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<p> </p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Consider a typical single member scenario, like the
2000 </span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">US</span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> presidential election. Say George W Bush (label B)
gets 101. Al Gore (label A) gets 100. Ralph Nader (label C) gets
10. (After his vote got squeezed from strategic voting.)</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Bush is elected on single preference votes. If there
were a second ballot, or instant run-off vote (IRV), Al Gore
wins on second preferences of Nader, the “spoiler” who is
eliminated.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">So, IRV passes on independence of irrelevant
alternatives (IIA). But IRV fails on the </span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Laplace</span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> law of preference gradation. (Orders of preference
vote gradually fall off in count importance.) This also means
that the IIA criterion is inconsistent with the </span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Laplace</span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> law.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Binomial STV avoids the dilemma of this
inconsistency.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Suppose IRV gives:</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> </span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">100 A C _</span> </p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">101 B _ _</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""><span style="mso-spacerun:yes"> </span>10 C A _</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> </span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">With IRV, A picks up the second preferences of C,
and wins with 110.</span> </p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Binomial STV counts abstentions, shown by the dash
lines. The third preferences are all abstentions, and they do
nothing to change the simple plurality count. It is conceivable
that in a less contentious world than ours, this could be the
case. But it is assumed that the voters have been informed that
last preferences can be given to count against candidates. And
the full slate of preferences is as follows:</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> </span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">100 A > C > B</span> </p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">101 B > A > C</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""><span style="mso-spacerun:yes"> </span>10 C > A
> B</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> </span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">The keep value quotient (kvq), of a candidate, is
the election keep value, divided by the exclusion keep value:</span>
</p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">the keep value is the quota, 211/2 = 105.5, divided
by candidate vote.</span></p>
<span style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""></span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">kvq A = 0/100. Here, zero means close to 0, giving a
very small fraction.</span>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> </span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">B = 110/101</span> </p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">C = 101/10</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> </span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Unity, or less, is the election (or exclusion)
threshold of an election (or exclusion) keep value. Less than
unity passes the threshold. So, A wins with binomial STV,
without breaking the </span><span style="font-size:16.0pt;
font-family:"Arial Rounded MT Bold"">Laplace</span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> law, or IIA.</span> </p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> </span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Suppose, however, that Bush supporters decide to
vote insincerely, by making Gore their last preference – even
tho Nader is the last person they want to see win, but know he
can’t, anyway. </span> </p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">(However, this scenario might be sincere in </span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">UK</span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">, with A as Labour, B as Tory, and C as Liberal
Democrat. In either case, a change in the vote, sincere or
otherwise, will change the count in a toward manner, with good
book-keeping.)</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> </span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""></span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">The preference slate becomes:</span> </p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> </span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">100 A > C > B</span> </p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">101 B > C > A</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""><span style="mso-spacerun:yes"> </span>10 C > A
> B</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> </span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Then, kvq becomes:</span> </p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">A = 101/100</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">B = 110/101</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">C = 0/10</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> </span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">There is a contradictory answer. B is closer to the
quota but A is closer to the quotient.</span> </p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">This is not a logical contradiction but a contingent
contradiction. Decision, as to the winner, is not a democratic
decision, but an administrative decision, at present FPTP, based
on a convention, reached by previous agreement. (Single majority
is the least democratic system, in the first place.)</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">A first approximation of an administrative decision
(It would be “spurious accuracy” to go further) is:</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">B quota deficit: 105.5/101 ~ 1.0446.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">A quotient deficit: 101/100 = 1.01.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> </span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Therefore, an administrative election is of Gore.
(The Supreme Court also made an administrative decision.) </span>
</p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">The result would most likely be similar, if Binomial
STV, used more accurate figures. To say nothing of the
investigation, by Greg Palast, of the electoral roll. (The Best
Democracy That Money Can Buy.) </span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""> </span><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">I repeat that for a democratic decision, as from
those Keltic reports, prevously cited, I don’t recommend less
than 4 or 5 member Andrae/Hare system (at-large STV/PR).</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Regards,</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold"">Richard Lung.</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""><br>
</span></p>
<p class="MsoNormal"><span
style="font-size:16.0pt;font-family:"Arial Rounded MT
Bold""><br>
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