<html>
<head>
<meta content="text/html; charset=ISO-8859-1"
http-equiv="Content-Type">
</head>
<body bgcolor="#FFFFFF" text="#000000">
A generalised STV (which is what is my invention of Binomial STV
[BTV]) does not have a residual FPTP in the last round.<br>
By including a rational exclusion count, BTV [Binomial Transferable
Vote] avoids the problem of excluding candidates, which seems to be
what much of the discussion on this forum is about.<br>
from<br>
Richard Lung.<br>
<br>
On 26/07/2017 16:12, Andy Jennings wrote:
<blockquote
cite="mid:CA+Df2ty34PE3rw-HY-bQA2phrsCtqp3gbERu1-pnEq+ZN16ezQ@mail.gmail.com"
type="cite">
<div dir="ltr">
<div>
<div>
<div>I think you're right that this matches BTV in the major
details. Is <a moz-do-not-send="true"
href="http://rangevoting.org/BucklinTV.html">http://rangevoting.org/BucklinTV.html</a>
the best reference for BTV? It doesn't have a page on
Electowiki, yet, right? We should add one.<br>
</div>
<div><br>
</div>
<div>There aren't many good, simple, rated-ballot,
multiwinner systems, so it deserves to get talked about
more, no?<br>
</div>
<br>
</div>
<div>I wasn't suggesting to change the name, but if you are...<br>
</div>
<div><br>
<br>
</div>
Regarding the quota: I see what you're saying about the
crumbs. I just have reservations about a quota that's not
even going to try to represent 1/(s+1) of the population. I
realize that STV does it and STV has a track record. But STV
does it because it might come down to a one-on-one at the end
and you want to say that a majority in the final round is the
same as the quota for all the other rounds. A rated system
doesn't have that restriction. I kind of like approval voting
in the last round, even if the winner only gets 30-40%.<br>
<br>
</div>
<div>If we choose one quota for the default, I'd hope we could
add a footnote that the other one was a possible alternative.<br>
</div>
<div><br>
<br>
</div>
<div>Tiebreaker and deweighting: I don't feel strongly about
these, but it's good that we're considering different options,
looking for simplicity but also looking for corners that cause
adverse incentives. I think it's better to recommend good
defaults than just including a bunch of options.<br>
<br>
</div>
<div>Tiebreaker: If we were to use Hare quota (and "approval
voting" in the last round), then the critical grade for the
last round is going to be 0(F), so a GMJ tiebreaker or "most
votes at or above critical" are not going to help break ties.
We'd either have to have a different rule for the last round,
or a second tiebreaker. "Most votes strictly above critical"
would do it.<br>
<br>
</div>
<div>Deweighting: If we wanted to, we could "assign" voters to
the representatives for whom they were deweighted. In that
case, it would be advantageous to deweight in chunks as large
as possible. So subtractive deweighting would be better than
multiplicative and rules that "deweight completely" are good.
But multiplicative is probably simpler.<br>
<br>
</div>
<div>~ Andy<br>
</div>
</div>
<div class="gmail_extra"><br>
<div class="gmail_quote">On Tue, Jul 25, 2017 at 8:58 AM,
Jameson Quinn <span dir="ltr"><<a moz-do-not-send="true"
href="mailto:jameson.quinn@gmail.com" target="_blank">jameson.quinn@gmail.com</a>></span>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
<div dir="ltr">
<div class="gmail_extra">This is a good idea.</div>
<div class="gmail_extra"><br>
</div>
<div class="gmail_extra">But on thinking about it further,
I'm not sure whether it's not the same as BTV.</div>
<div class="gmail_extra"><br>
</div>
<div class="gmail_extra">BTV, like Bucklin, works by
gradually lowering a "pseudo-approval threshold", and
electing and deweighting candidates as they reach a
quota of "pseudo-approvals". Andy's proposal, like MJ,
works by directly looking at the "quota-th" highest
rating, and electing and deweighting the candidate who's
highest by that measure.</div>
<div class="gmail_extra"><br>
</div>
<div class="gmail_extra">But of course, we know that,
aside from tiebreakers, MJ and Bucklin are the same
thing. So the more I think about it, the more I think
that (aside from quota choice, tiebreaker, and
deweighting scheme; none of which are really specified
by the label "BTV") Andy's proposal and BTV are the same
thing.</div>
<div class="gmail_extra"><br>
</div>
<div class="gmail_extra">I could be wrong about this...
