<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_1412418944258_17785">>> My problem is not that adding the third faction (C) means that the final<br>>> seat might go to C, but that adding C means that the relative merits of<br>>> giving the seat to A or B changes.</div><div id="yui_3_16_0_1_1412418944258_17787"><br></div><div id="yui_3_16_0_1_1412418944258_17783">>I do not understand your concern. If another faction of voters and<br>>their candidates join the election and obtain enough votes to merit a<br>>seat by changing the proportions of votes all other factions and their<br>>candidates receives, the third set of voters and candidates are<br>>*relevant* and should obtain a seat. This is not a case of an<br>>"irrelevant" candidate or group of voters since the candidate, in the<br>>case of achieving 1/9th of the votes, this group merits a seat next<br>>after the other two factions' have, together, elected 3 candidates.</div><div id="yui_3_16_0_1_1412418944258_17793"><br></div><div id="yui_3_16_0_1_1412418944258_17794" dir="ltr">I'm not saying that the C group shouldn't have a seat. What I'm saying is that in your system, adding C changes which out of A or B is more deserving of the final seat, which seems wrong to me. When the first three seats are allocated, with C as part of the election, according to your system, the order of how deserving each group is to the next seat is C>B>A. B is more deserving than A. However, if C is not there, you get A=B. But why should the presence/absence of C make a difference to whether 3 seats to faction A and 1 to faction B or two seats each to A and B is the more proportional result? It shouldn't. In that sense, C is irrelevant. Specifically, C is irrelevant to which out of A and B is furthest from their proportional allocation.</div><div id="yui_3_16_0_1_1412418944258_17815" dir="ltr"><br></div><div id="yui_3_16_0_1_1412418944258_17809"><br></div><div id="yui_3_16_0_1_1412418944258_17814">>Given your prior example:</div><div id="yui_3_16_0_1_1412418944258_17828">>5: A1, A2, A3, A4<br>>3: B1, B2, B3, B4<br>>1: C1, C2, C3, C4</div><div id="yui_3_16_0_1_1412418944258_17821">>How are you redefining the word "irrelevant" to label voting group C<br>>as "irrelevant"?</div><div id="yui_3_16_0_1_1412418944258_17829"><br></div><div id="yui_3_16_0_1_1412418944258_17852" dir="ltr">It's irrelevant to whether A or B is more deserving of the final seat (regardless of whether C is more deserving than both).</div><div id="yui_3_16_0_1_1412418944258_17830"><br></div><div id="yui_3_16_0_1_1412418944258_17795"><br></div><div id="yui_3_16_0_1_1412418944258_17797">>>So as before, we have:<br>><br>>> 5 voters (A): 2 seats<br>>> 3 voters (B): 1 seat<br>><br>>> and one seat left to assign. According to your system, it should go to C.<br>>> However, let's see what happens if we eliminate the B faction and its one<br>>> seat. We now have:<br>><br>>> 5 voters (A): 2 seats<br>><br>>> and one seat left to assign to either the A or C faction.</div><div id="yui_3_16_0_1_1412418944258_17798"><br>>You are, then, entirely changing the number of seats to assign from 4<br>>to 3? That should change something don't you think?</div><div id="yui_3_16_0_1_1412418944258_17838">>If there were four seats, and factions with, respectively 5 and 1<br>>voter, 3 seats go to the faction with 5 voters, and 1 goes to the<br>>other.</div><div id="yui_3_16_0_1_1412418944258_17853"><br></div><div id="yui_3_16_0_1_1412418944258_17854" dir="ltr">I didn't use this example initially because I thought you might say this, but no, changing the total number of seats doesn't matter if it doesn't affect the factions in question. All I'm saying is that if faction A already has two seats and faction C has none, which out of these two factions is more deserving of another seat based on the number of voters in each (5 and 1 respectively)? The fact that there might be another faction or indeed several factions with 1, 2 or 79 seats already doesn't change which is more deserving purely out of A and C, or which out of A and C is furthest away from their proportional allocation.</div><div id="yui_3_16_0_1_1412418944258_17839"><br></div><div id="yui_3_16_0_1_1412418944258_17840"><br></div><div id="yui_3_16_0_1_1412418944258_17841">>My method is exactly proportional, not minimizing the "wrong thing",<br>>and behaves exactly as it should if an "irrelevant" candidate, defined<br>>in the normal way as a *nonwinning* candidate, drops out of the<br>>contest.</div><div id="yui_3_16_0_1_1412418944258_17873"><br></div><div id="yui_3_16_0_1_1412418944258_17874" dir="ltr">It doesn't behave as you think it does. My previous examples may not have been clear to you why certain factions were irrelevant, but I will make a clearer case now that works on exactly the same principle.</div><div id="yui_3_16_0_1_1412418944258_17892" dir="ltr"><br></div><div id="yui_3_16_0_1_1412418944258_17891" dir="ltr">2 to elect, approval voting</div><div id="yui_3_16_0_1_1412418944258_17894" dir="ltr"><br></div><div id="yui_3_16_0_1_1412418944258_17893" dir="ltr">300: A1, A2</div><div id="yui_3_16_0_1_1412418944258_17895" dir="ltr">100: B1</div><div id="yui_3_16_0_1_1412418944258_17896" dir="ltr"><br></div><div id="yui_3_16_0_1_1412418944258_17897" dir="ltr">We've agreed before I think that there should be a tie between A1, A2 and A1, B1 (or even A2, B1). The A faction should have 1.5 seats and the B faction should have 0.5 seats. After the first seat goes to the A faction, they both deserve 0.5 seats more, so it result in a tie for the final seat. Now take this example:</div><div id="yui_3_16_0_1_1412418944258_17955" dir="ltr"><br></div><div id="yui_3_16_0_1_1412418944258_18106" dir="ltr">2 to elect, approval voting</div><div id="yui_3_16_0_1_1412418944258_17954" dir="ltr"><br></div><div id="yui_3_16_0_1_1412418944258_17953" dir="ltr">300: A1, A2</div><div id="yui_3_16_0_1_1412418944258_17952" dir="ltr">100: B1</div><div id="yui_3_16_0_1_1412418944258_17912" dir="ltr">1: C1</div><div id="yui_3_16_0_1_1412418944258_17913" dir="ltr"><br></div><div id="yui_3_16_0_1_1412418944258_17914" dir="ltr">What should the result be? A should have 1.496 seats, B should have 0.499 seats, and C should have 0.005 seats. A gets the first seat as before. But now, B is more deserving of the second seat than A according to your system. C is surely irrelevant here but it changes the result.</div><div id="yui_3_16_0_1_1412418944258_17890" dir="ltr"><br></div><div id="yui_3_16_0_1_1412418944258_17889" dir="ltr">Toby</div><div id="yui_3_16_0_1_1412418944258_18089"><br></div></div></body></html>