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<div>Hey Forest,<br><br>Thanks so much for the feedback and the kind welcome! That certainly is a lot to digest, but I did find your definition of it really helpful. I've been kinda busy recently, but I'd definitely love to take a crack at coding/implementing and visualizing the system at some point in the near future!<br><br>Would a system that uses the implicit fractional approval score really be equal to a system that takes the first and last place votes for each candidate? </div><div dir="auto"><br></div><div dir="auto">-Culi</div><div><br></div><div><br></div><div>Jan 23, 2022, 11:29 AM by forest.simmons21@gmail.com:<br></div><blockquote class="tutanota_quote" style="border-left: 1px solid #93A3B8; padding-left: 10px; margin-left: 5px;"><div dir="auto"><div>Culi,<br></div><div dir="auto"><br></div><div dir="auto">Great site!<br></div><div dir="auto"><br></div><div dir="auto">And great first EM post.<br></div><div dir="auto"><br></div><div dir="auto">Your "first minus last" score for each candidate is equivalent to what some of us call the implicit fractional approval score, which is your score plus the total number of ballots, all divided by two. <br></div><div dir="auto"><br></div><div dir="auto">Yours is simpler for people that are comfortable with integer arithmetic. The advantage of ours is that it is just the number of Top votes plus half of the number of non-Bottom votes ... no possibility of getting negative scores.<br></div><div dir="auto"><br></div><div dir="auto">Now here is the best (IMHO) use of your suggested scores:<br></div><div dir="auto"><br></div><div dir="auto">While more than one candidate remains, among these, eliminate the highest score candidate that does not pairwise defeat the one with the lowest score.<br></div><div dir="auto"><br></div><div dir="auto">Unlike the elimination method you suggested, this method, "Fractional Implicit Approval Chain Climbing," FIACC, is monotonic, clone free, and Banks efficient.<br></div><div dir="auto"><br></div><div dir="auto">As long as equal rankings and truncations are allowed, we can confidently (but humbly) affirm that FIACC is the best known "Universal Domain" method with these three properties.<br></div><div dir="auto"><br></div><div dir="auto">Universal Domain means RCV style ballots only. <br></div><div dir="auto"><br></div><div dir="auto">A Banks candidate is one that stands at the head of a maximal chain of candidates ordered by pairwise victory. <br></div><div dir="auto"><br></div><div dir="auto">Every Banks candidate is also a Landau candidate, which means it has a beatpath of two or fewer steps to any other candidate.<br></div><div dir="auto"><br></div><div dir="auto">If a method is not Landau efficient, then (embarrassingly) sometimes it will elect a candidate that is covered by some other candidate. This other candidate has a valid complaint or Pareto dominance over the winner with respect to pairwise wins, ties, and losses:<br></div><div dir="auto"><br></div><div dir="auto">Candidate X covers Y iff it not only defeats Y, but also defeats every candidate defeated by Y. <br></div><div dir="auto"><br></div><div dir="auto">Of the well known methods, only Kemeny-Young and Copeland are Landau efficient. But they both lack monotonicity, among other failings in comparison with our simple FIACC method.<br></div><div dir="auto"><br></div><div dir="auto">In particular, unlike Copeland, FIACC is highly resistant to Chicken and Burial attacks.<br></div><div dir="auto"><br></div><div dir="auto">And unlike K-Y, FIACC is computationally tractable, while K-Y is non-polynomially hard.<br></div><div dir="auto"><br></div><div dir="auto">I know that's a lot to digest ... but you can do it one bite at a time with patience.<br></div><div dir="auto"><br></div><div dir="auto">The method is simple ... and the three basic properties (monotonicity, clone independence, and Condorcet efficiency) are easy to understamd.<br></div><div dir="auto"><br></div><div dir="auto">It's only the Banks and Landau efficiency (that distiguish it from Ranked Pairs, Schulze, River, etc) that are a challenge to fully appreciate.