<div><br></div><div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Wed, Oct 18, 2023 at 04:08 Toby Pereira <<a href="mailto:tdp201b@yahoo.co.uk">tdp201b@yahoo.co.uk</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:13px"><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"></div>
<div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">I think Webster/<span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">Sainte-Laguë is generally accepted as the most mathematically accurate method of apportionment / party list PR,</span></div></div></div></blockquote><div dir="auto"><br></div><div dir="auto">Absolutely, Webster/Sainte-Lague is by far the most unbiased allocation-rule to have ever been used for PR on apportionment. It’s bias is very slight.</div><div dir="auto"><br></div><div dir="auto">It’s bias is so slight that, with a 150-seat at-large, no districts Parliament, if there are 17 small parties, each with 3% of the vote, summing to 51% or the vote, & one big party with 49% of the vote, the small parties together will get a majority of the seats.</div><div dir="auto"><br></div><div dir="auto">Sainte-Lague is what I propose for allocating Parliamentary seats.</div><div dir="auto"><br></div><div dir="auto">The entirety absolutely unbiased Bias-Free would be a little better, but the difference is tiny, insignificant.</div><div dir="auto"><br></div><div dir="auto">If it were up to me, the allocation would be by Bias-Free. But SL’s use of the arithmetical mean of the two consecutive integers as its round-off point, rounding to the nearest integer is so obvious, natural & plainly-motivated, & also traditionally-established, that plainly SL is the proposal more likely to be accepted.</div><div dir="auto"><br></div><div dir="auto"><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:13px"><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"> and any large party bias comes from assumptions about the distribution, </span></div></div></div></blockquote><div dir="auto"><br></div><div dir="auto">No. SL really is slightly biased in favor of large parties…just not enough to matter.</div><div dir="auto"><br></div><div dir="auto">But the allocation-rule currently used for allocating seats in the U.S.House of representatives, called “Equal-Proportions” is about twice as biased as Webster/Sainte-Lague. “Equal Proportion” is biased in favor of small states, which of course is why it was adopted & is still in use.</div><div dir="auto"><br></div><div dir="auto">Not that the House apportionment method makes any difference when each state, regardless of how small it is, get the same number of senators (two), & at least one House representative.</div><div dir="auto"><br></div><div dir="auto">No need to take my word for SL’s bias. Check out a number of sources. Some will mention SL’s slight large-favoring bias. …& yes some, especially the earlier writings, might mistakenly say that SL is unbiased, because its bias is so small as to easily not be noticed.</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:13px"><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">and this also calls into question what features we need to reduce the bias of. The following example has four parties (A, B, C, D) and the percentage voting for them:</span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br></span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">A: 38</span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">B: 38</span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">C: 12</span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">D: 12</span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br></span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">Under <span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)">Sainte-Laguë, with four seats A and B will get two each. So if this is the kind of distribution you get in general, you will see a large party bias. Whereas if the distribution was:</span></span></span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)"><br></span></span></span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)">A: 37</span></span></span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)">B: 37</span></span></span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)">C: 13</span></span></span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)">D: 13</span></span></span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)"><br></span></span></span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)">Then with four seats each party will win one. So this gives a small party bias. These are very simplistic examples just for illustrative purposes, and it might well be that under realistic distributions, you end up with more of a large party bias on average</span></span></span></div></div></div></blockquote><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto">The fewer the seats, the less often that small bias will show up & make a difference between SL & Bias-Free (BF). </div><div dir="auto"><br></div><div dir="auto">I once tried SL, BF, & “Equal Proportions” on the votes in an actual many-party at-large European List-PR election.</div><div dir="auto"><br></div><div dir="auto">All three methods gave the same seat-allocation.</div><div dir="auto"><br></div><div dir="auto">But in our 435-seat House of Representatives, it isn’t unusual for them to give different results.</div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:13px"><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)">. However, this doesn't change the fact that for a given election, <span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)">Sainte-Laguë gives the most proportionally accurate, and therefore least biased by a reasonable measure of bias, result, even if large parties fair better on average.