<html><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif;font-size:13px"><div id="yui_3_16_0_1_1412534331220_2616">On Sun, Oct 5, 2014 at 2:02 AM, Toby Pereira <<a href="mailto:tdp201b@yahoo.co.uk">tdp201b@yahoo.co.uk</a>> wrote:<br>> From: Kathy Dopp <<a href="mailto:kathy.dopp@gmail.com">kathy.dopp@gmail.com</a>><br>></div><div id="yui_3_16_0_1_1412534331220_2384"><br>><br>>> Well, it changes the overall proportion they should have, but it does not<br>>> change the 5:3 correct ratio of A to B seats.</div><div id="yui_3_16_0_1_1412534331220_2615"><br></div><div id="yui_3_16_0_1_1412534331220_2386">>Yes. However, it changes the NUMBER of seats allocated in the 5:3<br>>ratio, allocating those seats in EXACTLY proportional fashion. I.e.</div><div id="yui_3_16_0_1_1412534331220_2385">>For three seats:</div><div id="yui_3_16_0_1_1412534331220_2393">>5 voters 1.875 seats gives 2 seats<br>>3 voters 1.125 seats gives 1 seat</div><div id="yui_3_16_0_1_1412534331220_2647">>For four seats:</div><div id="yui_3_16_0_1_1412534331220_2646">>5 voters 2.5 seats - a tie for the forth seat gives 2 or 3 seats<br>>3 voters 1.5 seats - a tie for the forth seat gives 2 or 1 seats</div><div id="yui_3_16_0_1_1412534331220_2394">>It's just SIMPLE arithmetic.</div><div id="yui_3_16_0_1_1412534331220_2395">>If you don't like it, then you are arguing AGAINST PROPORTIONAL<br>>representation, which is your right.</div><div id="yui_3_16_0_1_1412534331220_2617"><br></div><div id="yui_3_16_0_1_1412534331220_2396" dir="ltr">The example wasn't about three or four seats. It was about four seats both times and who was more deserving of the fourth seat out of A and B with or without C's inclusion. (It doesn't matter that you might argue that C is more deserving than either when present because we can still order non-winning allocations in terms of proportionality.)</div><div id="yui_3_16_0_1_1412534331220_2653" dir="ltr"><br>>> I would argue that if [SNIPPED]<br></div><div id="yui_3_16_0_1_1412534331220_2413"><br>>Yes. I AGREE and so does my formula minimization algorithm.</div><div id="yui_3_16_0_1_1412534331220_2412"><br></div><div id="yui_3_16_0_1_1412534331220_2411" dir="ltr">OK - I should have added that it is specifically with factions 1 and 2 having the same voting patterns. I'll formulate it differently and give a specific example. So I would argue that if</div><div id="yui_3_16_0_1_1412534331220_2414" dir="ltr"><br></div><div id="yui_3_16_0_1_1412534331220_2415" dir="ltr">Faction 1: x seats</div><div id="yui_3_16_0_1_1412534331220_2416" dir="ltr">Faction 2: y seats</div><div id="yui_3_16_0_1_1412534331220_2417" dir="ltr">Faction 3: z seats</div><div id="yui_3_16_0_1_1412534331220_2424" dir="ltr"><br></div><div id="yui_3_16_0_1_1412534331220_2423" dir="ltr">is more proportional than</div><div id="yui_3_16_0_1_1412534331220_2422" dir="ltr"><br></div><div id="yui_3_16_0_1_1412534331220_2418" dir="ltr">Faction 1: x-1seats</div><div id="yui_3_16_0_1_1412534331220_2419" dir="ltr">Faction 2: y+1 seats</div><div id="yui_3_16_0_1_1412534331220_2420" dir="ltr">Faction 3: z seats</div><div id="yui_3_16_0_1_1412534331220_2421" dir="ltr"><br></div><div