[EM] Easy fix to Alaska's ranked-choice voting

[Colin Champion]

On 14/11/2022 03:54, Forest Simmons wrote..
> many wise things
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.

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.
    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).
    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.
    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.
    CJC

[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.
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