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<div class="moz-cite-prefix">On 02/06/2022 11:28, Richard Lung
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:dba3f569-b1ca-0d6f-4062-b5c22f58ceca@ukscientists.com">
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<p><br>
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<p> </p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">Sometimes the keep value quotient, in binomial
STV, does not help to decide an election. It may even make the
contest less decisive. Never the less, the quotient is an
extra source of rational information, to that provided by the
quota, as to the decision or indecision of the public.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">The simple plurality method generally implies,
representatively, that it should not be in a single-member
system, but at least in a two member system, and often in a
three or four member system.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">Likewise, I recommend a minimum of a 4 or 5 member
system for binomial STV, for sufficiently representative
elections, to produce decisive results.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">The draft Scottish constitution recommended a
minimum of four member STV constituencies. The Irish
constitutional convention recommended a minimum of five-member
STV constituencies.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">The McAllister report on the Welsh Parliament
cited an academic consensus on four to seven member
constituencies for sufficient diversity of representation.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">Four Welsh reports have recommended the single
transferable vote.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold""> </span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">Thus, a lack of decisiveness, in single-member
binomial STV, is not necessarily a problem of BSTV but it is a
problem of single, double and even triple member
constituencies. The insistence on a decisive election winner
is a presumption of social choice theory.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">The incompleteness theorem of Kurt Gödel is not an
insistence on the “Impossibility” of deductive science. It
took the theorem of Kenneth Arrow to assert that for logical
democracy. (The assertion, that no election method is perfect,
is not a scientific statement, and can be disregarded as
such.)<br>
</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">A first principle of the philosophy of science is
not to presume what one is supposed to be trying to prove. The
search for knowledge requires that ones assumptions may be
disproved. </span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">What elections demonstrate, from the irrational
simple plurality count, to the rationalistic binomial STV, is
that popular opinion may be indecisive. There may be no
demonstrable winner.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">What first past the post does do is to provide an
administratively convenient decision, rather than a
necessarily popular decision.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">Meek method also incorporates a help to the
returning officer. Quota reduction with exhausted preferences
makes for less equitable placements, but facilitates election
to the final seat, in the multi-member constituency.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">Thus, the impossibility theorem insistence on
decisive results amounts to an imperative for an
administrative decision, and not necessarily popular
representation. But the </span><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">United States</span><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold""> is a republic, a thing of the people, not a thing
of Administration, or a “rebureau.” <br>
</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">Regards,</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT
Bold"">Richard Lung.<br>
</span></p>
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<div class="moz-cite-prefix">On 31/05/2022 01:29, Forest Simmons
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CANUDvfq=1S=HyRNeVCtvRUv_Du+fPm12qV69NnujFYVRqRoB5w@mail.gmail.com">
<div dir="auto">
<div>Kristofer noted in passing a very important and
under-appreciated advantage of Condorcet methods:
<div dir="auto"><br>
</div>
<div dir="auto"><span>It can be shown that, for methods
where a majority can always force an </span><span>outcome
by coordinating how they vote, then modifying the method
so that it</span><span> elects the Condorcet winner if
there is one never increases the </span><span>proportion
of elections where strategy is useful, and may indeed
reduce it.</span><br>
</div>
<div dir="auto"><br>
</div>
This is a good reason to routinely include in the
