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BTV is what I call Binomial Transferable Vote<br>
V/(S + 1/2) is what I call the Harmonic Mean quota. It is a
"compromise" but it is a principled compromise.<br>
Both are described in my book, Scientific Method of Elections.<br>
<br>
from<br>
Richard Lung.<br>
<br>
<br>
On 25/07/2017 16:58, Jameson Quinn wrote:
<blockquote
cite="mid:CAO82iZzQUbM4C1UEgJ=y_su5J0vf33RqKMzicb+WNy-dvU_GSg@mail.gmail.com"
type="cite">
<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">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">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>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
<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="HOEnZb"><font color="#888888"><br>
<br>
~ Andy Jennings<br>
<br>
</font></span></div>
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</blockquote>
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<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>
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