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I introduced a Harmonic Mean quota as the happy medium of the Hare
and Droop quotas, because both have democratic deficiencies. It is
explained in my book Scientific Method of Elections, as is my
generalisation of STV: Binomial STV (free from Smashwords and in the
pdf Archive).<br>
<br>
from<br>
Richard Lung.<br>
<br>
<br>
<br>
<br>
On 06/06/2017 11:43, Toby Pereira wrote:
<blockquote cite="mid:57242998.4933904.1496745802627@mail.yahoo.com"
type="cite">
<div style="color:#000; background-color:#fff;
font-family:Helvetica Neue, Helvetica, Arial, Lucida Grande,
sans-serif;font-size:13px">
<div id="yui_3_16_0_1_1496733772650_5418" dir="ltr"><span
id="yui_3_16_0_1_1496733772650_5417">Just to finish the
thought on this, under Sainte-Laguë/Hare proportionality ,
for a party/faction to guarantee themselves s seats, then I
think they would need s-1 Hare quotas and then a Droop quota
for their last seat, but it would be a Droop quota
considering only the remaining seats and voters rather than
all of them.</span></div>
<div id="yui_3_16_0_1_1496733772650_5624" dir="ltr"><span><br>
</span></div>
<div id="yui_3_16_0_1_1496733772650_5489" dir="ltr"><span
id="yui_3_16_0_1_1496733772650_5631">For example, let's say
there are five seats.</span></div>
<div id="yui_3_16_0_1_1496733772650_5623" dir="ltr"><span><br>
</span></div>
<div id="yui_3_16_0_1_1496733772650_5622" dir="ltr"><span
id="yui_3_16_0_1_1496733772650_5621">To guarantee one seat,
a party would need 0 Hare quotas and one Droop, so 1/6 of
the total vote.</span></div>
<div id="yui_3_16_0_1_1496733772650_5490" dir="ltr"><span><br>
</span></div>
<div id="yui_3_16_0_1_1496733772650_5620" dir="ltr"><span
id="yui_3_16_0_1_1496733772650_5619">To guarantee two seats,
a party would need 1 Hare quota and one Droop quota of four
seats, so 1/5 + 4/5*1/5 = 9/25 or 0.36 of the vote</span></div>
<div id="yui_3_16_0_1_1496733772650_5618" dir="ltr"><span><br>
</span></div>
<div id="yui_3_16_0_1_1496733772650_5492" dir="ltr"><span
id="yui_3_16_0_1_1496733772650_5491">To guarantee three
seats, they would need 2 Hare quotas and one Droop quota of
three seats, so 2/5 + 3/5*1/4 = 11/20 or 0.55 of the vote.</span></div>
<div id="yui_3_16_0_1_1496733772650_5526" dir="ltr"><span><br>
</span></div>
<div id="yui_3_16_0_1_1496733772650_5527" dir="ltr"><span
id="yui_3_16_0_1_1496733772650_5528">To guarantee four
seats, they'd need 3 Hare quotas and one Droop of two seats,
so 3/5 + 2/5*1/3 = 11/15 or 0.73 of the vote.</span></div>
<div id="yui_3_16_0_1_1496733772650_5642" dir="ltr"><span><br>
</span></div>
<div id="yui_3_16_0_1_1496733772650_5680" dir="ltr"><span
id="yui_3_16_0_1_1496733772650_5679">To guarantee five
seats, they'd need 4 Hare quotas and one Droop of one seats,
so 4/5 + 1/5*1/2 = 9/10 = 0.9 of the vote.</span></div>
<div dir="ltr"><span><br>
</span></div>
<div id="yui_3_16_0_1_1496733772650_5797" dir="ltr"><span
id="yui_3_16_0_1_1496733772650_5796">I think this is correct
now. According to the Wikipedia <a moz-do-not-send="true"
id="yui_3_16_0_1_1496733772650_5795"
href="https://en.wikipedia.org/wiki/Proportionality_for_Solid_Coalitions">https://en.wikipedia.org/wiki/Proportionality_for_Solid_Coalitions</a> the
Hare version of proportionality for solid coalitions
