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On 14/11/2022 03:54, Forest Simmons wrote..<br>
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<div dir="auto">many wise things<br>
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<font face="Helvetica, Arial, sans-serif">I think Forest slightly
missed my point - I was arguing that SPE could be proposed *as an
alternative* to truncation, since I surmised (incorrectly) that
truncation might have been justified by a desire to avoid
quadratic counting costs. Hence there would be no cutoff as part
of the voting procedure, and no natural concept of implicit
approval. If there is political opposition to mechanical counting,
then proposing a linear-time countable method seems to me better
than either putting up with truncation or fighting unnecessary
battles.<br>
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I don't know why linear-time countability dropped out of
consideration. In 1275 Llull proposed the "league table" method
now often named after Copeland, but with one difference - he
didn't suggest ranked preference voting (after all, paper hadn't
been invented then, let alone computers). Instead he called for
m(m-1)/2 pairwise subelections. In 1299, presumably recognising
the unworkability of this, he proposed a "knockout" method
comprising just m-1 pairwise subelections which amounts to SPE
with an arbitrary agenda. I think this was in one of his writings
which got lost.<br>
A little later, taking advantage of the invention of paper,
Nicholas of Cusa proposed the Borda count in conjunction with
ranked preference voting. Borda reinvented his ideas in the 18th
century. Condorcet (in his Essai) got bogged down in problems
arising from cycles, and partially extricated himself with a
quadratic-time algorithm which is a simplified ranked pairs. In
his later writings he reinvented Llull's league table method and
instantly rejected it on account of its quadratic cost. In its
place he advocated what I take to be a defective form of Bucklin's
method.[1] This was adopted in Geneva and "found not to work" (I
don't know the details, but Bucklin's method is quite a large step
backwards).<br>
Nanson carried on from Condorcet. He agreed that the quadratic
cost made Llull's league table unworkable, wasn't attracted to
Bucklin's method, and instead proposed his own. He may have been a
little optimistic in his costings, but at worst his method is m
log m.<br>
That seems to be the end of the discussion. When Black proposed
his method in the middle of the last century, voting technology
was no different than in Condorcet's day, but he doesn't seem to
have worried about the counting costs. Llull's knockout reappeared
as SPE with a pre-ranking stage to eliminate the obvious
asymmetry, but since quadratic-time pre-rankings are often
assumed, counting time hasn't always been the main consideration.<br>
CJC<br>
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[1]. I always confuse Bucklin's method with Baldwin's. I wish the
latter was called the "Trinity College" method, since it was
invented before Baldwin's time. The Trinity College Dialectic
Society was founded at Nanson's university a few years before
Nanson wrote his memoir, so its voting method was presumably an
early version of Nanson's. <br>
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