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<font face="Helvetica, Arial, sans-serif">A possible explanation for
the discrepancy between my result and Darlington's is that in my
evaluation every ballot had the same number of ties and in
Darlington's the numbers differed.<br>
On the face of it, WV doesn't treat voters equally. If we
defined "winning votes" as "the number of voters who prefer A to B
plus half the number who rank them equally", then every voter
would contribute m(m-1)/2 winning votes and WV would be equivalent
(I think) to Margins. But instead we define winning votes
asymmetrically so that WV is *not* equivalent to margins but
voters contribute different numbers of winning votes depending on
the number of ties in their ballots. I can imagine this leading to
artefacts which Darlington's evaluation would pick up and mine
would miss. If this is what happened, then even Darlington's
evaluation must be too lenient to WV since he doesn't include
effects which would in fact arise, such as voters truncating
differentially according to their political viewpoint. <br>
Maybe these things have been taken into account; I have no
idea, having never seen the thinking behind WV.<br>
CJC<br>
</font><br>
<div class="moz-cite-prefix">On 21/09/2023 03:35, Forest Simmons
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CANUDvfpjKFS0ndjNdHWMqYeyjhHGDwEufotEa943us6rdyjmFQ@mail.gmail.com">
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<div dir="auto">I think that if you were looking at the success
rates of unilateral burial options along with the basic burial
defense of truncation below sincere CW ... then the difference
between Winning Votes and Margins would be more striking (still
in favor of wv).</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Wed, Sep 20, 2023, 2:12 PM
Michael Ossipoff <<a href="mailto:email9648742@gmail.com"
moz-do-not-send="true">email9648742@gmail.com</a>> wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
<div dir="auto">Thanks for the experiment. I hope that
Tideman’s organization won’t be promoting the old margins
version of RP. …unless just for maybe choosing between
pizza-toppings or movies.</div>
<div><br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Wed, Sep 20, 2023 at
07:30 Colin Champion <<a
href="mailto:colin.champion@routemaster.app"
target="_blank" rel="noreferrer"
moz-do-not-send="true">colin.champion@routemaster.app</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
<div> <font face="Helvetica, Arial, sans-serif">Well, I
coded up Minimax(WV) for my own evaluation. Rather
to my disgust (and contrary to Darlington) I find
that it does indeed outperform Margins for truncated
sincere ballots. I ran a large number of trials with
10001 voters under a spatial model, 8 candidates
being truncated to 4. Minimax (margins)=83.35%
correct, minimax(wv)=84.09%. Other methods which
outperformed standard minimax in the simulation
include Approval Sorted Margins (in an ordinal
version suggested by Ted Stern): 84.14%; Black:
84.22%; Smith,Borda: 84.22%. <br>
Hastily written and unreliable code, not to be
trusted. <br>
CJC<br>
</font></div>
<div><br>
<div>On 18/09/2023 22:30, Michael Ossipoff wrote:<br>
</div>
<blockquote type="cite">
<div dir="auto">Hi Colin—</div>
<div dir="auto"><br>
</div>
<div dir="auto">Yes, margins beats wv for
social-utility under sincere voting when there’s
that vanishingly rare natural top-cycle.</div>
<div dir="auto"><br>
</div>
<div dir="auto">But Darlington & Tideman
evidently aren’t considering resistance to
offensive strategy, which is a much bigger threat
than natural top-cycles.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Protecting the CW from offensive
strategy is more important than SU in natural
top-cycles.</div>
<div dir="auto"><br>
</div>
<div dir="auto">…& is better for SU.</div>
<div><br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Mon, Sep
18, 2023 at 07:03 Colin Champion <<a
href="mailto:colin.champion@routemaster.app"
target="_blank" rel="noreferrer"
moz-do-not-send="true">colin.champion@routemaster.app</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0
0 0 .8ex;border-left:1px #ccc
solid;padding-left:1ex">
<div> <font face="Helvetica, Arial,
