<div dir="ltr">Chris is correct. "by most" = "by a majority". Maximum is "<b><i>the</i></b> most".<div><br></div><div>Perhaps I should avoid that word, but I was trying to use small words, as in Randall Munroe's "Thing Explainer".</div></div><div class="gmail_extra"><br><div class="gmail_quote">2016-09-13 6:28 GMT-04:00 C.Benham <span dir="ltr"><<a href="mailto:cbenham@adam.com.au" target="_blank">cbenham@adam.com.au</a>></span>:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div bgcolor="#FFFFFF" text="#000000">
<div>Kevin,<br>
<br>
I take "downvoted by most" to mean down-voted by most of the
voters, meaning down-voted on more than half the ballots.<br>
<br>
Your interpretation would be "the most downvoted".<br>
<br>
Chris Benham<div><div class="h5"><br>
<br>
<br>
On 9/13/2016 2:56 PM, Kevin Venzke wrote:<br>
</div></div></div>
<blockquote type="cite"><div><div class="h5">
<div style="color:#000;background-color:#fff;font-family:HelveticaNeue,Helvetica Neue,Helvetica,Arial,Lucida Grande,sans-serif;font-size:12px">
<div><font size="+1">Hi
Jameson,</font></div>
<div><font size="+1"><br>
</font></div>
<div><font size="+1">"Downvoted
by most" means the candidate with the single greatest number
of downvotes? This could be the (voted, unique) majority
favorite couldn't it?</font></div>
<div><font size="+1"><br>
</font></div>
<div dir="ltr"><font size="+1">How does this violate "irrelevant ballots"? I must
be misunderstanding it. Does "max amount of upvotes" mean
100% of the voters, or just the greatest number of upvotes
that occurs?</font></div>
<div><font size="+1"><br>
</font></div>
<div><font size="+1">I
do like antiplurality mechanisms.</font></div>
<div><font size="+1"><br>
</font></div>
<div><font size="+1">Kevin</font></div>
<div><br>
<br>
</div>
<div style="display:block">
<div style="font-family:HelveticaNeue,Helvetica Neue,Helvetica,Arial,Lucida Grande,sans-serif;font-size:12px">
<div style="font-family:HelveticaNeue,Helvetica Neue,Helvetica,Arial,Lucida Grande,sans-serif;font-size:16px">
<div dir="ltr">
<font face="Arial" size="2">
<hr size="1"> <b><span style="font-weight:bold">De :</span></b>
Jameson Quinn <a href="mailto:jameson.quinn@gmail.com" target="_blank"><jameson.quinn@gmail.com></a><br>
<b><span style="font-weight:bold">À :</span></b>
Kevin Venzke <a href="mailto:stepjak@yahoo.fr" target="_blank"><stepjak@yahoo.fr></a>;
electionsciencefoundation
<a href="mailto:electionscience@googlegroups.com" target="_blank"><electionscience@googlegroups.<wbr>com></a> <br>
<b><span style="font-weight:bold">Cc :</span></b> EM
<a href="mailto:election-methods@lists.electorama.com" target="_blank"><election-methods@lists.<wbr>electorama.com></a><br>
<b><span style="font-weight:bold">Envoyé le :</span></b>
Lundi 12 septembre 2016 20h37<br>
<b><span style="font-weight:bold">Objet :</span></b>
Re: [EM] Fwd: Fwd: U/P voting: new name for simple
3-level method.<br>
</font> </div>
<div><br>
<div>
<div>
<div dir="ltr">Here's
a new proposed variant of U/P with a simple
default:
<div><br clear="none">
</div>
<div>Voters may rate each candidate as
"unacceptable" (downvote), "preferred" (upvote),
or "acceptable" (neither). Default is neither.</div>
<div><br clear="none">
</div>
<div>Any
candidate downvoted by most, or with fewer than
half the max amount of upvotes, is disqualified,
unless that would disqualify everyone. The
winner is the remaining candidate with the most
upvotes.</div>
<div><br clear="none">