can anybody else check my logic here?</div>
<div class="gmail_extra"><br>
</div>
<div class="gmail_extra">Still. Even if this is just a new
name for BTV, it's a good excuse to discuss that system.</div>
<div class="gmail_extra"><br>
</div>
<div class="gmail_extra">We could talk about how good it
is. Pretty excellent! I like that it avoids the horrible
center-squeeze breakage of STV. Even though the problems
with center squeeze are much less in a multiwinner
setting than in IRV, it's still ugly.</div>
<div class="gmail_extra"><br>
</div>
<div class="gmail_extra">When designing <a
moz-do-not-send="true"
href="http://wiki.electorama.com/wiki/Geographic_Open_List/Delegated_%28GOLD%29_voting"
target="_blank">GOLD</a>, I chose STV rather than BTV
as a substrate. That wasn't because I prefer STV
theoretically; it's just because of its longer track
record.</div>
<div class="gmail_extra"><br>
</div>
<div class="gmail_extra">Also, we could talk about the
ancillary design decisions: quota choice, tiebreaker,
and deweighting scheme.</div>
<div class="gmail_extra"><br>
</div>
<div class="gmail_extra">Quota choice: I tend to prefer
Droop, or a compromise V/(S+.5), over Hare. Basically,
when you're assigning the last seat, you're left with
the voters who are most atypical; the "crumbs" of the
party system. If you use a Hare quota, then at best
you'll find a candidate with some appeal to a full
quota; but realistically, you might just find the
biggest of a group of crumbs, who could easily have
support from just 35-40% of a quota (based on 1/e, my
SWAG for this kind of situation). If you go with a
Droop quota, on the other hand, the entire pool is 2
quotas; and 2/e is 70-80% of a quota, much closer to
fair.</div>
<div class="gmail_extra"><br>
</div>
<div class="gmail_extra">Andy's suggested deweighting
scheme might help encourage bigger crumbs, but I'm not
sure about that.</div>
<div class="gmail_extra"><br>
</div>
<div class="gmail_extra">Tiebreaker: I don't have a lot to
say about this. GMJ-style seems like a good choice.</div>
<div class="gmail_extra"><br>
</div>
<div class="gmail_extra">Deweighting: This is where things
get interesting. You don't want to have too much of a
free-riding incentive, but you do want to deweight the
votes which are "more satisfied" with the winners and
not-deweight those which are "less satisfied" with the
future potential winners.</div>
<div class="gmail_extra"><br>
</div>
<div class="gmail_extra">I like Andy's concept of
subtractive, rather than multiplicative, deweighting. It
makes things a little bit harder to describe, but it
does mean that somebody who is "halfway decisive" twice
will be fully deweighted, rather than keeping 1/4 of
their voting weight; that seems fair to me.</div>
<div class="gmail_extra"><br>
</div>
<div class="gmail_extra">I think that Andy's rejected idea
of "for those who only gave the new winner the threshold
rating, deweight them last" was doing it wrong, so I'm
not surprised that he decided it led to too big of a
free rider incentive. If you're doing a GMJ tiebreaker
anyway, then from a BTV point of view, those voters are
essentially giving a fraction of an approval to the new
winner. I think that only that fraction of their ballot
should be at risk for deweighting; so their subtractive
deweighting should be the minimum of their GMJ fraction
and the overall deweighting.</div>
<div class="gmail_extra"><br>
</div>
<div class="gmail_extra">The other way to do things is to
try to avoid deweighting voters insofar as they still
have useful opinions about the remaining candidates.
That's what Andy's proposed "completely deweight those
who rate all remaining candidates at 0" rule would do.
But this could still leave a very "crumbly" remainder at
the end; imagine if the 100 candidates for the last seat
each had 1% of the remainder giving them a top-rating.</div>
<div class="gmail_extra"><br>
</div>
<div class="gmail_extra">So I can imagine more complicated
schemes to do this. For instance:</div>
<div class="gmail_extra"><br>
</div>
<div class="gmail_extra">
<ol>
<li>Find the R candidates with the highest quota-th
ratings, where R is the remaining number of seats.
