Re: [EAI] Please - Don't state preferences yet!
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Re: [EAI] Please - Don't state preferences yet!
On Mon, 23 Jul 2007 15:23:36 +0100, Harald Tveit Alvestrand
<harald at alvestrand.no> wrote:
Note - my message was intended to start the discussion on the subject on
how to decide on a MIME type. I am NOT recording people's position until
we've decided what mechanism to use to decide!
Ah! The methods you have proposed is known as "Alternative Vote", or "AV".
It usually works fine, but can sometimes go completely wrong. For example,
in the Lilliput Referendum to decide on which end an egg should be opened,
the alternatives were:
Big-Endian
Little-Endian
Scrambled-egg
Naturally, the Big-Endians all voted for Big first and Little last, with
Scrambled in the middle. The Little-Endians all votes for Little first and
Big last, with Scrambled in the middle.
Only 1 person actually put Scranbled first, and hence it got eliminated
from the count, leaving a dead heat between Big and Little. Whereas in
fact, if Scrambled has won, everybody would have been reasonably happy
(their real desire was to ensure that the other main party failed, rather
than that their own succeeded). Hence the compromise got squeezed out.
The ideal mathod, designed by the Marquis de Condorcet, copes better with
such situations, since it examines the complete matrix of how many people
prefer each possible option over each of the others.
So with 50 people voting 1. Big, 2. Scrambled, 3. Little
and 50 people voting 1. Little, 2. Scrambled, 3. Big
and 1 person voting 1. Scrambled 2. [don't care between B and L]
you get the matrix
B S L
B - 50 50
S 50 - 50
L 51 51 -
And Scrambled wins because it was preferred over Big by 51:50
and it was preferred ov Little by 51:50.
The Condorcet can result in a tie (but so can AV). And it can also result
in a cycle (but very rarely does, and when it does it indicates a totally
confused electorate).
I have a program, written in C, that will work it all out, which I can
supply on request. For example, on the group of people who have voted so
far (which is not terribly meaningful, given that lots more people have
not yet voted at all), my program would give:
K:
message/intl-email--------------------------------------------------------+
J:
message/ima------------------------------------------------------------+ |
I: message/utf8-email--------------------------------------------------+
| |
H: message/utf8eai--------------------------------------------------+ |
| |
G: message/eai---------------------------------------------------+ | |
| |
F: message/i18n-email-----------------------------------------+ | | |
| |
E: message/mail--------------------------------------------+ | | | |
| |
D: message/global---------------------------------------+ | | | | |
| |
C: message/international-----------------------------+ | | | | | |
| |
B: message/i18n-----------------------------------+ | | | | | | |
| |
A: message/utf8smtp----------------------------+ | | | | | | | |
| |
| | | | | | | | |
| |
Klensin - - 2 3 1 - - - -
- 4
Lindsey 4 5 6 7 8 1 10 9 3
11 2
Newman - 7 1 2 4 6 9 8 5
10 3
Zoltan 5 8 1 7 6 4 10 11 3
9 2
RESULT:
C: message/international is preferred to A: message/utf8smtp by 3 : 1
C: message/international is preferred to B: message/i18n by 3 : 1
C: message/international is preferred to D: message/global by 4 : 0
C: message/international is preferred to E: message/mail by 3 : 1
C: message/international is preferred to F: message/i18n-email by 3 : 1
C: message/international is preferred to G: message/eai by 4 : 0
C: message/international is preferred to H: message/utf8eai by 4 : 0
C: message/international is preferred to I: message/utf8-email by 3 : 1
C: message/international is preferred to J: message/ima by 4 : 0
C: message/international is preferred to K: message/intl-email by 3 : 1
C: message/international is therefore a condorcet winner
The following matrix shows the votes in more detail.