</div>
<div>The
"fewer than half the max" rule prevents
dark-horse winners, without resorting to strange
defaults. It has no effect on a two-way chicken
dilemma. Though in theory it could affect an
evenly-balanced three-way chicken dilemma (in a
four-way race), I think there's a negligible
chance that such a scenario would be so
balanced.</div>
<div><br clear="none">
</div>
<div>I
know that Chris doesn't like this method's
violation of "irrelevant ballots". Myself, I
think that no voters are irrelevant; even if
they don't express an opinion between the two
frontrunners, they may have one. (True, they may
not; but that's not the first assumption I'd
make.)</div>
</div>
<div><br clear="none">
<div>2016-09-12
20:22 GMT-04:00 Kevin Venzke <span dir="ltr"><<a rel="nofollow" shape="rect" href="mailto:stepjak@yahoo.fr" target="_blank">stepjak@yahoo.fr</a>></span>:<br clear="none">
<div>
<blockquote style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div>
<div style="color:#000;background-color:#fff;font-family:HelveticaNeue,Helvetica Neue,Helvetica,Arial,Lucida Grande,sans-serif;font-size:12px">
<div>
<div>
<div style="color:#000;background-color:#fff;font-family:HelveticaNeue,Helvetica Neue,Helvetica,Arial,Lucida Grande,sans-serif;font-size:12px">
<div><span>Hi
Jameson,</span></div>
<div><span><br clear="none">
</span></div>
<div dir="ltr"><span>I think it is a positive
thing that the MTA B/C
majority coalition can give
their sincere preferences (!),
while using the strategy
they're expected to use (i.e.
middle slot as tiebreaker
given multiple majorities),
without risk of this strategy
backfiring. (Voters can
accidentally elect the less
preferred of B or C, but that
is the inescapable chicken
dilemma, I would say.)</span></div>
<div dir="ltr"><span><br clear="none">
</span></div>
<div dir="ltr"><span>I have some sympathy for your
claim that C should not be
able to win with few top
ratings. But that sympathy is
not tied to Borda counts, it
is based on wanting to reduce
the truncation incentive for
the B voters. This, U/P does
not really do, because the
B>C voters would be taking
a large risk that they are
helping to put C (alone) over
the threshold of majority
approval.</span></div>
<div dir="ltr"><span><br clear="none">
</span></div>
<div dir="ltr"><span>So I don't think either of
these ballot sets is likely
under U/P, and it sounds like
you agree with that and think
it is good (because it deters
a pathological ballot set)? Do
you have a stance (or at
least, see use in determining
a stance) on how U/P voters in
these scenarios should be
voting?</span></div>
<div dir="ltr"><span><br clear="none">
</span></div>
<div dir="ltr"><span>Kevin</span></div>
<div><br clear="none">
<br clear="none">
</div>
</div>
</div>
</div>
<div>
<div style="font-family:HelveticaNeue,Helvetica Neue,Helvetica,Arial,Lucida Grande,sans-serif;font-size:12px">
<div style="font-family:HelveticaNeue,Helvetica Neue,Helvetica,Arial,Lucida Grande,sans-serif;font-size:16px">
<div dir="ltr"><span> <font face="Arial" size="2"> </font></span>
<hr size="1"> <b><span style="font-weight:bold">De :</span></b>
Jameson Quinn <<a rel="nofollow" shape="rect" href="mailto:jameson.quinn@gmail.com" target="_blank">jameson.quinn@gmail.com</a>><br clear="none">
<b><span style="font-weight:bold">À :</span></b>
EM <<a rel="nofollow" shape="rect" href="mailto:election-methods@lists.electorama.com" target="_blank">election-methods@lists.