description of every Universal Domain single winner method
that satisfies the Majority Criterion, verbiage to the
effect ...</div>
<div dir="auto"><br>
</div>
<div dir="auto">"Lacking a candidate that outranks any
opponent on more ballots than not ..."</div>
<div dir="auto"><br>
</div>
<div dir="auto">-Forest</div>
<div dir="auto"><br>
<div class="gmail_quote" dir="auto">
<div dir="ltr" class="gmail_attr">El sáb., 28 de may. de
2022 9:43 a. m., Kristofer Munsterhjelm <<a
href="mailto:km_elmet@t-online.de"
moz-do-not-send="true" class="moz-txt-link-freetext">km_elmet@t-online.de</a>>
escribió:<br>
</div>
<blockquote class="gmail_quote">On 24.05.2022 21:05,
Richard Lung wrote:<br>
> <br>
> The snag is that these and other criteria were
invented for what<br>
> amounts to uninomial elections, that is elections
that don't have both,<br>
> or either, a rational election count and a rational
exclusion count.<br>
> Together they make possible the application of the
binomial theorem, to<br>
> higher order counts. My binomial STV hand count is
just a first order<br>
> binomial count of one election count and one
exclusion count. <br>
<br>
The criteria are method-agnostic: for any ranked voting
method (in this<br>
case, that supports truncation), if someone gives you a
failure example,<br>
you can verify if the method passes or fails the
criterion without<br>
knowing anything about the internals of the method.<br>
<br>
Put differently, suppose that in a scenario perhaps
reminiscent of<br>
Roadside Picnic, a mysterious device falls out of the
sky. And it turns<br>
out that this mysterious device calls elections: you can
input ranked<br>
ballots with a set of buttons and get the results shown
as a series of<br>
lights on the other end.<br>
<br>
Then as long as it allows for ballots with truncation,
it's possible to<br>
check if a particular ballot where A-first voters
truncate can be used<br>
to induce a later-no-harm failure.<br>
<br>
Whether the strange technology that makes up the device
implements<br>
rational election and exclusion counts doesn't matter.
As long as it's a<br>
ranked voting method outputting winners and supporting
truncation, the<br>
question "does this pass later-no-harm?" makes sense.<br>
<br>
The same goes for things like monotonicity,
participation, consistency,<br>
Smith, Condorcet, etc. The criteria say something about
the desired<br>
behavior of a method. Nothing about the inner workings
makes the<br>
criteria inapplicable (apart from some exceptions like
the polynomial<br>
runtime criterion).<br>
<br>
Without a mathematical description of the method, you
couldn't be sure<br>
it actually passes later-no-harm or later-no-help, but
as soon as you<br>
found a counterexample, that would settle the question
in the negative.<br>
<br>
> I am not aware of any untoward effects of tactical
voting on the bstv<br>
> system. I am aware of it doing away with residual
irrationalities to<br>
> traditional stv, including Meek method. Tho I
accept that traditional<br>
> stv (zero-order stv in relation to binomial stv) is
a robust system,<br>
> in practise, as the Hare system of at-large stv/pr.<br>
<br>
As a ranked method, it must fail IIA, which means that
strategy must<br>
sometimes be possible. And as it fails Condorcet, the
obvious starting<br>
place to look is for an election where it doesn't pass
Condorcet. For<br>
instance, this:<br>
<br>
549: A>B>C<br>
366: B>A>C<br>
366: B>C>A<br>
366: C>A>B<br>
<br>
A is the Condorcet winner. The first preferences are:<br>
A: 549, B: 732, C: 366<br>
and last preferences:<br>
A: 366, B: 366, C: 915<br>
<br>
so the ratios are:<br>
A: 366/549 = 0.67<br>
B: 366/732 = 0.5<br>
C: 915/366 = 2.5<br>
<br>
so B wins. Then the C>A>B voters have an incentive
to vote A>C>B instead<br>
(compromising), after which the counts are:<br>
<br>
A: 366/915 = 0.29<br>
B: 366/732 = 0.5<br>
C: 915/0 = infinity<br>
<br>
and A wins. The C>A>B voters prefer A to B, so the
strategy is to their<br>
benefit.<br>
<br>
It can be shown that, for methods where a majority can
always force an<br>
outcome by coordinating how they vote, then modifying
the method so that<br>
it elects the Condorcet winner if there is one never
increases the<br>
proportion of elections where strategy is useful, and
may indeed reduce it.<br>
<br>
> BSTV counts require values for all preference
positions, which are<br>
> equal to the number of candidates. Any preference
position may be an<br>
> abstention. A citizen who never voted but made an
exception of their<br>
> dislike for Donald or Hilary could abstain on their
first preference<br>
> but vote for either on their second preference,
effecting an<br>
> exclusion, because there is only one vacancy.<br>
<br>
> That is the theory of it. I don't know how well it
would work in<br>
> practise, because there never has been a practise.
