[EM] proposal: weighted pairwise comparison

[Stephane Rouillon]

Dgamble997 at aol.com a écrit :

> I wrote:
>
> >>What I'm interested in at the moment is going beyond IRV, Condorcet
> and
> >>Approval towards a single winner system that gives high utility,
> >>generally preferred winners.
>
> James Armytage-Green replied:
>
> >Sounds interesting. What do you have in mind specifically?
>
>
> Ranked Approval
>
> How you vote
>
> Voters may approve as few or as many candidates as they wish.
>
> Voters then rank the candidates they have approved (equal ranking
> allowed). You can only rank candidates who you approve.

I like that. This is the same input I use for SPPA to produce a
proportional multiple-winners result...

> How you decide the winner:
>
> If no candidate is approved on a majority of ballots the most approved
> candidate wins.
>
> If one candidate is approved on a majority of ballots then that
> candidate wins.
>
> 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.
>
> Several examples
>
> Example 1
>
> 45 A 100> B 70 > C 0
> 10 B 100> A 70 > C 0
> 5 B 100> C 70 > A 0
> 40 C 100> B 70 > A 0
>
> Translates using zero-info approval strategy to:
>
> 45 A>B
> 10 B>A
> 5   B>C
> 40 C>B
>
> Approval scores:
>
> A 55
> B 100
> C 45
>
> A pairwise comparison is conducted between A and B:
>
> A v B   45 v 55
>
> B wins.
>
> Example 2
>
> 45 A 100> B 10 > C 0
> 10 B 100> A 90 > C 0
> 5 B 100> C 90 > A 0
> 40 C 100> B 10 > A 0
>
> Translates using zero info approval strategy into:
>
> 45 A
> 10 B>A
> 5   B>C
> 40 C
>
> Approval scores:
>
> A 55
> B 15
> C 45
>
> A is the only candidate approved by a majority and therefore A wins.
>
> Example 3
>
> 55 A 100> B 70> C 0
> 10 B 100> A 70 > C 0
> 35 C100 > B70 > A 0
>
> Translates using zero-info approval strategy to:
>
> 55 A>B
> 10 B>A
> 35 C>B
>
> Approval scores:
>
> A 65
> B 100
> C 35
>
> A pairwise comparison is conducted between A and B:
>
> A v B   55 v 45
>
> A wins.
>
> Example 4
>
> 26: Bush 100 > Dean 10 > Kerry 0
> 22: Bush 100 > Kerry 10 > Dean 0
> 26: Dean 100 > Kerry 90 > Bush 0
> 1: Dean 100 > Bush 50 > Kerry 0
> 21: Kerry 100 > Dean 90 > Bush 0
> 4: Kerry 100 > Bush 50 > Dean 0
>
> 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.
>
> Bush not approved translates into the ballots:
>
> 26: Bush
> 22: Bush
> 26: Dean > Kerry
> 1: Dean
> 21: Kerry> Dean
> 4: Kerry
>
> Approval scores:
>
> Bush 48
> Dean 48
> Kerry 51
>
> Kerry is the only candidate approved by a majority of voters therefore
> Kerry wins.
>
> With Bush approved translates into the ballots:
>
> 26: Bush
> 22: Bush
> 26: Dean > Kerry
> 1: Dean > Bush
> 21: Kerry> Dean
> 4: Kerry > Bush
>
>
> Approval scores:
>
> Bush 53
> Dean 48
> Kerry 51
>
> Pairwise comparison between Bush and Kerry.
>
> Kerry versus Bush     51 v 49
>
> Kerry wins.
>
> 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.
>
> 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.

I do not think it is equivalent to IRV or Condocet methods with residual
approval weights (methods I presented some time ago),
but I will look at your method....

>
>
> Comments, criticisms ?
>
> David Gamble
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