<br></div><div dir="auto"><br></div><div dir="auto">To emphasize the simplicity of the method itself, I repeat the complete definition here for reference:<br></div><div dir="auto"><br></div><div dir="auto"><span style=""><span class="font" style="font-family:sans-serif">While more than one candidate remains, among these, eliminate the highest score candidate that does not pairwise defeat the one with the lowest score.</span></span><br></div><div dir="auto"><span style=""><span class="font" style="font-family:sans-serif"></span></span><br></div><div dir="auto"><span class="font" style="font-family:sans-serif">Assuming you know what "scores" we're talking about and what "pairwise defeat" means, that procedure completely and unambiguously defines the method.</span><br></div><div dir="auto"><span class="font" style="font-family:sans-serif"></span><br></div><div dir="auto"><span class="font" style="font-family:sans-serif">Do you know anybody who can do the same for their favorite complete method with the same unambiguous precision in fewer than twenty-five words?</span><br></div><div dir="auto"><span class="font" style="font-family:sans-serif"></span><br></div><div dir="auto"><span class="font" style="font-family:sans-serif">[Copeland is not by itself a complete method, just like Condorcet is not a complete method ... they require "completions" to resolve ubiquitous ties and cycles.]</span><br></div><div dir="auto"><span class="font" style="font-family:sans-serif"></span><br></div><div dir="auto"><span class="font" style="font-family:sans-serif">Once again, welcome, and thanks for your great first post to the EM list, and invitation to your site.</span><br></div><div dir="auto"><span class="font" style="font-family:sans-serif"></span><br></div><div dir="auto"><span class="font" style="font-family:sans-serif">-Forest</span><br></div><div dir="auto"><span class="font" style="font-family:sans-serif"></span><br></div><div dir="auto"><span class="font" style="font-family:sans-serif">Forest</span><br></div><div dir="auto"><span class="font" style="font-family:sans-serif"></span><br></div><div dir="auto"><br></div><div dir="auto"><div><br></div><div dir="auto" class=""><div class="" dir="ltr">El sáb., 22 de ene. de 2022 12:03 p. m., <<a href="mailto:culitif@tuta.io" rel="noopener noreferrer" target="_blank">culitif@tuta.io</a>> escribió:<br></div><blockquote style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex" class=""><div><div dir="auto">Hello all,<br></div><div dir="auto"><br></div><div dir="auto"><div>I'm Culi, I'm a recent subscriber. Took a social choice theory in college and have wanted to make visualizations for electoral methods ever since. I recently finally got some time to create something like that! <br></div><div><br></div><div>It's basically a tool that compares the outcome of an election in RCV, Coomb's RCV, and a third method which I have yet to find out the name of (I'd appreciate help with it). It's all explained more on the site, but basically it tries to take into account both first-choice and last-choice picks into deciding which candidate to drop every round. <br></div><div><br></div><div>I'd love to someday expand the tool to show how a number of other single-winner electoral methods would result in the same election. I built a similar tool a while ago in Python but never got to deploy it. I only got so far as to simulate the election in FPTP, RCV, Borda Count, Coombs, Copeland, Quadratic Voting, and Contingent Vote. <br></div><div><br></div><div>Now that I have web development skills I'd love to rebuild it and make it into an educational tool to let people compare different voting systems. I'd also love some day to code out some of the electoral methods discussed here on this mailing list! <br></div><div><br></div><div>Anyways, here's what the site currently looks like (I'll have a better url later I promise). I'd love any feedback and suggestions for the name of the third voting method:<br></div><div><br></div><div><a rel="noopener noreferrer" target="_blank" href="https://elegant-shaw-2cb49a.netlify.app/votevote">https://elegant-shaw-2cb49a.netlify.app/votevote</a><br></div><div><br></div><div>Best,<br></div><div>Culi.<br></div></div></div><div>----<br></div><div> Election-Methods mailing list - see <a target="_blank" rel="noopener noreferrer" href="https://electorama.com/em">https://electorama.com/em</a> for list info<br></div></blockquote></div></div></div></blockquote><div dir="auto"><br></div> </body>
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