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<div dir="ltr" data-setdir="false">I think Webster/<span>Sainte-Laguë is generally accepted as the most mathematically accurate method of apportionment / party list PR, and any large party bias comes from assumptions about the distribution, 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" data-setdir="false"><span><br></span></div><div dir="ltr" data-setdir="false"><span>A: 38</span></div><div dir="ltr" data-setdir="false"><span>B: 38</span></div><div dir="ltr" data-setdir="false"><span>C: 12</span></div><div dir="ltr" data-setdir="false"><span>D: 12</span></div><div dir="ltr" data-setdir="false"><span><br></span></div><div dir="ltr" data-setdir="false"><span>Under <span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">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" data-setdir="false"><span><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><br></span></span></span></div><div dir="ltr" data-setdir="false"><span><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">A: 37</span></span></span></div><div dir="ltr" data-setdir="false"><span><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">B: 37</span></span></span></div><div dir="ltr" data-setdir="false"><span><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">C: 13</span></span></span></div><div dir="ltr" data-setdir="false"><span><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">D: 13</span></span></span></div><div dir="ltr" data-setdir="false"><span><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><br></span></span></span></div><div dir="ltr" data-setdir="false"><span><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">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. However, this doesn't change the fact that for a given election, <span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">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 dir="ltr" data-setdir="false"><span><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><br></span></span></span></span></span></div><div dir="ltr" data-setdir="false"><span><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">Changing the divisor to shift the bias towards smaller parties may seem like a good solution, but as well as coming at the cost of proportional accuracy, it works under the assumption that large parties form an entity 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" data-setdir="false"><span><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><br></span></span></span></span></span></div><div dir="ltr" data-setdir="false"><span><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">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" data-setdir="false"><span><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><br></span></span></span></span></span></div><div dir="ltr" data-setdir="false"><span><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">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" data-setdir="false"><span><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><br></span></span></span></span></span></div><div dir="ltr" data-setdir="false"><span><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">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" data-setdir="false"><span><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><br></span></span></span></span></span></div><div dir="ltr" data-setdir="false"><span><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif;">Toby</span></span></span></span></span></div><div><br></div><div><br></div>
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On Tuesday, 17 October 2023 at 22:09:41 BST, Michael Ossipoff <email9648742@gmail.com> wrote:
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<div><div id="ydp202d185cyiv9648205447">Though you’re certainly certainly welcome to your theories, sorry but your source is mistaken.<div><br></div><div>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><br></div><div>I’ve told the unbiased allocation rule, & have supplied journal-paper references, & have, last month here, outlined its derivation.</div><div><br></div><div>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><br></div><div>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><br></div><div>Open-list PR includes voting for the people who will be seated by the platform-lists.</div><div><br></div><div>Open-List PR is incomparably more easily, transparently & easily-verifiably counted than the cumbersome days-long STV-count.</div><div><br></div><div>…which, even with computers, & even when used to elect only one winner, has a way of taking days.</div><div><br></div><div>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><br></div><div><br></div><div><br></div><div><br></div>
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