<html><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif;font-size:13px"><div><span></span></div><div id="yui_3_16_0_1_1412418944258_7648" dir="ltr">Kathy</div><div id="yui_3_16_0_1_1412418944258_7647" dir="ltr"><br></div><div dir="ltr">I'd already sent that last e-mail before seeing this, but it seems your method is essentially the Largest Remainder method <a href="http://en.wikipedia.org/wiki/Largest_remainder_method">http://en.wikipedia.org/wiki/Largest_remainder_method</a> It comes with its own problems such as the Alabama paradox <a href="http://en.wikipedia.org/wiki/Apportionment_paradox#Alabama_paradox">http://en.wikipedia.org/wiki/Apportionment_paradox#Alabama_paradox</a> where increasing the seats available can actually cause a party to lose seats.</div><div id="yui_3_16_0_1_1412418944258_7665" dir="ltr"><br></div><div id="yui_3_16_0_1_1412418944258_7666" dir="ltr">Toby</div><div id="yui_3_16_0_1_1412418944258_7667"><br> </div><blockquote id="yui_3_16_0_1_1412418944258_7663" style="padding-left: 5px; margin-top: 5px; margin-left: 5px; border-left-color: rgb(16, 16, 255); border-left-width: 2px; border-left-style: solid;"> <div id="yui_3_16_0_1_1412418944258_7662" style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 13px;"> <div id="yui_3_16_0_1_1412418944258_7661" style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 12px;"> <div id="yui_3_16_0_1_1412418944258_7660" dir="ltr"> <hr size="1" id="yui_3_16_0_1_1412418944258_7664"> <font id="yui_3_16_0_1_1412418944258_7668" face="Arial" size="2"> <b><span style="font-weight: bold;">From:</span></b> Kathy Dopp <kathy.dopp@gmail.com><br> <b><span style="font-weight: bold;">To:</span></b> Toby Pereira <tdp201b@yahoo.co.uk> <br><b><span style="font-weight: bold;">Cc:</span></b> Kristofer Munsterhjelm <km_elmet@t-online.de>; EM <election-methods@lists.electorama.com> <br> <b><span style="font-weight: bold;">Sent:</span></b> Saturday, 4 October 2014, 17:07<br> <b><span style="font-weight: bold;">Subject:</span></b> Re: [EM] General PR question (from Andy Jennings in 2011)<br> </font> </div> <div class="y_msg_container" id="yui_3_16_0_1_1412418944258_7669"><br>Toby,<br clear="none"><br clear="none"><br clear="none"><br clear="none">After looking at how the Sainte-Laguë and D'Hondt methods work, a<br clear="none">similar algorithmic approach to implementing my method can be easily<br clear="none">shown to always provide proportionate results in terms of seat<br clear="none">allocation.<br clear="none"><br clear="none">So instead of calculating the somewhat complex (for the average voter)<br clear="none">Sum over i of (v_i/v*Absolute(v_i/v - s_i/s))<br clear="none"><br clear="none"><br clear="none">The algorithm for my method, as you noticed, would be simply to:<br clear="none">(1) multiple the overall ratio of the (total # seats)/(total #<br clear="none">voters) times the number of voters in each voting group<br clear="none">(2) the integer portion of each result is the number of seats assigned<div class="qtdSeparateBR"><br><br></div><div class="yqt5320568040" id="yqtfd55989"><br clear="none">to each group</div><br clear="none">(3) order the remainder decimal portion of each voting group's result<br clear="none">from greatest to least and beginning at the top (group with the<br clear="none">largest remainder) assign one more seat to each group until the total<br clear="none">number of seats to be elected is achieved.<br clear="none"><br clear="none">(4) Although unlikely in most elections, some tie-breaking procedure<br clear="none">could be needed: E.g. If there are ties towards the end of the<br clear="none">allocation procedure, some random selection or asking tied groups at<br clear="none">the end of the allocation process to co-select a winner, or possibly,<br clear="none">the number of seats could be increased by the number of groups - 1 who<br clear="none">tie for the last seat allocation.<br clear="none"><br clear="none"><br clear="none">I am unclear why, exactly, either the Sainte-Laguë and D'Hondt methods<br clear="none">would always give exactly proportionate results in all cases, but it<br clear="none">is easy to understand, simply by the cancellation of the units of<br clear="none">analysis seats/voters * voters = seats (as physicists always do) that<br clear="none">the above algorithm always would given the most proportionate outcomes<br clear="none">in seats (disregarding exactly tie votes).<br><br></div> </div> </div> </blockquote> </div></body></html>