electorama.com</a>> <br clear="none">
<b><span style="font-weight:bold">Envoyé
le :</span></b> Dimanche 11
septembre 2016 1h51<br clear="none">
<b><span style="font-weight:bold">Objet :</span></b>
[EM] Fwd: Fwd: U/P voting: new
name for simple 3-level method.<br clear="none">
</div>
<div>
<div>
<div><br clear="none">
<div><br clear="none">
<br clear="none">
</div>
<div>
<div>
<div dir="ltr">
<div>
<div dir="ltr">
<div>
<div><span>2016-09-10 21:26 GMT-04:00
C.Benham <span dir="ltr"><<a rel="nofollow" shape="rect" href="mailto:cbenham@adam.com.au" target="_blank">cbenham@adam.com.au</a>></span>:<br clear="none">
</span>
<blockquote style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><span>On 9/11/2016 5:02 AM,
Kevin Venzke
wrote:<br clear="none">
<br clear="none">
</span>
<blockquote style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
43: A<br clear="none">
24: B>C<br clear="none">
23: C>B<br clear="none">
10: D<br clear="none">
<br clear="none">
Under MTA the
B and C voters
are being
completely
reasonable:
They hope for
majority
approval but
can still hope
for a win if
they<br clear="none">
don't get it.<br clear="none">
<br clear="none">
Strategy is
less likely to
produce these
ballots under
U/P because
the B and C
voters are
taking a
gamble. To get
a similar
outcome<br clear="none">
they have to
vote B=C.
Anyone who
doesn't is
functionally
defecting!<br clear="none">
</blockquote>
<br clear="none">
C: A very
good example!
Assuming MTA
and MCA use
Top Ratings
scores to
break Approval
ties, they
both elect the
Condorcet
winner B.<br clear="none">
</blockquote>
<div><br clear="none">
</div>
<div>But
both could be
shifted to C
with a single
C-only ballot,
even if the
B:C ratio were
46:1 instead
of 24:23.</div>
<span></span>
<div> </div>
<blockquote style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<br clear="none">
U/P's
under-use of
the middle
ratings slot
means that it
relies more on
its "majority
disqualification" mechanism which seems to make it more<br clear="none">
vulnerable to
irrelevant
ballots, as in
the example.<br clear="none">
<br clear="none">
Under U/P,
without the
irrelevant D
ballots, A and
D are
disqualified
and B is the
glorious
winner. With
them, B and C
and D are
disqualified
and (without
needing<br clear="none">
any others to
be
disqualified)
A wins.<br clear="none">
<br clear="none">
This causes me
to reject U/P
as clearly
worse than MTA
and MCA. Of
the three I
(again) rate
MTA as the
least bad.<br clear="none">
</blockquote>
<div><br clear="none">
</div>
<div>I think
MTA is pretty
darn good. I
still prefer
U/P.</div>
<div><br clear="none">
</div>
<div>I think
that scenarios
like the above
are
fundamentally
pathological;
any possible
winner has
only minority
approval, so
that even
assuming all
ballots are
semi-honest,
any of them
could be a
true Condorcet
loser. Thus, I
believe that
it's more
important for
a system to
try to avoid
scenarios like
the above,
than to try to
find a perfect
winner in such
a scenario. In
fact, in the
related
scenario:</div>
<div><br clear="none">
</div>
<div><br clear="none">
43: A<br clear="none">
40: B>C</div>
<div>6:
C>B<br clear="none">
1: C<br clear="none">
10: D<br clear="none">
</div>
<div><br clear="none">
</div>
<div>... I
think that a
case can be
made for
either A or B.
After all,
they'd be tied
if we try to
approximate
Score by using
truncatable
Borda here.
But no serious
case can be
made for C or
D, even though
C wins MTA and
MCA.</div>
<div><br clear="none">
</div>
<div>Anyway,
I think U/P
does a better
job trying to
discourage the
kind of
strategy that
would lead to
a scenario
like the
above. And
part of that
is the default
rule which
Chris has
criticized.</div>
<div><br clear="none">
</div>
<div>One
possible
alternative
default rule:
ballots
alternate
between
defaulting to
"acceptable"
and to
"unacceptable".
Each ballot
clearly states
which default
it uses, and
there is a
place on the
ballot to
globally
change that
default. (I
doubt Chris
will like this
idea, but it
is at least
straightforward,
explicit, and
easy to
describe.)</div>
<div><br clear="none">
</div>
<blockquote style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<br clear="none">
Chris Benham<br clear="none">
<br clear="none">
<br clear="none">
</blockquote>
</div>
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</blockquote>
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