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<div dir="ltr" data-setdir="false">If a voter's lower ranks exclude candidates as much as higher ranks count in their favour, then I can't see how the result will end up looking anything like proportional representation, which I believe is still your goal. Take a simple case with two parties (or factions as parties don't need to be explicit), the larger of which has 2/3 of the support and the smaller 1/3. The candidates from the smaller party will be at the top on 1/3 of the ballots, and in a normal PR method would get about a third of the seats. But with this binomial count, they would be excluded and more besides by the 2/3 ranking them at the bottom.</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">Toby</div><div><br></div>
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On Friday, 5 April 2024 at 21:33:52 BST, Richard Lung <voting@ukscientists.com> wrote:
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<div><div dir="ltr"><br></div><div dir="ltr">Thank you, Filip,<br></div><div dir="ltr"><br></div><div dir="ltr">The first order Binomial STV is one election count and one exclusion <br></div><div dir="ltr">count, exactly like it (being symmetrical; an iteration). For the <br></div><div dir="ltr">election count I use Meek method of surplus transfers. The distinction, <br></div><div dir="ltr">of that computer count, over the traditional hand counts, is that <br></div><div dir="ltr">preferences, for an already elected candidate, with a quota, are still <br></div><div dir="ltr">recorded. Meek did that by updating the candidate keep value (the quota <br></div><div dir="ltr">divided by a candidates total transferable vote).<br></div><div dir="ltr"><br></div><div dir="ltr">Unlike Meek method, I do keep values for every candidate, losers as well <br></div><div dir="ltr">as winners. Candidates in deficit of a quota have keep values of more <br></div><div dir="ltr">than unity, signifying they are excluded. The exclusion count is run <br></div><div dir="ltr">exactly like the election count but with the preferences reversed, so a <br></div><div dir="ltr">quota now becomes an exclusion quota. The rule is simple: an election <br></div><div dir="ltr">count elects candidates reaching the quota. An exclusion count excludes <br></div><div dir="ltr">candidates reaching a quota. One voters preferences is another voters <br></div><div dir="ltr">unpreferences. There is no difference in principle between them.<br></div><div dir="ltr"><br></div><div dir="ltr">Binomial STV (symbolised as STV^; first order Binomial STV would be <br></div><div dir="ltr">STV^1. Any order bimomial STV would be STV^n. Preceding forms of STV, <br></div><div dir="ltr">including Meek method, are STV^0. The ballot paper looks just like any <br></div><div dir="ltr">Ranked Choice Vote. But the instructions are different. Every voting <br></div><div dir="ltr">method has voters instructions.<br></div><div dir="ltr"><br></div><div dir="ltr">The instructions are, in the case of your example: There are four seats <br></div><div dir="ltr">available and ten candidates to choose from. Your first four preferences <br></div><div dir="ltr">would more or less help to elect candidates. Your next 6 preferences (if <br></div><div dir="ltr">you choose to make them) would less or more help to exclude those <br></div><div dir="ltr">candidates. So, a tenth preference counts as much against a candidate, <br></div><div dir="ltr">as your first preference would count for a candidate. But you don't have <br></div><div dir="ltr">to give any order of preference. A carte blanche is equivalent to NOTA. <br></div><div dir="ltr">If a quota of abstentions is reached, one of the seats is left empty. <br></div><div dir="ltr">This election also gives voters the rational power to exclude candidates.<br></div><div dir="ltr"><br></div><div dir="ltr">Some candidates may be both popular and unpopular enough to gain both <br></div><div dir="ltr">election and exclusion quotas. They are both "alive" and "dead" to the <br></div><div dir="ltr">electorate. (A case of "Schrodingers candidate" according to Forest <br></div><div dir="ltr">Simmons.) Whether they are elected or excluded is determined by a <br></div><div dir="ltr">Quotient of the exclusion quota divided by the election quota. If the <br></div><div dir="ltr">ratio is one or less, they are elected; if not, excluded. (The Quotient <br></div><div dir="ltr">is the square of a geometric mean.)<br></div><div dir="ltr"><br></div><div dir="ltr">When inverted, the exclusion count is like a second-opinion election. <br></div><div dir="ltr">The geometric means of the candidates election keep values and inverse <br></div><div dir="ltr">exclusion keep value establish the over-all order of popularity of the <br></div><div dir="ltr">candidates (from lowest to highest over-all keep values.<br></div><div dir="ltr"><br></div><div dir="ltr">All the voters abstentions have to be counted, to establish whether they <br></div><div dir="ltr">care more to elect or exclude candidates. This also means there is no <br></div><div dir="ltr">reduction of the quota with abstentions, as in Meek method. Counting <br></div><div dir="ltr">abstentions observes the conservation of (preferential) information.<br></div><div dir="ltr"><br></div><div dir="ltr">I hired a programmer for first order Binomial STV, which, unlike the <br></div><div dir="ltr">higher orders, should be much simpler than Meek method, and simpler in <br></div><div dir="ltr">conception than the hand counts. However I have always supported them <br></div><div dir="ltr">all my adult life, and am now an old man.<br></div><div dir="ltr"><br></div><div dir="ltr">Kristofer found the GitHub link to the programmers coding, which he sent me:<br></div><div dir="ltr"><br></div><div dir="ltr"><a href="https://github.com/Esrot-Clients/STV_CSV/tree/master" rel="nofollow" target="_blank">https://github.com/Esrot-Clients/STV_CSV/tree/master</a><br></div><div dir="ltr"><br></div><div dir="ltr">The programmer also sent me a "frontend" for the use of voters:<br></div><div dir="ltr"><br></div><div dir="ltr"><a href="https://votingstv.cloud/" rel="nofollow" target="_blank">https://votingstv.cloud/</a><br></div><div dir="ltr"><br></div><div dir="ltr">And he sent me two manuals, which I cannot attach, in case useful to a <br></div><div dir="ltr">technical person, unlike myself, because the moderator doen't allow <br></div><div dir="ltr">messages over a certain size. I think it was a different reason last time.<br></div><div dir="ltr"><br></div><div dir="ltr">Regards,<br></div><div dir="ltr"><br></div><div dir="ltr">Richard Lung.<br></div><div dir="ltr"><br></div><div dir="ltr">----<br></div><div dir="ltr">Election-Methods mailing list - see <a href="https://electorama.com/em" rel="nofollow" target="_blank">https://electorama.com/em</a> for list info<br></div></div>
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