In other words, the prospective winners if you
proceeded from here on without any deweighting.<br>
</li>
<li>Of the deweight-able votes (counting only the GMJ
subtractive portion ot threshold votes), find the Q
which have the lowest max rating for those R
candidates. Deweight these completely.</li>
</ol>
<div>Note that the incentive of the above is not so much
to downvote early winners, as with traditional free
riding (though of course that is still possible if you
downvote them below their winning threshold), but
rather to up-vote late winners. That creates a
couter-free-riding incentive; a possibility I'd never
considered before.</div>
<div>....</div>
<div><br>
</div>
<div>But all-in-all, I think that Andy's suggested
deweighting scheme is pretty good, and I'd rather go
for "simple" than "theoretically awesome" here.</div>
</div>
<div class="gmail_extra"><br>
</div>
<div class="gmail_extra">Jameson</div>
<div class="gmail_extra"><br>
</div>
<div class="gmail_extra"><br>
<div class="gmail_quote">
<div>
<div class="h5">2017-07-24 21:58 GMT-07:00 Andy
Jennings <span dir="ltr"><<a
moz-do-not-send="true"
href="mailto:elections@jenningsstory.com"
target="_blank">elections@jenningsstory.com</a>></span>:<br>
</div>
</div>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
<div>
<div class="h5">
<div dir="ltr">Here's a multiwinner system
that's so simple that it should have a name,
but I don't think it does. Let me know if it
does.<br>
<br>
It uses rated ballots. The goal is to
repeatedly find the candidate whose top
quota's-worth of grades are highest and elect
that candidate, then de-weight a quota's-worth
of voters. Some names worth considering:<br>
<br>
Sequential Best Assignment<br>
Sequential Constituent Matching<br>
Sequential Quota Allocation<br>
<br>
The method:<br>
<br>
N = Number of voters<br>
S = Number of seats<br>
<br>
1. Every voter grades every candidate. (I'd
say 4 or 6 grades.)<br>
<br>
2. Each voter starts with weight 1.<br>
<br>
3. Choose quota Q = N / S. (*)<br>
<br>
4. For each candidate, calculate the minimum
of their top Q grades. Let G be the highest
minimum. Elect the candidate with that
minimum. (Break ties as in GMJ: calculate for
each candidate what fraction of their G grades
are in their top Q grades, and elect the
candidate with the smallest such fraction.
Break further ties by choosing the candidate
with the least number of G grades in their top
Q grades.)<br>
<br>
5. Deweight some voters to decrease the total
voter weight by Q, in this manner:<br>
a) any voter who gave the minimum grade to
all remaining candidates is deweighted to 0.<br>
b) for the voters not deweighted in (a) who
gave this candidate a grade of G or above,
find the deweighting D such that when the
deweighting formula:<br>
<br>
W_new = max(W_old - D, 0)<br>
<br>
is applied, the total voter weight in this
round is decreased by Q. (**)<br>
<br>
6. Repeat steps 4 and 5, applying voter
weights when calculating the top Q grades,
until S seats are filled.<br>
<br>
<br>
(*) With this quota, when you are filling say,
4 seats, then 25% of the voting weight gets
used up with each seat filled. 25% of the
voting weight will remain when choosing the
last seat. That last seat will be determined
by the tie-breaker rule, so it is essentially
equivalent to approval voting, with any
above-bottom grade counting as approval.<br>
<br>
The other common choice of quota, Q = N / (S +
1), could also be considered. When filling 4
seats, then, 20% of the voting weight gets
used up with each seat filled. 40% of the
voting weight remains to choose the last seat,
so the last seat is essentially filled with a
median-based method (GMJ). 20% of the voters'
opinions are, by design, left without a
representative.<br>
<br>
(**) I thought about another step (a') where
anyone who gave a grade strictly above G was
deweighted completely, but I think it gives
the voters too much incentive to down-weight
candidates who they think can get elected
without their help.<br>
<br>
I also considered another step (a'') where
anyone who graded the chosen candidates
strictly above all other candidates was
deweighted completely, but I don't think
there's much benefit for the added complexity.<br>
<br>
<br>
Any thoughts on which quota is better or on
the right name?<span
class="m_-2399388108750202778HOEnZb"><font
color="#888888"><br>
<br>
~ Andy Jennings<br>
<br>
</font></span></div>
<br>
</div>
</div>
----<br>
Election-Methods mailing list - see <a
moz-do-not-send="true"
href="http://electorama.com/em" rel="noreferrer"
target="_blank">http://electorama.com/em</a> for
list info<br>
<br>
</blockquote>
</div>
<br>
</div>
</div>
</blockquote>
</div>
<br>
</div>
<br>
<fieldset class="mimeAttachmentHeader"></fieldset>
<br>
<pre wrap="">----
Election-Methods mailing list - see <a class="moz-txt-link-freetext" href="http://electorama.com/em">http://electorama.com/em</a> for list info
</pre>
</blockquote>
<br>
<br>
<pre class="moz-signature" cols="72">--
Richard Lung.
<a class="moz-txt-link-freetext" href="http://www.voting.ukscientists.com">http://www.voting.ukscientists.com</a>
Democracy Science series 3 free e-books in pdf:
<a class="moz-txt-link-freetext" href="https://plus.google.com/106191200795605365085">https://plus.google.com/106191200795605365085</a>
E-books in epub format:
<a class="moz-txt-link-freetext" href="https://www.smashwords.com/profile/view/democracyscience">https://www.smashwords.com/profile/view/democracyscience</a>
</pre>
</body>
</html>