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<div dir="ltr" data-setdir="false">I have another couple of questions. You said that the zero points are what you'd get by picking candidates at random. But does this not depend on how the candidates are distributed? Are they just uniformly spread across the voting space? How did repeatedly electing the plurality loser end up so proportional? Also would it be possible to post the result as the raw numbers in addition to the graph?</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">Thanks</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 Tuesday 10 September 2024 at 21:32:33 BST, Kristofer Munsterhjelm <km-elmet@munsterhjelm.no> wrote:
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<div><div dir="ltr">On 2024-09-10 14:21, Toby Pereira wrote:<br clear="none">> Kristofer<br clear="none">> <br clear="none">> This is very interesting. Thank you for doing this analysis.<br clear="none"><br clear="none">That's good to hear :-) Often I feel like nothing happens when I post. <br clear="none">It's good to know that people appreciate my posts.<br clear="none"><br clear="none">> Random ballots, as I understand your implementation, I think would<br clear="none">> not be strategyproof. If there are c candidates to be elected, then<br clear="none">> every voter ranks their top c. And then you sequentially pick c<br clear="none">> ballots at random, electing the top-ranked unelected candidate on<br clear="none">> each ballot. Is that correct? In that case, I think if a voter is<br clear="none">> fairly confident that their favourite candidate will be elected<br clear="none">> anyway, it makes sense for them to put other candidates above them<br clear="none">> that might not get elected anyway. If my second favourite candidate<br clear="none">> is not very popular among other voters, and my favourite is, I am<br clear="none">> likely to put my second favourite top.<br clear="none"><br clear="none">That's a good point. I guess PR methods almost always come with an <br clear="none">incentive for vote management. It would be interesting to find out just <br clear="none">how hard the implication is: how PR you can make a method and not have <br clear="none">vote management, or how proportional you can make a strategyproof method.<br clear="none"><br clear="none">> Another lottery method you might want to consider is COWPEA Lottery. <br clear="none">> This uses approval ballots. For each candidate to be elected, ballots <br clear="none">> are selected at random to act as tie-breaks. At first, every candidate <br clear="none">> is in the running. Pick a ballot, and then only those approved on that <br clear="none">> ballot are still in the running and so on, until one is left. If a <br clear="none">> ballot reduces the number of candidates in the running to zero, it is <br clear="none">> ignored. This method can also be used with the KP-transformation for a <br clear="none">> score voting variant (like the relationship of PAV to harmonic voting).<br clear="none"><br clear="none">I haven't run any approval type methods yet because that depends on just <br clear="none">how the voters render their preferences into Approval. But KPT should be <br clear="none">doable. I'd also like to implement the Phragmen family and Monroe, and <br clear="none">some ideas I have for a proportional (sequential) adjustable PR method <br clear="none">that reduces to single-winner Condorcet.<br clear="none"><br clear="none">Other methods that would be nice to implement are CPO-STV, Forest's <br clear="none">CFPRM ("Condorcet-flavored PR method"), and CIVS' PR method.<br clear="none"><br clear="none">So I have no difficulties finding out things that I could do. It's doing <br clear="none">them that's the hard part :-)<div class="ydp90c1ef0cyqt0700484228" id="ydp90c1ef0cyqtfd56869"><br clear="none"><br clear="none">-km<br clear="none"></div></div></div>
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