Hi, everyone. I was just sent a note letting me know my last message was in an
unreadable format (a copy of it here:
http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20080308/a1502ffe/attachment.html),
so I thought I'd resend it using Thunderbird instead of the web-based email
program I used before. If someone can let me know if the formatting is garbled
(I know the content is often garbled, but that's a given :) ) then please let
me know. Thanks!
(I wouldn't re-send it, but I'd like it to appear in the archive correctly. Not
sure what happened last time, though). The text between the underlines
("________") is what I wrote before.
_______________________________
Snipping the message:
**********************
On Mar 3, 2008, at 1:45 , <[EMAIL PROTECTED]> <[EMAIL PROTECTED]> wrote:
> [EMAIL PROTECTED]:
>
> >>Can you also clarify a bit how step 3 is counted when some candidate X is
> >>beaten by two other candidates (Y and Z).
> >>I find the proposed method interesting since it seems to aim at electing
> >>good winners (using a function minimizes the problems caused to the
> >>voters, from one point of view).
>
> I'd be happy to try. Do you have an example election for me to play with?
> I'm assuming you mean where I said
>
>
> 3. If there is no Condorcet winner, find the shortest distance (sum of
> individual ranges) necessary to produce a Condorcet winner.
>
Sorry for some delay in replying. Here's one quick example.
1: A=10 B=2 C=1 D=0
1: A=10 C=7 B=6 D=0
1: B=10 C=6 A=5 D=0
3: C=10 D=5 A=1 B=0
3: D=10 B=4 A=3 C=0
C is now beaten by both A and B, and C has to win them both in order to become
a Condorcet winner. What is the "shortest distance (sum of individual ranges)"
for C in this example and how do you count it?
**************
Okay, here's how I did it by hand (sorry if it's a bit cryptic).
Given the following:
1: A=10 B=2 C=1 D=0
1: A=10 C=7 B=6 D=0
1: B=10 C=6 A=5 D=0
3: C=10 D=5 A=1 B=0
3: D=10 B=4 A=3 C=0
The question was: "C is now beaten by both A and B, and C has to win them both
in order to become a Condorcet winner. What is the "shortest distance (sum of
individual ranges)" for C in this example and how do you count it?"
Here are the number of pairs each way:
A>B (1+1+3)
A>C (1+1+3)
A>D (1+1+1)
B>A (1+3)
B>C (1+1+3)
B>D (1+1+1)
C>A (1+3)
C>B (1+3)
C>D (1+1+1+3)
D>A (3+3)
D>B (3+3)
D>C (3)
Simplifying (numbers in parenthesis indicate surplus votes) and showing the
pair relations:
A>B (1)
A>C (1)
B<C (1)
C>D (3)
D>A (3)
D>B (3)
To remove the relation A>B, it would take 1 vote, the smallest total distance
of which is 1 (1-0).
To remove the relation A>C, it would take 1 vote, the smallest total distance
of which is 3 [(10-7) or (3-0)]
To remove the relation B>C, it would take 1 vote, the smallest total distance
of which is 1 (2-1)
To remove the relation C>D, it would take 3 votes, the smallest total distance
of which is 11 [(1-0)+(10-5)+(10-5)]
To remove the relation D>A, it would take 3 votes, the smallest total distance
of which is 12 [(5-1)+(5-1)+(5-1)]
To remove the relation D>B, it would take 3 votes, the smallest total distance
of which is 15[(5-0)+(5-0)+(5-0)]
To make A the weak Condorcet winner (A>=B,C,D), removing the relation D>A is
sufficient. The total distance is 12.
To make B the weak Condorcet winner (B>=A,C,D), removing the relation A>B and
D>B is sufficient. The total distance is 16 (1+15)
To make C the weak Condorcet winner (C>=A,B,D), removing the relation A>C and
B>C is sufficient. The total distance is 4 (3+1)
To make D the weak Condorcet winner (D>=A,B,C), removing the relation C>D is
sufficient. The total distance is 11.
Using this method, C would be the winner, since 4 is the shortest distance. The
complete order is C>D>A>B.
(I use the weak Condorcet criterion, because an infinitesimal amount added to
either candidate in a tie is sufficient to create a winner.)
Let me know if anything is unclear, and I'll try to give a better explanation
(grin).
I might play around with the same election and see what removing the lowest
order of preferences (and not just the closest preferences) would yield.
Michael Rouse.
____________________________________
Anyway, if it's garbled but readable enough to see this line, let me know. Or
if it came through fine, that would be nice to know, and I might try a test
with the webmail program again. Thanks!
Mike
----
Election-Methods mailing list - see http://electorama.com/em for list info