</span></span></span></span></span></div></div></div></blockquote><div dir="auto"><br></div><div dir="auto">Yes, & the bias changes the result from the BF allocation fairly rarely unless the at-large Parliament is huge. …& then the difference witl mostly be for the 2nd seat. (SL specifies the rounding-point for the 1st seat as .7 instead of.5. That .7 rounding-point should be used with BF. …for the same reason, to disincentivize party-splitting strategy.</div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:13px"><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)"></span></span></span></span></span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)"><br></span></span></span></span></span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)">Changing the divisor to shift the bias towards smaller parties may seem like a good solution, </span></span></span></span></span></div></div></div></blockquote><div dir="auto"><br></div><div dir="auto">Divisor-methods, such as SL, BF, d’Hondt, & “Equal Proportions”, choose the divisor (sometimes called a “quota”) so that when you divide each parties quotas (result of dividing the party’s votes by the quota), & then round-off by the particular method’s rounding-rule, the total number of seats allocated sums to the desired house-size.</div><div dir="auto"><br></div><div dir="auto">Start with the Hare-quota (total-votes. divided by desired house-size).</div><div dir="auto"><br></div><div dir="auto">Divide each party’s votes by that quota. </div><div dir="auto"><br></div><div dir="auto">If that gives the desired total number of seats, then you’re done. </div><div dir="auto"><br></div><div dir="auto">But if there are too many seats allocated, then try a slightly larger quota.</div><div dir="auto"><br></div><div dir="auto">If there are slightly too few seats allocated, then try a slightly smaller quota.</div><div dir="auto"><br></div><div dir="auto">Find the right quota, the one that gives the right house-size, by trial & error.</div><div dir="auto"><br></div><div dir="auto">From what I read, that’s how the divisor-methods were defined in the early days of House-apportionment, & for some time after.</div><div dir="auto"><br></div><div dir="auto">Of course, for PR, a systematic procedure is used, to avoid speaking of trial & error in the definition.</div><div dir="auto"><br></div><div dir="auto">The procedure starts with all parties having zero seats (as the would with a sufficiently large quota), & with the seats assigned to the parties as they round up one at a time as the quota is gradually lowered.</div><div dir="auto"><br></div><div dir="auto">That’s the basis of the systematic-procedure by which the divisor methods are defined.</div><div dir="auto"><br></div><div dir="auto">For each next seat, they divide each party’s total votes by the round-up point for that party’s next seat.</div><div dir="auto"><br></div><div dir="auto">…which shows which party will round up next as the quota is lowered.</div><div dir="auto"><br></div><div dir="auto">Note that it isn’t necessary to refer to the constantly decreasing quota when doing or defining the method.</div><div dir="auto"><br></div><div dir="auto">The methods differ from eachother by how the rounding-point is determined from the pair of consecutive integers consisting of the party’s current number of seats (“a”), & the next integer (“b”).</div><div dir="auto"><br></div><div dir="auto">i.e. For SL, the rounding-point, R, is the arithmetical-mean of a & b.</div><div dir="auto"><br></div><div dir="auto">(a+b)/2</div><div dir="auto"><br></div><div dir="auto">For BF:</div><div dir="auto"><br></div><div dir="auto">R = (1/e)((b^b)/(a^a)).</div><div dir="auto"><br></div><div dir="auto">i.e. divide b^b by a^a. Then divide the result by e.</div><div dir="auto"><br></div><div dir="auto">e is the base of the natural logarithms, equal to about 2.718…</div><div dir="auto"><br></div><div dir="auto">d’Hondt’s R = b.</div><div dir="auto"><br></div><div dir="auto">i.e. you don’t get your 3rd seat unless you have at least 3 quotas. In other words, everyone rounds down.</div><div dir="auto"><br></div><div dir="auto">So SL’s R is the arithmetical mean of a & b.</div><div dir="auto"><br></div><div dir="auto">“Equal-Proportions” R is the geometric mean of a & b.</div><div dir="auto"><br></div><div dir="auto">Some people aesthetically like that, but it results in about twice as much bias as SL.</div><div dir="auto"><br></div><div dir="auto">Incidentally, BF’s R is called the identric-mean of a & b.</div><div dir="auto"> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:13px"><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)">but as well as coming at the cost of proportional accuracy, it works under the assumption that large parties form an entity or themselves so that if one large party gets more than its proportional share, it's better for a small party rather than another large party to also get more than its proportional share.</span></span></span></span></span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)"><br></span></span></span></span></span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)">So in my first example, to reduce bias, you might decide to give A 2 seats, B 1 seat, C 1 seat and D 0 seats. So if you consider A and C as a pair, your bias is toward the large party and with B and D, your bias is towards the small party. However, what we actually have is four separate parties. A and B are not in league with each other and neither are C and D. So trying to reduce bias on party size in this way is based on false assumptions and you end up biasing the result in other ways - it's not just about large v small. The most proportionally accurate result is 2, 2, 0, 0, not 2, 1, 1, 0.