[EM] Required Number Votes in a Matrix
Kristofer Munsterhjelm
km_elmet at t-online.de
Tue May 20 12:38:22 PDT 2014
On 05/20/2014 05:31 AM, DNOW1 at aol.com wrote:
> Many of the examples by folks have INCOMPLETE votes in a N x N matrix.
Er, they don't have incomplete votes in the matrix. They usually don't
mention the matrix at all.
> That is improper.
> A mini Approval Boundary Example --
>
> 50 AB
> 1 B
> 49 Z
> 100
>
> IF Approval is being used, then B wins -- 51 B, 50 A, 49 Z.
> Choice A is obviously very hurt by the 2nd choice votes for B.
>
> IF all voters are required to use Number Votes for all choices, then
> there would be --
> Single office
> 50 ABZ
> 1 B??
> 49 Z??
> 100
>
> Who wins then -- with what election method ???
Some election methods can provide an outcome even with incomplete
rankings. For instance, for Condorcet, consider:
50: A>B
1: B
49: Z
Then the raw matrix is:
(against)
A B Z
A ## 50 50
B 1 ## 51
Z 49 49 ##
and the (derived) wv matrix is
A B Z
A ## 50 50
B 0 ## 51
Z 0 0 ##
so the ranking is: A gets first place (beats B and Z). B gets second
(beats Z), and Z gets third (is beaten by both).
> Thus - If there are N choices, then should the first N-1 choices be
> deemed *YES* votes ???
The usual implicit Approval interpretation is that listed candidates are
considered yes votes and those not listed are considered no.
For instance:
50: A>B
here the Approval information is "yes to A and B, no to Z".
With explicit approvals, this notation is sometimes used on the list:
2: A>>B>Z
meaning "yes to A, no to B and Z".
> How many of the *complex* election methods have ANY chance whatever of
> becoming such an Amendment ???
>
> See the chaos about the mere statutory math for apportioning USA Reps
> among the States.
The surprising thing there is that the apportionment math is *more*
complex than it needs to be; probably for a combination of mathematical
elegance (that didn't turn out to be so elegant after all) and political
convenience.
Before the present Huntington-Hill system, the US apportionment used
Webster's method, which can be pretty simply put: each state gets as
many representatives as its state population divided by x, rounded off.
The variable x is set so that the total comes out to the total number of
seats in the House.
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