# [EM] proposal: weighted pairwise comparison

Dgamble997 at aol.com Dgamble997 at aol.com
Mon Jun 14 14:57:02 PDT 2004

```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.

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 e
xplored 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.

David Gamble

If two or more candidates

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