id="yui_3_16_0_1_1412534331220_2425" dir="ltr">then if the only change in votes concerns faction 3, this would mean that</div><div id="yui_3_16_0_1_1412534331220_2426" dir="ltr"><br></div><div id="yui_3_16_0_1_1412534331220_2415" dir="ltr">Faction 1: x seats</div><div id="yui_3_16_0_1_1412534331220_2416" dir="ltr">Faction 2: y seats</div><div id="yui_3_16_0_1_1412534331220_2417" dir="ltr">Faction 3: z seats</div><div id="yui_3_16_0_1_1412534331220_2424" dir="ltr"><br></div><div id="yui_3_16_0_1_1412534331220_2423" dir="ltr">is still more proportional than</div><div id="yui_3_16_0_1_1412534331220_2422" dir="ltr"><br></div><div id="yui_3_16_0_1_1412534331220_2418" dir="ltr">Faction 1: x-1seats</div><div id="yui_3_16_0_1_1412534331220_2419" dir="ltr">Faction 2: y+1 seats</div><div id="yui_3_16_0_1_1412534331220_2420" dir="ltr">Faction 3: z seats</div><div id="yui_3_16_0_1_1412534331220_2409"><br></div><div id="yui_3_16_0_1_1412534331220_2446" dir="ltr">For example:</div><div id="yui_3_16_0_1_1412534331220_2447" dir="ltr"><br></div><div id="yui_3_16_0_1_1412534331220_2448" dir="ltr">2 to elect</div><div id="yui_3_16_0_1_1412534331220_2437" dir="ltr"><br></div><div id="yui_3_16_0_1_1412534331220_2464" dir="ltr">Faction 1: 302</div><div id="yui_3_16_0_1_1412534331220_2438" dir="ltr">Faction 2: 100</div><div id="yui_3_16_0_1_1412534331220_2439" dir="ltr">Faction 3: 1</div><div id="yui_3_16_0_1_1412534331220_2520" dir="ltr"><br></div><div id="yui_3_16_0_1_1412534331220_2524" dir="ltr">The proportional allocations are:</div><div id="yui_3_16_0_1_1412534331220_2516" dir="ltr"><br></div><div id="yui_3_16_0_1_1412534331220_2517" dir="ltr">Faction 1: 1.499</div><div id="yui_3_16_0_1_1412534331220_2525" dir="ltr">Faction 2: 0.496</div><div id="yui_3_16_0_1_1412534331220_2540" dir="ltr">Faction 3: 0.005</div><div id="yui_3_16_0_1_1412534331220_2576" dir="ltr"><br></div><div id="yui_3_16_0_1_1412534331220_2557" dir="ltr">Faction 1 would win both seats. However, if we have:</div><div id="yui_3_16_0_1_1412534331220_2558" dir="ltr"><br></div><div id="yui_3_16_0_1_1412534331220_2559" dir="ltr">Faction 1: 302</div><div id="yui_3_16_0_1_1412534331220_2560" dir="ltr">Faction 2: 100</div><div id="yui_3_16_0_1_1412534331220_2561" dir="ltr">Faction 3: 3</div><div id="yui_3_16_0_1_1412534331220_2583" dir="ltr"><br></div><div id="yui_3_16_0_1_1412534331220_2593" dir="ltr">The proportional allocations are:</div><div id="yui_3_16_0_1_1412534331220_2584" dir="ltr"><br></div><div id="yui_3_16_0_1_1412534331220_2585" dir="ltr">Faction 1: 1.491</div><div id="yui_3_16_0_1_1412534331220_2599" dir="ltr">Faction 2: 0.494</div><div id="yui_3_16_0_1_1412534331220_2607" dir="ltr">Faction 3: 0.015</div><div id="yui_3_16_0_1_1412534331220_2613" dir="ltr"><br></div><div id="yui_3_16_0_1_1412534331220_2614" dir="ltr">This would make it one seat all between factions 1 and 2. This is why I would argue that there are better definitions of proportionality than your method.</div><div id="yui_3_16_0_1_1412534331220_2661" dir="ltr"><br></div><div id="yui_3_16_0_1_1412534331220_2662" dir="ltr">Toby</div></div></body></html>