But I do know that<br>
> democracy is minimised, and evidently works badly,
based on single<br>
> vacancies, in the Anglo-American systems.<br>
<br>
> Fully fledged binomial stv, FAB STV, does not work
on less than 4 or <br>
> 5 member constituencies, the minimum requirement
for a democracy of<br>
> all the people being represented by their choices.<br>
<br>
> Thank you for your examples. They have helped
clarify my thinking -- somewhat!<br>
> According to my (accident-prone) working, A wins on
a keep value of 38957/58966.<br>
> B also has a less than unity keep value of
38957/39366. The <br>
> difference is that one can say A has been elected
on a quota of<br>
> 48961.5, with 58966 first preferences.<br>
> But B has not reached the elective quota. Tho B has
not reached the<br>
> exclusion quota, that only says B has not been
excluded.<br>
<br>
So by the keep values: A's first preference count is
58966 and last<br>
preference count is 38957, since the keep value is
38957/58966.<br>
<br>
You say that B's keep value is 38957/39366, i.e. first
preference count<br>
of 39366 and last preference count of 38957. But that
seems to be in<br>
reverse order. Indeed, your HTML page shows that it is
39366/38957.<br>
<br>
>From the keep values, it seems that truncations are
not included when<br>
counting last preferences. I was pretty sure that BSTV
would fail<br>
later-no-harm because the standard way of counting
truncations, as STV<br>
does, is to consider everybody not ranked to be
equal-ranked for last;<br>
and if you had done that, then it would be possible to
induce later-no-harm.<br>
<br>
The good news is that you avoid this particular problem
if you count<br>
anything past truncation simply as abstentions. So I
guessed wrong,<br>
which was then cleared up by the example, which shows
how useful they<br>
are :-)<br>
<br>
However, instead it seems that you get later-no-*help*
failure. Consider<br>
this modified election:<br>
<br>
18125: A<br>
20035: A>B>C<br>
18722: A>C>B<br>
34488: B>A>C<br>
38634: C>B>A<br>
<br>
By my count, the first preferences are: A: 56882, B:
34488, C: 38634<br>
and the last preferences are: A: 38634, B:
18722, C: 54523<br>
and the last to first ratios are: A: 0.68, B:
0.54, C: 1.41<br>
<br>
so B wins. But if now the A voters fill out their ballot
by voting<br>
A>C>B, then B's last preference count changes to
36847 and A wins<br>
instead. This is a violation of later-no-help.<br>
<br>
Ordinary STV passes both.<br>
<br>
I should note that Condorcet methods, that I prefer,
fail both. My point<br>
isn't as much that later-no-harm and later-no-help are
intrinsically<br>
good, as that it's much easier to check a claim by
concrete evidence<br>
than by references to personal terminology (which may be
hard to<br>
understand for others or take a lot of time to get
acquainted with).<br>
<br>
<br>
On a final note, I would say that always counting
truncation as<br>
abstention could lead to an unknown candidate problem:
suppose there's a<br>
candidate who nobody has heard of and thus nobody
bothers to rank. But<br>
he has a dedicated following all of whom rank him first.
If nobody<br>
obtains a majority, then this candidate could win, e.g.
something like:<br>
<br>
3300: A>B>C<br>
3300: B>C>A<br>
3200: C>A>B<br>
2: D<br>
<br>
I'm also not entirely sure what's going on with the
quota transfers. If,<br>
in the single-winner case, someone who exceeds the quota
is<br>
automatically elected, then there's no need for any
transfers. However,<br>
if passing the quota doesn't guarantee victory, then
later-no-harm<br>
failure might actually be possible. Suppose A is just
above the quota<br>
and B is just below it (with B closer to the majority
line), then if the<br>
A voters only vote for A, A might win; but if they vote
A>B, then the<br>
surplus might be transferred to B and make B win.
Perhaps. As I said,<br>
I'm not sure how the logic works in that case.<br>
<br>
-km<br>
----<br>
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</blockquote>
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