BR>
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If two or more candidates are approved by a majority of voters pairwise comparisons are conducted between these candidates to determine the winner. In the case of a Condorcet cycle the most approved candidate wins.<BR>
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<U>Several examples<BR>
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Example 1<BR>
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</U>45 A 100> B 70 > C 0<BR>
10 B 100> A 70 > C 0<BR>
5 B 100> C 70 > A 0<BR>
40 C 100> B 70 > A 0 <BR>
<BR>
Translates using zero-info approval strategy to:<BR>
<BR>
45 A>B<BR>
10 B>A<BR>
5 B>C<BR>
40 C>B<BR>
<BR>
Approval scores:<BR>
<BR>
A 55<BR>
B 100<BR>
C 45<BR>
<BR>
A pairwise comparison is conducted between A and B:<BR>
<BR>
A v B 45 v 55 <BR>
<BR>
B wins.<BR>
<BR>
<U>Example 2<BR>
<BR>
</U>45 A 100> B 10 > C 0<BR>
10 B 100> A 90 > C 0<BR>
5 B 100> C 90 > A 0<BR>
40 C 100> B 10 > A 0<BR>
<BR>
Translates using zero info approval strategy into:<BR>
<BR>
45 A<BR>
10 B>A<BR>
5 B>C<BR>
40 C<BR>
<BR>
Approval scores:<BR>
<BR>
A 55<BR>
B 15<BR>
C 45<BR>
<BR>
A is the only candidate approved by a majority and therefore A wins.<BR>
<BR>
<U>Example 3<BR>
<BR>
</U>55 A 100> B 70> C 0<BR>
10 B 100> A 70 > C 0<BR>
35 C100 > B70 > A 0<BR>
<BR>
Translates using zero-info approval strategy to:<BR>
<BR>
55 A>B<BR>
10 B>A<BR>
35 C>B<BR>
<BR>
Approval scores:<BR>
<BR>
A 65<BR>
B 100<BR>
C 35<BR>
<BR>
A pairwise comparison is conducted between A and B:<BR>
<BR>
A v B 55 v 45 <BR>
<BR>
A wins.<BR>
<BR>
<U>Example 4</U><BR>
<BR>
26: Bush 100 > Dean 10 > Kerry 0<BR>
22: Bush 100 > Kerry 10 > Dean 0<BR>
26: Dean 100 > Kerry 90 > Bush 0<BR>
1: Dean 100 > Bush 50 > Kerry 0<BR>
21: Kerry 100 > Dean 90 > Bush 0<BR>
4: Kerry 100 > Bush 50 > Dean 0<BR>
<BR>
In this example the mean rating for the Dean>Bush>Kerry voter and the Kerry>Bush>Dean voters is 50 which is Bush's rating so I'll work the method with Bush approved by these voters and Bush not approved.<BR>
<BR>
Bush not approved translates into the ballots:<BR>
<BR>
26: Bush<BR>
22: Bush<BR>
26: Dean > Kerry<BR>
1: Dean<BR>
21: Kerry> Dean<BR>
4: Kerry<BR>
<BR>
Approval scores:<BR>
<BR>
Bush 48<BR>
Dean 48<BR>
Kerry 51<BR>
<BR>
Kerry is the only candidate approved by a majority of voters therefore Kerry wins.<BR>
<BR>
With Bush approved translates into the ballots:<BR>
<BR>
26: Bush<BR>
22: Bush<BR>
26: Dean > Kerry<BR>
1: Dean > Bush<BR>
21: Kerry> Dean<BR>
4: Kerry > Bush<BR>
<BR>
<BR>
Approval scores:<BR>
<BR>
Bush 53<BR>
Dean 48<BR>
Kerry 51<BR>
<BR>
Pairwise comparison between Bush and Kerry.<BR>
<BR>
Kerry versus Bush 51 v 49<BR>
<BR>
Kerry wins.<BR>
<BR>
The idea is that when voters cast sincere ballots the method will elect a high utility generally preferred winner if there is one. I have only partially explored voting strategies as regards this method.<BR>
<BR>
One final point I am fairly certain on is that a very similar or identical method has been proposed on this list by somebody else ( possibly Kevin Venzke ) but I'm sure who or when.<BR>
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Comments, criticisms ?<BR>
<BR>
David Gamble<BR>
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