[EM] The powers of YES/NO/Approval are unequal; J prog calculates Borda weights

[Craig Carey]

At 08:19 20.10.00 +1300 Friday, Craig Carey wrote:

Correction: I suggested that Borda was easy to code up using J, but seems to
not easy.
Here is a calculation of the matrix of Borda weights in the standard Borda
method:

    ]b=.(|:(|.p)*(|.>:/~p))+(|.|:>/~p)*(p-1)%2[p=.i.10

9 8   7   6   5   4   3   2   1   0
9 8   7   6   5   4   3   2   1   0
9 8   7   6   5   4   3   2 0.5 0.5
9 8   7   6   5   4   3   1   1   1
9 8   7   6   5   4 1.5 1.5 1.5 1.5
9 8   7   6   5   2   2   2   2   2
9 8   7   6 2.5 2.5 2.5 2.5 2.5 2.5
9 8   7   3   3   3   3   3   3   3
9 8 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5
9 4   4   4   4   4   4   4   4   4


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At 22:39 19.10.00 -0400 Thursday, DEMOREP1 at aol.com wrote:
...
 >YES = 1
 >
 >NO = 0
...
 >D- See world education test scores of the industrialized nations.
 >
 >What are the I.Q.'s of Mr. Bush and Mr. Gore ---- the major choices for U.S.
 >President in 2000 as determined by various presidential primaries (by about
 >10-15 percent of the U.S. voters who took the time and effort to vote in 
such
 >primaries) ???
...

If you were concerned about your method needing to fit the needs of an
uneducated public, then why not normalize the weights of each paper. For
elections with at least 2 winners and at least 4 candidates, a paper with
2 YES crosses on it has more power than a paper with 1 YES cross mark.

Why not make the defence for Borda/Approval that maybe the advocates of those
methods may be silent over. Tell us this Demorep, if you can:

     why is it desirable/essential to have 'voters' power to affect the
     election results', vary widely?. You must have that as a principle or
     something since it is so easy to adjust the method so that instead your
     ideas upholds the ideal and human right of 'equal suffrage'. This also
     applies in a similar way to the so called "Approval Vote" method, a rights
     violating method unsuitable for use in large public elections.


Here are 2 power formulae:

(1) Power1 = Min((Sum i)[W1 - w(i)], (Sum i)[w(i) - W0]),
                  W1=(Max j)w(j),
                  W0=(Min j)w(j)

(2) Power2 = (Min u)(Sum i)abs(w(i)-u)

In the 'Approval' method of Demorep, two crosses might make w look like this:
w = (1, 1, 0, 0, 0, 0, 0, 0)

Power1 = Min(6,2) = 2
Power2 = (Min u)(2*abs(1-u)+6*abs(u-0)) = (Min u)(2-2*u+6*abs(u)) = 2

So the weight of a paper with 2 crosses would be multiplied by 0.5. A better
solution _could be_ to discard the method or instruct that all the votes had
to be used.

Perhaps Demorep could tell the list how it is democratic to deprive voters of
their right to "equal suffrage" (Article 25(b) International Covenant on Civil
and Political Rights). Is this too strongly put Demorep?.

What is you objection to calculating a power of a paper and normalising the
power of each person's vote. STV has no such problem.