requires a full Hare quota for each seat, but I think this
is a more sophisticated definition.</span></div>
<div id="yui_3_16_0_1_1496733772650_5807"><br>
</div>
<div id="yui_3_16_0_1_1496733772650_5840"><br>
</div>
<div class="qtdSeparateBR" id="yui_3_16_0_1_1496733772650_5410"><br>
<br>
</div>
<div class="yahoo_quoted" id="yui_3_16_0_1_1496733772650_5350"
style="display: block;">
<div id="yui_3_16_0_1_1496733772650_5349" style="font-family:
Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;
font-size: 13px;">
<div id="yui_3_16_0_1_1496733772650_5348"
style="font-family: HelveticaNeue, Helvetica Neue,
Helvetica, Arial, Lucida Grande, Sans-Serif; font-size:
16px;">
<div id="yui_3_16_0_1_1496733772650_5347" dir="ltr"> <font
id="yui_3_16_0_1_1496733772650_5346" face="Arial"
size="2">
<hr id="yui_3_16_0_1_1496733772650_5409" size="1"> <b
id="yui_3_16_0_1_1496733772650_5536"><span
id="yui_3_16_0_1_1496733772650_5535"
style="font-weight: bold;">From:</span></b> Toby
Pereira <a class="moz-txt-link-rfc2396E"
href="mailto:tdp201b@yahoo.co.uk"><tdp201b@yahoo.co.uk></a><br>
<b id="yui_3_16_0_1_1496733772650_5538"><span
id="yui_3_16_0_1_1496733772650_5537"
style="font-weight: bold;">To:</span></b>
Kristofer Munsterhjelm <a
class="moz-txt-link-rfc2396E"
href="mailto:km_elmet@t-online.de"><km_elmet@t-online.de></a>;
VoteFair <a class="moz-txt-link-rfc2396E"
href="mailto:electionmethods@votefair.org"><electionmethods@votefair.org></a>;
<a class="moz-txt-link-rfc2396E"
href="mailto:election-methods@lists.electorama.com">"election-methods@lists.electorama.com"</a>
<a class="moz-txt-link-rfc2396E"
href="mailto:election-methods@lists.electorama.com"><election-methods@lists.electorama.com></a>
<br>
<b id="yui_3_16_0_1_1496733772650_5494"><span
id="yui_3_16_0_1_1496733772650_5493"
style="font-weight: bold;">Sent:</span></b>
Monday, 5 June 2017, 18:23<br>
<b><span style="font-weight: bold;">Subject:</span></b>
Re: [EM] Resume: Proportional multi-winner ranked
voting methods - guidelines?<br>
</font> </div>
<div class="y_msg_container"
id="yui_3_16_0_1_1496733772650_5351"><br>
<div id="yiv7522587144">
<div id="yui_3_16_0_1_1496733772650_5407">
<div id="yui_3_16_0_1_1496733772650_5406"
style="color: rgb(0, 0, 0); font-family: Helvetica
Neue, Helvetica, Arial, Lucida Grande, sans-serif;
font-size: 13px; background-color: rgb(255, 255,
255);">
<div id="yui_3_16_0_1_1496733772650_5408"><span
id="yui_3_16_0_1_1496733772650_5419">I think
that's wrong actually. Forget that last post!</span></div>
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id="yiv7522587144yui_3_16_0_1_1496653143426_13715"><br
clear="none">
<br clear="none">
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<div class="yiv7522587144yqt3344238213"
id="yiv7522587144yqt92422">
<div class="yiv7522587144yahoo_quoted"
id="yiv7522587144yui_3_16_0_1_1496653143426_13709"
style="display: block;">
<div
id="yiv7522587144yui_3_16_0_1_1496653143426_13708"
style="font-family: Helvetica Neue,
Helvetica, Arial, Lucida Grande, sans-serif;
font-size: 13px;">
<div
id="yiv7522587144yui_3_16_0_1_1496653143426_13707"
style="font-family: HelveticaNeue,
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Grande, Sans-Serif; font-size: 16px;">
<div
id="yiv7522587144yui_3_16_0_1_1496653143426_13706"
dir="ltr"> <font
id="yiv7522587144yui_3_16_0_1_1496653143426_13714"