sans-serif">Thanks to Kevin and Michael
for pointing out a feature of minimax I
was unaware of. I had however seen Richard
Darlington's paper [1] in which he
referred to 'several studies' comparing
margins with winning votes. He reports
that margins 'was the big winner in all of
them'. I suppose I'll have to look deeper.<br>
Colin<br>
[1]. <a
href="https://arxiv.org/abs/1807.01366"
target="_blank" rel="noreferrer"
moz-do-not-send="true">https://arxiv.org/abs/1807.01366</a><br>
</font></div>
<div><br>
<div>On 18/09/2023 07:57, Michael Ossipoff
wrote:<br>
</div>
<blockquote type="cite">
<div><br>
</div>
<div><br>
<div class="gmail_quote" dir="auto">
<div dir="ltr" class="gmail_attr">----------
Forwarded message ---------<br>
From: <strong
class="gmail_sendername"
dir="auto">Michael Ossipoff</strong>
<span dir="auto"><<a
href="mailto:email9648742@gmail.com"
target="_blank" rel="noreferrer"
moz-do-not-send="true">email9648742@gmail.com</a>></span><br>
Date: Sun, Sep 17, 2023 at 22:54<br>
Subject: Re: [EM] Ranked Pairs<br>
To: Forest Simmons <<a
href="mailto:forest.simmons21@gmail.com"
target="_blank" rel="noreferrer"
moz-do-not-send="true">forest.simmons21@gmail.com</a>><br>
</div>
<div class="gmail_quote" dir="auto"><br>
</div>
This was meant to be sent by “Reply
All”, in order to post it. So now I’m
forwarding it to EM.<br>
<br>
<div dir="auto">Forest—</div>
<div dir="auto"><br>
</div>
<div dir="auto">But wv prevents
truncation (strategic or otherwise)
from taking the win from a CW.</div>
<div dir="auto"><br>
</div>
<div dir="auto">…&, with, wv,
refusing to rank anymore you don’t
approve will cause offensive
order-reversal by their preferrers
to backfire.</div>
<div dir="auto"><br>
</div>
<div dir="auto">I’d always take that
precaution, & would advise
others to.</div>
<div dir="auto"><br>
</div>
<div dir="auto">When we discussed
these guarantees years ago they
seemed absolute, & we still have
the guarantee-criteria based on
them…met by wv versions of MinMax,
RP, CSSD, & Smith//MinMax.</div>
<div dir="auto"><br>
</div>
<div dir="auto">…&, with MinMax,
whose winner can come from anywhere,
not just from the top-cycle, &
so, offensive order-reversal, when
there are a fair number of
candidates, is unpredictable &
risky for its perpetrators, even if
the precaution of
deterrent-truncation isn’t taken.</div>
<div><br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On
Sun, Sep 17, 2023 at 21:17
Forest Simmons <<a
href="mailto:forest.simmons21@gmail.com"
target="_blank"
rel="noreferrer"
moz-do-not-send="true">forest.simmons21@gmail.com</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote"
style="margin:0px 0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)">
<div dir="auto">
<div><br>
<br>
<div class="gmail_quote">
<div dir="ltr"
class="gmail_attr">On
Sat, Sep 16, 2023, 9:42
PM Michael Ossipoff <<a
href="mailto:email9648742@gmail.com" target="_blank" rel="noreferrer"
moz-do-not-send="true">email9648742@gmail.com</a>>
wrote:<br>
</div>
<blockquote
class="gmail_quote"
style="margin:0px 0px
0px
0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)">
<div dir="auto">Is that
RP(wv), or RP(margins)
?</div>
<div dir="auto"><br>
</div>
<div dir="auto">RP(wv)
would thwart &
deter offensive
strategy, an important
property in public
elections.</div>
<div dir="auto"><br>
</div>
<div dir="auto">…&,
actually, it seems to
me that MinMax(wv)
would do that better.</div>
<div dir="auto"><br>
</div>
<div dir="auto">That’s
because, choosing only
from the Smith Set RP,
limits it’s choice to
the strategic
top-cycle that created
by the offensive
strategists.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Suppose
that the CW’s
preferrers don’t do
defensive truncation
(never rank anyone you
wouldn’t approve in
Approval, or whose
preferrers you regard
as likely to
offensively
order-reverse) ?</div>
<div dir="auto"><br>
</div>
<div dir="auto">Knowing
that RP will limit its
choice to their small
strategic top-cycle,
it would be easier for
the strategists to be
fairly sur that their
candidate would win in
that top-cycle.</div>
<div dir="auto"><br>
</div>
<div dir="auto">But,
with MinMax, the
winner is chosen more
broadly, & could
be anywhere in the
candidate-set.
