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<font face="Helvetica, Arial, sans-serif">That's neat. (But... )<br>
CJC<br>
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<div class="moz-cite-prefix">On 13/09/2023 11:35, Kristofer
Munsterhjelm wrote:<br>
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<blockquote type="cite"
cite="mid:57e85536-f330-a196-f247-dadc70010455@t-online.de">On
9/13/23 09:18, Colin Champion wrote:
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<blockquote type="cite">I notice that RP is the only election
method mentioned by name in the Virginia agenda.
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A while ago I ran some simulations on elections with truncated
ballots. Something I noticed was that the presence of RP in the
list of methods made the software unacceptably slow. I didn't
look into the cause, but there's a natural explanation, which is
the fact that RP is known to be NP-complete when it deals
correctly with tied margins, i.e. by exhausting over all their
permutations. Presumably if some candidates are unpopular and
ballots are extensively truncated, then tied margins are much
likelier than with complete ballots.
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I gather that practical implementations of RP choose a random
permutation rather than exhausting. This seems to me to bring a
danger. The presence of a few vanity candidates (truncated off
almost all ballots) may lead to ties, and this may lead to a
comfortable winner looking as though he owes his victory to a
coin-toss. Obviously this undermines the legitimacy of his win.
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Since RP passes LIIA and Smith, it should be possible to answer
such suspicion by first doing RP, then eliminating every candidate
ranked below the lowest ranked Smith set candidate, and then
showing that the ranking between the remaining candidates does not
change.
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-km
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