face="Arial" size="2"> </font>
<hr
id="yiv7522587144yui_3_16_0_1_1496653143426_13713"
size="1"> <b><span
style="font-weight: bold;">From:</span></b>
Toby Pereira <a
class="moz-txt-link-rfc2396E"
href="mailto:tdp201b@yahoo.co.uk"><tdp201b@yahoo.co.uk></a><br
clear="none">
<b><span style="font-weight: bold;">To:</span></b>
Kristofer Munsterhjelm <a
class="moz-txt-link-rfc2396E"
href="mailto:km_elmet@t-online.de"><km_elmet@t-online.de></a>;
VoteFair <a
class="moz-txt-link-rfc2396E"
href="mailto:electionmethods@votefair.org"><electionmethods@votefair.org></a>;
<a class="moz-txt-link-rfc2396E"
href="mailto:election-methods@lists.electorama.com">"election-methods@lists.electorama.com"</a>
<a class="moz-txt-link-rfc2396E"
href="mailto:election-methods@lists.electorama.com"><election-methods@lists.electorama.com></a>
<br clear="none">
<b><span style="font-weight: bold;">Sent:</span></b>
Monday, 5 June 2017, 18:19<br
clear="none">
<b><span style="font-weight: bold;">Subject:</span></b>
Re: [EM] Resume: Proportional
multi-winner ranked voting methods -
guidelines?<br clear="none">
</div>
<div class="yiv7522587144y_msg_container"
id="yiv7522587144yui_3_16_0_1_1496653143426_13716"><br clear="none">
<div id="yiv7522587144">
<div
id="yiv7522587144yui_3_16_0_1_1496653143426_13718">
<div
id="yiv7522587144yui_3_16_0_1_1496653143426_13717"
style="color: rgb(0, 0, 0);
font-family: Helvetica Neue,
Helvetica, Arial, Lucida Grande,
sans-serif; font-size: 13px;
background-color: rgb(255, 255,
255);">
<div
id="yiv7522587144yui_3_16_0_1_1496653143426_12079"
dir="ltr"><span
id="yiv7522587144yui_3_16_0_1_1496653143426_12078">By
the way, a sensible Hare
version of proportionality for
solid coalitions would be that
for a faction to be guaranteed
s seats, then they should need
s - 0.5 Hare quotas (or just
over), rather than s Hare
quotas. In the single-winner
case, this would translate to
50% of the vote. This is what
Sainte-Laguë guarantees.</span></div>
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class="yiv7522587144qtdSeparateBR"
id="yiv7522587144yui_3_16_0_1_1496653143426_12071"><br clear="none">
<br clear="none">
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<div
class="yiv7522587144yqt9110754160"
id="yiv7522587144yqt52335">
<div
class="yiv7522587144yahoo_quoted"
id="yiv7522587144yui_3_16_0_1_1496653143426_12067" style="display:
block;">
<div
id="yiv7522587144yui_3_16_0_1_1496653143426_12066"
style="font-family:
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style="font-family:
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id="yiv7522587144yui_3_16_0_1_1496653143426_12063"
face="Arial" size="2">
</font>
<hr size="1"> <b><span
style="font-weight:
bold;">From:</span></b>
Toby Pereira <a
class="moz-txt-link-rfc2396E"
href="mailto:tdp201b@yahoo.co.uk"><tdp201b@yahoo.co.uk></a><br
clear="none">
<b><span
style="font-weight:
bold;">To:</span></b>
Kristofer Munsterhjelm <a
class="moz-txt-link-rfc2396E" href="mailto:km_elmet@t-online.de"><km_elmet@t-online.de></a>;
VoteFair <a
class="moz-txt-link-rfc2396E"
href="mailto:electionmethods@votefair.org"><electionmethods@votefair.org></a>;
<a
class="moz-txt-link-rfc2396E"
href="mailto:election-methods@lists.electorama.com">"election-methods@lists.electorama.com"</a>
<a
class="moz-txt-link-rfc2396E"
