<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_1412486485565_5621">From: Kathy Dopp <<a id="yui_3_16_0_1_1412486485565_5614" href="mailto:kathy.dopp@gmail.com">kathy.dopp@gmail.com</a>><br><br>>> What I'm saying is<br>>> that in your system, adding C changes which out of A or B is more deserving<br>>> of the final seat, which seems wrong to me.</div><div id="yui_3_16_0_1_1412486485565_5507"><br></div><div id="yui_3_16_0_1_1412486485565_5504">>First, adding more voters (group C) means that the denominator of the<br>>ratio (proportion) for each (every) voting group changes.</div><div id="yui_3_16_0_1_1412486485565_5505">>How could I change the denominator of the quantity v_i/v (the<br>>proportion of each voting group) without changing the proportion of<br>>seats that each group should have?</div><div id="yui_3_16_0_1_1412486485565_5508"><br></div><div id="yui_3_16_0_1_1412486485565_5509" dir="ltr">Well, it changes the overall proportion they should have, but it does not change the 5:3 correct ratio of A to B seats. I would argue that if</div><div id="yui_3_16_0_1_1412486485565_5510" dir="ltr"><br></div><div id="yui_3_16_0_1_1412486485565_5511" dir="ltr">Faction 1: w seats</div><div id="yui_3_16_0_1_1412486485565_5512" dir="ltr">Faction 2: x seats</div><div id="yui_3_16_0_1_1412486485565_5513" dir="ltr">Faction 3: y seats</div><div id="yui_3_16_0_1_1412486485565_5514" dir="ltr"><br></div><div id="yui_3_16_0_1_1412486485565_5515" dir="ltr">is more proportional than</div><div id="yui_3_16_0_1_1412486485565_5516" dir="ltr"><br></div><div id="yui_3_16_0_1_1412486485565_5517" dir="ltr">Faction 1: w+1 seats</div><div id="yui_3_16_0_1_1412486485565_5518" dir="ltr">Faction 2: x-1 seats</div><div id="yui_3_16_0_1_1412486485565_5519" dir="ltr">Faction 3: y seats</div><div id="yui_3_16_0_1_1412486485565_5524" dir="ltr"><br></div><div id="yui_3_16_0_1_1412486485565_5523" dir="ltr">then with the same voting patterns</div><div id="yui_3_16_0_1_1412486485565_5522" dir="ltr"><br></div><div id="yui_3_16_0_1_1412486485565_5521" dir="ltr">Faction 1: w seats</div><div id="yui_3_16_0_1_1412486485565_5520" dir="ltr">Faction 2: x seats</div><div id="yui_3_16_0_1_1412486485565_5528" dir="ltr">Faction 3: z seats</div><div id="yui_3_16_0_1_1412486485565_5527" dir="ltr"><br></div><div id="yui_3_16_0_1_1412486485565_5529" dir="ltr">is more proportional than</div><div id="yui_3_16_0_1_1412486485565_5530" dir="ltr"><br></div><div id="yui_3_16_0_1_1412486485565_5531" dir="ltr">Faction 1: w+1 seats</div><div id="yui_3_16_0_1_1412486485565_5532" dir="ltr">Faction 2: x-1 seats</div><div id="yui_3_16_0_1_1412486485565_5525" dir="ltr">Faction 3: z seats</div><div dir="ltr"><br></div><div id="yui_3_16_0_1_1412486485565_5549" dir="ltr">for any x, y, w, z. Sainte-Laguë, D'Hondt and my system fit this criterion.</div><div id="yui_3_16_0_1_1412486485565_5526" dir="ltr"><br></div><div id="yui_3_16_0_1_1412486485565_5499"><br></div><div id="yui_3_16_0_1_1412486485565_5550"><br>>> When [AFTER] the first three seats are<br>>> allocated, with C as part of the election, according to your system, the<br>>> order of how deserving each group is to the next seat is C>B>A. B is more<br>>> deserving than A.</div><div id="yui_3_16_0_1_1412486485565_5556"><br></div><div id="yui_3_16_0_1_1412486485565_5553">>Yes.</div><div id="yui_3_16_0_1_1412486485565_5555"><br></div><div id="yui_3_16_0_1_1412486485565_5552">>> However, if C is not there, you get A=B.</div><div id="yui_3_16_0_1_1412486485565_5557"><br></div><div id="yui_3_16_0_1_1412486485565_5551">>No. I think what you mean to say is that after allocating 2 winning<br>>seats to group A and 1 to group B, group A and group B both are owed<br>>1/2 a seat each to be proportionately fair, so that 2 candidates<br>>each for group A and group B would be equally proportionately fair as<br>>3 candidates for group A and 1 for group B.