</span></span></span></span></span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)"><br></span></span></span></span></span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)">As for the other point, STV (and other candidate-based PR methods) do not exclude parties; they just give voters the choice whether to vote for party candidates or any independents that might be standing. People are also just as likely to vote for parties based on the face, hairdo or personality of their leader, and party promises are also not enforceable. Party-list PR is more democratically limited than candidate-based PR.</span></span></span></span></span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)"><br></span></span></span></span></span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)">And to finish on a more hypothetical note, one solution that would remove large/small party bias and also make determining the result of the election much simpler would be to use a non-deterministic method. E.g. party A in my first example could win more or less than their proportional share, but would win 38% of the seats on average.</span></span></span></span></span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)"><br></span></span></span></span></span></div><div dir="ltr" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><span style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;color:rgb(0,0,0)">Toby</span></span></span></span></span></div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br></div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br></div>
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On Tuesday, 17 October 2023 at 22:09:41 BST, Michael Ossipoff <<a href="mailto:email9648742@gmail.com" target="_blank" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">email9648742@gmail.com</a>> wrote:
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</div></div></div><div><div id="m_-934711198426239354ydp202d185cyahoo_quoted_7625624729"><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:13px;color:rgb(38,40,42)"><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"></div></div></div></div><div><div id="m_-934711198426239354ydp202d185cyahoo_quoted_7625624729"><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:13px;color:rgb(38,40,42)"><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><div id="m_-934711198426239354ydp202d185cyiv9648205447" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">Though you’re certainly certainly welcome to your theories, sorry but your source is mistaken.<div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br></div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">If you’d do a little reading, you’d find that there’s a consensus that Webster/Sainte-Lague, while very nearly unbiased, & while the most unbiased of the allocation rules that are or have been used, is slightly biased in favor of larger parties (or states).</div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br></div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">I’ve told the unbiased allocation rule, & have supplied journal-paper references, & have, last month here, outlined its derivation.</div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br></div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">Thank you for reminding us that you prefer voting only for faces, hairdos, & personalities, with their vague, unreliable & unenforceable promises, instead of for policy platforms.</div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br></div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">Though about 2/3 of the world’s countries use PR, only a tiny fraction of them use STV. They nearly all use Party-List PR, a referendum on policy.</div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br></div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">Open-list PR includes voting for the people who will be seated by the platform-lists.</div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br></div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">Open-List PR is incomparably more easily, transparently & easily-verifiably counted than the cumbersome days-long STV-count.</div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br></div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">…which, even with computers, & even when used to elect only one winner, has a way of taking days.</div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br></div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">I don’t have time to keep replying to these posts. I’ll make us if the settings to re-route them from the inbox.</div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br></div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br></div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br></div><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br></div>
</div></div></div></div></div><div><div id="m_-934711198426239354ydp202d185cyahoo_quoted_7625624729"><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:13px;color:rgb(38,40,42)"><div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">----<br>Election-Methods mailing list - see <a href="https://electorama.com/em" rel="nofollow" target="_blank" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">https://electorama.com/em</a> for list info<br></div>
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