The number at [row,column] indicates the number of voters who placed the
[row] option ahead of the [column] option in their order of preference
K: message/intl-email--------------------------------------------------+
| J: message/ima----------------------------------------------------+ |
| | I: message/utf8-email----------------------------------------+ | |
| | | H: message/utf8eai--------------------------------------+ | | |
| | | | G: message/eai-------------------------------------+ | | | |
| | | | | F: message/i18n-email-------------------------+ | | | | |
| | | | | | E: message/mail--------------------------+ | | | | | |
| | | | | | | D: message/global-------------------+ | | | | | | |
| | | | | | | | C: message/international-------+ | | | | | | | |
| | | | | | | | | B: message/i18n-----------+ | | | | | | | | |
| | | | | | | | | | A: message/utf8smtp--+ | | | | | | | | | |
| | | | | | | | | | +----------------- \\ 2 1 2 2 0 2 2 0 2 0
| | | | | | | | | +------------------- 1 \\ 1 1 1 0 3 3 0 3 0
| | | | | | | | +--------------------- 3 3 \\ 4 3 3 4 4 3 4 3
| | | | | | | +----------------------- 2 3 0 \\ 2 2 4 4 2 4 2
| | | | | | +------------------------- 2 3 1 2 \\ 2 4 4 2 4 1
| | | | | +--------------------------- 3 3 1 2 2 \\ 3 3 1 3 1
| | | | +----------------------------- 1 0 0 0 0 0 \\ 1 0 2 0
| | | +------------------------------- 1 0 0 0 0 0 2 \\ 0 2 0
| | +--------------------------------- 3 3 1 2 2 2 3 3 \\ 3 0
| +----------------------------------- 1 0 0 0 0 0 1 1 0 \\ 0
+------------------------------------- 4 4 1 2 3 3 4 4 4 4 \\
The second matrix shows the effect of subtracting [column,row] from
[row.column] so as to give the majority in favour of [row] as against
[column].
Observe that the winning row(s) has no negative entries.
K: message/intl-email--------------------------------------------------+
| J: message/ima----------------------------------------------------+ |
| | I: message/utf8-email----------------------------------------+ | |
| | | H: message/utf8eai--------------------------------------+ | | |
| | | | G: message/eai-------------------------------------+ | | | |
| | | | | F: message/i18n-email-------------------------+ | | | | |
| | | | | | E: message/mail--------------------------+ | | | | | |
| | | | | | | D: message/global-------------------+ | | | | | | |
| | | | | | | | C: message/international-------+ | | | | | | | |
| | | | | | | | | B: message/i18n-----------+ | | | | | | | | |
| | | | | | | | | | A: message/utf8smtp--+ | | | | | | | | | |
| | | | | | | | | | +----------------- \\ 1 -2 0 0 -3 1 1 -3 1 -4
| | | | | | | | | +------------------- -1 \\ -2 -2 -2 -3 3 3 -3 3 -4
| | | | | | | | +--------------------- 2 2 \\ 4 2 2 4 4 2 4 2
winner
| | | | | | | +----------------------- 0 2 -4 \\ 0 0 4 4 0 4 0
| | | | | | +------------------------- 0 2 -2 0 \\ 0 4 4 0 4 -2
| | | | | +--------------------------- 3 3 -2 0 0 \\ 3 3 -1 3 -2
| | | | +----------------------------- -1 -3 -4 -4 -4 -3 \\ -1 -3 1 -4
| | | +------------------------------- -1 -3 -4 -4 -4 -3 1 \\ -3 1 -4
| | +--------------------------------- 3 3 -2 0 0 1 3 3 \\ 3 -4
| +----------------------------------- -1 -3 -4 -4 -4 -3 -1 -1 -3 \\ -4
+------------------------------------- 4 4 -2 0 2 2 4 4 4 4 \\
--
Charles H. Lindsey ---------At Home, doing my own thing------------------------
Tel: +44 161 436 6131 ;
Web: http://www.cs.man.ac.uk/~chl
Email: chl at clerew.man.ac.uk Snail: 5 Clerewood Ave, CHEADLE, SK8 3JU, U.K.
PGP: 2C15F1A9 Fingerprint: 73 6D C2 51 93 A0 01 E7 65 E8 64 7E 14 A4 AB A5
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