</div><div id="yui_3_16_0_1_1412486485565_5564"><br></div><div id="yui_3_16_0_1_1412486485565_5565" dir="ltr">So you mean "yes". That's what I meant for A=B in this context.</div><div id="yui_3_16_0_1_1412486485565_5558"><br>>> But why should<br>>> the presence/absence of C make a difference to whether 3 seats to faction A<br>>> and 1 to faction B or two seats each to A and B is the more proportional<br>>> result?</div><div id="yui_3_16_0_1_1412486485565_5576"><br></div><div id="yui_3_16_0_1_1412486485565_5574">>C's presence makes a difference because group C wins one of the 4<br>>seats, so that only 3 seats are divied up between group A and B. C's<br>>leaving does not change (by one iota) the division of the first 3<br>>winning seats. Group C's absence merely makes a 4th seat available to<br>>divy up between two groups rather than between three groups!</div><div id="yui_3_16_0_1_1412486485565_5577"><br></div><div id="yui_3_16_0_1_1412486485565_5578" dir="ltr">No. I was talking about which of A and B was more deserving of the fourth seat even if C was more deserving than both, so assuming C has no seats.</div><div id="yui_3_16_0_1_1412486485565_5571"><br>>> It shouldn't. In that sense, C is irrelevant. Specifically, C is<br>>> irrelevant to which out of A and B is furthest from their proportional<br>>> allocation.</div><div id="yui_3_16_0_1_1412486485565_5586"><br></div><div id="yui_3_16_0_1_1412486485565_5572">>AGAIN, you are using a perverted definition of "irrelevant" that I<br>>know of no one else who agrees with you. Group C is awarded 1 WINNING<br>>CANDIDATE, so if group C is absent, there is one (1) more candidate to<br>>award to the remaining groups.</div><div><br></div><div id="yui_3_16_0_1_1412486485565_5649" dir="ltr">See above.</div><div id="yui_3_16_0_1_1412486485565_5579"><br></div><div id="yui_3_16_0_1_1412486485565_5642">><br>><br>>Given your prior example:</div><div id="yui_3_16_0_1_1412486485565_5641"><br>>>5: A1, A2, A3, A4<br>>>3: B1, B2, B3, B4<br id="yui_3_16_0_1_1412486485565_5639">>>1: C1, C2, C3, C4</div><div id="yui_3_16_0_1_1412486485565_5643"><br>>How are you redefining the word "irrelevant" to label voting group C<br>>as "irrelevant"?<br>><br>>> It's irrelevant to whether A or B is more deserving of the final seat<br>>> (regardless of whether C is more deserving than both).</div><div id="yui_3_16_0_1_1412486485565_5587"><br>>Obviously not. If group C does not exist, there are only 8 voters in<br>>your example, not 9 voters. Therefore, the relative proportions MUST<br>>change between the two remaining groups unless you think magically<br>>reducing the denominator in the proportion of voters calculation<br id="yui_3_16_0_1_1412486485565_5588">>should not alter the proportion of voters that each group comprises.</div><div id="yui_3_16_0_1_1412486485565_5495">>Again, you seem to have difficulty with the way the arithmetic of<br>>fractions work, as I believe I observed in the first of your emails I<br>>responded to in this thread.</div><div id="yui_3_16_0_1_1412486485565_5597"><br></div><div id="yui_3_16_0_1_1412486485565_5596" dir="ltr">You admitted you'd misunderstood what I was saying about fractions earlier. You can't then retrospectively wipe that from history because you don't like what I'm saying now. Sainte-Laguë and D'Hondt both fit the criterion I'm talking about, so it's not obviously wrong.</div><div id="yui_3_16_0_1_1412486485565_5595"><br>>I think we're just going around in circles, so I'm ignoring the rest<br>>of your response.</div><div id="yui_3_16_0_1_1412486485565_5604"><br></div><div id="yui_3_16_0_1_1412486485565_5491">Well, the last example that you ignored was the simplest and probably example of why Sainte-Laguë and D'Hondt have this superior property that your method doesn't.</div><div id="yui_3_16_0_1_1412486485565_5492"><br></div><div id="yui_3_16_0_1_1412486485565_5493" dir="ltr">Toby<br></div></div></body></html>