On May 13, 2010, at 10:25 PM, robert bristow-johnson wrote:
On May 13, 2010, at 10:08 PM, Dave Ketchum wrote:
I read of arranging ballot data in a triangle, rather than in a
matrix as usually described. A minor detail, but what would be
easiest for ballot counters is most important while they count,
though rearranging for later processing would be possible.
in all cases, i am assuming that a computer is tabulating the
ballots. to count Condorcet by hand is difficult, because (if
number of candidates is N) you would have to update up to N*(N-1)/2
numbers out of N*(N-1) for each ballot handled, rather than 1 of N
numbers as is done for FPTP (the latter lets you sort to piles for
quick double checking).
That reads as if you were trying for a prize for large numbers.
Suppose someone bullet votes; N-1 is the most pairs you can find
reason for updating - 3(N-1) if the voter ranked three.
Read my post where I describe less labor for counting:
Q elements in an N array if the voter ranks Q candidates.
P elements in N*N if the Q elements were composed of P pairs (0
for a bullet vote; 6 for Q=4).
the reason i prefer that triangle (which is just like the NxN matrix
with half of the elements folded over the main diagonal and also
sorted in order of the Condorcet ranking (assuming no cycles, if
there are cycles, even one not including the CW, the triangle won't
look so pretty) is because it displays the result in such a way that
you can immediately infer the who-beats-who results from it. even
though i haven't seen it anywhere else before, i make no claim to
novelty. i really just can't understand why anyone would use the
NxN square matrix. it's really hard to glance at it and see what
numbers to pair together.
--
r b-j [email protected]
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