href="mailto:election-methods@lists.electorama.com"><election-methods@lists.electorama.com></a>
<br clear="none">
<b><span
style="font-weight:
bold;">Sent:</span></b>
Monday, 5 June 2017,
18:09<br clear="none">
<b
id="yiv7522587144yui_3_16_0_1_1496653143426_13720"><span
id="yiv7522587144yui_3_16_0_1_1496653143426_13719" style="font-weight:
bold;">Subject:</span></b>
Re: [EM] Resume:
Proportional
multi-winner ranked
voting methods -
guidelines?<br
clear="none">
</div>
<div
class="yiv7522587144y_msg_container"
id="yiv7522587144yui_3_16_0_1_1496653143426_12123"><br clear="none">
<div id="yiv7522587144">
<div
id="yiv7522587144yui_3_16_0_1_1496653143426_12125">
<div
id="yiv7522587144yui_3_16_0_1_1496653143426_12124"
style="color:
rgb(0, 0, 0);
font-family:
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Lucida Grande,
sans-serif;
font-size: 13px;
background-color:
rgb(255, 255,
255);">
<div><span></span></div>
<div
class="yiv7522587144qtdSeparateBR"
id="yiv7522587144yui_3_16_0_1_1496653143426_10847" dir="ltr">As I was
saying before,
while Droop
proportionality
has gained a lot
of currency as a
criterion, it's
just a special
case of
proportionality
for solid
coalitions. We
could just as
easily talk
about Hare
proportionality.
For example, the
Sainte-Laguë
party list
method doesn't
obey Droop
proportionality,
but is seen as
more
mathematically
proportional
than D'Hondt,
which does obey
it. But
Sainte-Laguë
does obey
proportionality
for solid
coalitions more
generally. The
point is that
Droop
proportionality
itself is not a
deal breaker for
a method, and I
find it slightly
overused.<br
clear="none">
<br clear="none">
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block;">
<div
id="yiv7522587144yui_3_16_0_1_1496653143426_10835"
style="font-family:
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Neue,
Helvetica,
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sans-serif;
font-size:
13px;">
<div
id="yiv7522587144yui_3_16_0_1_1496653143426_10834"
style="font-family:
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dir="ltr"> <font
id="yiv7522587144yui_3_16_0_1_1496653143426_10832" face="Arial" size="2">
</font>
<div
class="yiv7522587144yqt4964028973"
id="yiv7522587144yqtfd88723">
<hr
id="yiv7522587144yui_3_16_0_1_1496653143426_10846"
size="1"> <b><span
style="font-weight:
bold;">From:</span></b>
Kristofer
Munsterhjelm <a
class="moz-txt-link-rfc2396E" href="mailto:km_elmet@t-online.de"><km_elmet@t-online.de></a><br
clear="none">
<br
id="yiv7522587144yui_3_16_0_1_1496653143426_10844"
clear="none">
<br
clear="none">
Perhaps Droop
proportionality
isn't the
exact
proportionality
measure <br
clear="none">
one would want
- for
instance, for
my Bucklin
methods, I've
tried to <br
clear="none">
base them on
divisor
methods rather
than on hard
quotas - but I
think <br
clear="none">
the concept
that "some
voters who
broadly agree
on a group of
candidates <br
clear="none">
should see one
of them
elected" is a
good one. That
is, that a
group of <br
clear="none">
voters can
have "their"
seat without
having to
agree on a
strategy.</div>
</div>
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<pre wrap="">----
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</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>
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