<!DOCTYPE html>
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
</head>
<body>
<p><br>
</p>
<p><!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:ApplyBreakingRules/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:UseFELayout/>
</w:Compatibility>
<w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel>
</w:WordDocument>
</xml><![endif]--><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-parent:"";
mso-padding-alt:0cm 5.4pt 0cm 5.4pt;
mso-para-margin:0cm;
mso-para-margin-bottom:.0001pt;
mso-pagination:widow-orphan;
font-size:10.0pt;
font-family:"Times New Roman";
mso-fareast-font-family:"Times New Roman";}
</style>
<![endif]-->
</p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT Bold"">The
Hare quota gives maximum proportional representation. The Droop
quota gives
minimum proportional representation. The reason why we have the
Droop quota at
all is because career politicians wouldn’t tolerate the
competition of large
multi-member constituencies.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT Bold"">Droop
is not an improvement on Hare, except in the eyes of
monopolistic politicians.
However both quotas are to some extent undemocratic. Candidates
may be elected
to the Droop quota without a statistically significant margin of
victory over
rival candidates.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT Bold"">Whereas
the Hare quota, in relatively small constituencies, cannot elect
candidates at
all, without the deference of some voters, over their personal
wishes, say, for
some party line, or according to some religious instruction.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT Bold"">To
overcome the mutual democratic deficiencies of both the Hare
quota and the
Droop quota, I introduced their Harmonic Mean quota
(votes/(seats+1/2) since
the average of harmonic series is the harmonic mean. (It
is one of the four averages, in my voting method, FAB STV: Four
Averages
Binomial Single Transferablee Vote.)</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT Bold"">I
discovered later that my harmonic mean quota was the equivalent
of Webster/St
Lague apportionment. So I have no reason to believe that divisor
systems are
any better than quota systems. They are just complementary means
of reckoning.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT Bold"">Divisor
methods (mis)applied to party list systems divide the voters
into conflicting
herds. Because, these voting methods lack a transferable vote to
express unity
as well as division.</span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT Bold""> Regards, </span></p>
<p class="MsoNormal"><span
style="font-size:14.0pt;font-family:"Arial Rounded MT Bold"">Richard
Lung<br>
</span></p>
<p><br>
</p>
<div class="moz-cite-prefix">On 25/04/2024 02:38, Closed Limelike
Curves wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CA+euzPjoHQndaDRsg4mEerc9hy249PsLbEAYYtxtGHns0cnR1Q@mail.gmail.com">
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<div dir="ltr">Funnily enough, I'm actually thinking that wiki
article needs to be rewritten from scratch (probably into a
section on a broader article on electoral quotas). It doesn't do
a very good job of going over the tradeoffs between the two
quotas, which are:
<div>1. Droop preserves majorities. (A candidate with a majority
of the vote will always win a majority of seats.)</div>
<div>2. Droop is less vulnerable to strategy, because a Droop
quota can always enforce their preferences over another
candidate (if a Droop quota prefers A to B, then bullet voting
A ensures A has more support than B).</div>
<div>3. Hare is <i>unbiased</i>, making it more proportional
than Droop; every party will, on average, receive a number of
seats proportional to their share of the vote. Droop is biased
towards large parties.</div>
<div>4. Anti-Droop (nonstandard name; divide by n-1 instead of
n+1) will always preserve minorities (a party with less than a
majority of the vote will always receive less than a majority
of the seats). Anti-Droop is biased towards small parties.
I've never seen a serious proposal for it.</div>
<div><br>
</div>
<div>Most mathematicians consider quota methods inferior to
divisor methods in general; HH+Webster satisfy quota in
practice anyways.</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Thu, Apr 18, 2024 at
12:38 PM Joseph Malkevitch <<a
href="mailto:jmalkevitch@york.cuny.edu" target="_blank"
moz-do-not-send="true" class="moz-txt-link-freetext">jmalkevitch@york.cuny.edu</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote"
style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div>
<div dir="ltr">
<div
style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
This Wiki article may help explain the "issues" related
to the use of the Droop and Hare quotas.</div>
<div
style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
<br>
</div>
<div
style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
<a
href="https://en.wikipedia.org/wiki/Comparison_of_the_Hare_and_Droop_quotas"
id="m_-7606255286892721022m_630065074292471010LPlnk192613"
target="_blank" moz-do-not-send="true"
class="moz-txt-link-freetext">https://en.wikipedia.org/wiki/Comparison_of_the_Hare_and_Droop_quotas</a></div>
<div
style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
<br>
</div>
<div
style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
Best,</div>
<div
style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
<br>
</div>
<div
style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
Joe</div>
<div
style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
<br>
</div>
<div
style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
<br>
</div>
<div
id="m_-7606255286892721022m_630065074292471010Signature">
<div
style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
——————————————</div>
<div
style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
Joseph Malkevitch</div>
<div
style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
<br>
</div>
<div
style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
Email:</div>
<div
style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
<a href="mailto:jmalkevitch@york.cuny.edu"
target="_blank" moz-do-not-send="true"
class="moz-txt-link-freetext">jmalkevitch@york.cuny.edu</a></div>
<div
style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
Web page:</div>
<div
style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
<a href="http://york.cuny.edu/~malk/" target="_blank"
moz-do-not-send="true" class="moz-txt-link-freetext">http://york.cuny.edu/~malk/</a></div>
</div>
</div>
----<br>
Election-Methods mailing list - see <a
href="https://electorama.com/em" rel="noreferrer"
target="_blank" moz-do-not-send="true"
class="moz-txt-link-freetext">https://electorama.com/em</a>
for list info<br>
</div>
</blockquote>
</div>
<br>
<fieldset class="moz-mime-attachment-header"></fieldset>
<pre class="moz-quote-pre" wrap="">----
Election-Methods mailing list - see <a class="moz-txt-link-freetext" href="https://electorama.com/em">https://electorama.com/em</a> for list info
</pre>
</blockquote>
</body>
</html>