…making it more
difficult & risky
to confidently do
offensive
order/reversal.</div>
<div dir="auto"><br>
</div>
<div dir="auto">RP(margins)
might the best choice
for a completely
honest electorate, but
MinMax(wv) seems
better for public
elections, due to its
better thwarting &
deterrence of
offensive strategy.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Yes,
MinMax doesn’t meet
the luxury cosmetic
look-good criteria
that RP meets. </div>
<div dir="auto"><br>
</div>
<div dir="auto">But for
one thing, I remind
you that natural (
sincere) top-cycles
are vanishingly-rare.</div>
</blockquote>
</div>
</div>
<div dir="auto"><br>
</div>
<div dir="auto">This is the
same conclusión I have come
around to. </div>
<div dir="auto"><br>
</div>
<div dir="auto">And methods
that break a three member
top cycle at the weakest
link tend to reward the
burier faction.</div>
</div>
<div dir="auto">
<div dir="auto">
<div class="gmail_quote">
<blockquote
class="gmail_quote"
style="margin:0px 0px
0px
0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)">
<div dir="auto"><br>
</div>
<div dir="auto">So do
you want to have less
strategy-protection,
in order for the
result to maybe look
better in a
vanishingly rare
natural top/cycle?</div>
<div dir="auto"><br>
</div>
<div dir="auto">…&
how bad is a violation
of Condorcet-Loser
anyway. “Beaten by
all the other
alternatives” sounds
like some kind of
unanimity, but of
course it isn’t. It
isn’t like a
Pareto-violation. I
remind you that the
MinMax winner has
fewer voters
preferring some
particular candidate
over him than anyone
else does.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Clone-Criterion
violation? How bad
that really in MinMax,
especially when we’re
talking about a
vanishingly rare
natural top-cycle?</div>
<div dir="auto"><br>
</div>
<div dir="auto">RP(margins)
for a completely
honest electorate.</div>
<div dir="auto"><br>
</div>
<div dir="auto">MinMax(wv)
for public elections.</div>
<div dir="auto"><br>
</div>
<div dir="auto">..&
about a primary to
reduce the candidates
to 5: Forget the
primary. If you think
people will have
trouble rank-ordering
lots of candidates, I
remind you that, to
vote among them in a
primary, they’d still
have to examine &
choose among the
initial many
candidates.</div>
<div dir="auto"><br>
</div>
<div dir="auto">…harder
than ranking only the
ones you know &
regard as deserving
& definitely in
your accepts&
preferred set.</div>
<div dir="auto"><br>
<div
class="gmail_quote"
dir="auto">
<div dir="ltr"
class="gmail_attr">On
Wed, Sep 13, 2023
at 00:18 Colin
Champion <<a
href="mailto:colin.champion@routemaster.app"
rel="noreferrer
noreferrer"
target="_blank"
moz-do-not-send="true">colin.champion@routemaster.app</a>> wrote:<br>
</div>
<blockquote
class="gmail_quote"
style="margin:0px
0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)">I
notice that RP is
the only election
method mentioned
by name in the <br>
Virginia agenda.<br>
<br>
A while ago I ran
some simulations
on elections with
truncated ballots.
<br>
Something I
noticed was that
the presence of RP
in the list of
methods <br>
made the software
unacceptably slow.
I didn't look into
the cause, but <br>
there's a natural
explanation, which
is the fact that
RP is known to be
<br>
NP-complete when
it deals correctly
with tied margins,
i.e. by <br>
exhausting over
all their
permutations.
Presumably if some
candidates <br>
are unpopular and
ballots are
extensively
truncated, then
tied margins <br>
are much likelier
than with complete
ballots.<br>
<br>
I gather that
practical
implementations of
RP choose a random
<br>
permutation rather
than exhausting.
This seems to me
to bring a danger.
<br>
The presence of a
few vanity
candidates
(truncated off
almost all <br>
ballots) may lead
to ties, and this
may lead to a
comfortable winner
<br>
looking as though
he owes his
victory to a
coin-toss.
Obviously this <br>
undermines the
legitimacy of his
win.<br>
<br>
CJC<br>
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