<html><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif;font-size:16px"><font id="yui_3_16_0_1_1412765264319_2855" style="font-size: 13px;">From: Kathy Dopp <<a id="yui_3_16_0_1_1412765264319_2720" href="mailto:kathy.dopp@gmail.com">kathy.dopp@gmail.com</a>><br><br> <div id="yui_3_16_0_1_1412765264319_2866">On Tue, Oct 7, 2014 at 5:23 PM, Toby Pereira <<a href="mailto:tdp201b@yahoo.co.uk">tdp201b@yahoo.co.uk</a>> wrote:</div><div id="yui_3_16_0_1_1412765264319_2858">>> Perhaps there's a more proportional method than a "truly proportionate<br>>> allocation of seats to voters"! But what I would say is that there are<br>>> several methods that people might deem to be proportional, and so to say<br>>> that yours is *the* method would probably cause some disagreement.</div><div id="yui_3_16_0_1_1412765264319_2859"><br></div><div id="yui_3_16_0_1_1412765264319_2717">>My method of minimizing the formula Sum(v_i *Absolute(v_i/v - s_i/s))<br>>picks the set of winners that is as close as possible to exactly<br>>proportional allocation of seats for the proportion of voters in each<br>>voter group (group voting for the same combination of candidates) out<br>>of the total number of voters. If the number of voters in each group<br>>or total winning seats is altered, as in your examples, the<br>>proportions for each group changes, and, so, the seat allocation may<br>>also change, as you saw.</div><div id="yui_3_16_0_1_1412765264319_2930"><br></div><div id="yui_3_16_0_1_1412765264319_2860">>In my opinion, a voting method that allocates winners in the exact<br>>proportion to their proportion of the voter population is the best<br>>possible. I, personally, would not want to eliminate the smallest<br>>voting groups from the calculations of proportions as do some party<br>>list systems that have a lower threshold for inclusion. I.e. I would<br>>include every voter group in the calculation regardless of the number<br>>of voters it has.</div><div><br></div><div id="yui_3_16_0_1_1412765264319_2857">>I.e. I really like my method of allocating approval vote seats<br>>proportionately, and it has more power than either the Sainte-Laguë or<br>>D'Hondt methods in that it also works well for overlapping candidate<br>>support (ie. for general approval voting of any number of candidates<br>>and seats), not merely for selecting winners for party list type<br>>systems.</div><div id="yui_3_16_0_1_1412765264319_2867"><br></div><div id="yui_3_16_0_1_1412765264319_2715">>It's hard to argue with my formula's exactly proportional<br>>representation. The scenarios you suggest are very unlikely and do<br>>not bother me at all if they would occur because it is hard to argue<br>>with the outcome always being exactly proportionate IMO. I like it,<br>>perhaps better than any other proportional method due to the<br>>simplicity of approval ballots and the fairness of the formula for<br>>selecting the winning candidates.</div><div id="yui_3_16_0_1_1412765264319_2709"><br></div><div id="yui_3_16_0_1_1412765264319_2710">-- </div><div id="yui_3_16_0_1_1412765264319_2713"><font id="yui_3_16_0_1_1412765264319_2905" style="font-size: 13px;">>Kathy Dopp</font></div></font><div id="yui_3_16_0_1_1412765264319_2865" dir="ltr"><font id="yui_3_16_0_1_1412765264319_2906" style="font-size: 13px;"></font><br></div><div align="left" id="yui_3_16_0_1_1412765264319_2907" dir="ltr"><font id="yui_3_16_0_1_1412765264319_2908" style="font-size: 13px;">Well, I don't think it's that hard to argue for other methods. I would agree that your method does give exact proportionality where it's possible, but where a perfectly proportional result isn't possible, different systems look at minimising different measures. And you haven't demonstrated why your method is uniquely the best, or more proportional than the others. My system, for example, uses squared rather than absolute deviation (and uses a different measure of deviation anyway) and it gives the results that I wanted it to when I tested it, including stable results for the largest two factions when the size of the third tiny faction changes, and the three-way tie from the other example. It doesn't work by ignoring or eliminating smaller factions; it just works in a way that produces these results anyway. And it too gives exact proportionality where no rounding is required.</font></div><div align="left" id="yui_3_16_0_1_1412765264319_2965" dir="ltr"><font style="font-size: 13px;"></font><br></div><div align="left" id="yui_3_16_0_1_1412765264319_2966" dir="ltr"><font id="yui_3_16_0_1_1412765264319_2992" style="font-size: 13px;">And I'm still unsure how to translate your method into approval voting with overlapping factions.</font></div><div align="left" id="yui_3_16_0_1_1412765264319_2967" dir="ltr"><font style="font-size: 13px;"></font><br></div><div align="left" id="yui_3_16_0_1_1412765264319_2968" dir="ltr"><font style="font-size: 13px;">Toby</font></div></div></body></html>