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More examples, both here and elsewhere, would be helpful. E.g. showing that in a 2-winner contest, out of 100 voters, 34 supporters of only candidate C could get represented by C, with the other voters choosing between A and B. Comparing different PR schemes with the same scenarios would be instructional. ★NealMcB★ ( talk) 14:07, 10 March 2017 (UTC) reply

In particular, an example in which the ballots demonstrate the ability to vote for more than the number of winners, and/or in which PAV winners are different than block plurality, would be good. ★NealMcB★ ( talk) 17:40, 17 September 2018 (UTC) reply

Sounds great to me! Closed Limelike Curves ( talk) 04:04, 16 February 2024 (UTC) reply

I propose that Sequential proportional approval voting be merged into Proportional approval voting. The two articles describe the same election method. They describe the method using different names, but the logic itself is mathematically identical. Dhalsim2 ( talk) 23:48, 29 June 2018 (UTC) reply

Thank you for noticing the similarity, but the articles should not be merged. As the references in both articles clearly show, these are two different topics. Someone incorrectly added the sentence to Proportional approval voting saying the particular method was invented by Thiele and rediscovered by Simmons. The references do not support this. The table on page 122 of Kilgore's 2010 paper shows the two methods giving different results. StarryGrandma ( talk) 00:59, 1 July 2018 (UTC) reply

Thiele invented both methods. Sources: 1. (here the method is called Thiele's optimization method) http://www2.math.uu.se/~svante/papers/sjV9.pdf, 2. Math PhD Warren D. Smith acknowledges Warren D. Smith of discovering a special case of his harmonic method for when approval ballots are used. That special case is PAV https://rangevoting.org/QualityMulti.html#acknow — Preceding unsigned comment added by ParkerFriedland ( talk • contribs) 06:45, 6 June 2019 (UTC) reply

I read Kilgore's paper in its entirety and worked through each of his examples by hand and by computer. I do now acknowledge that PAV and SPAV can yield different results. I was previously confused due to the example in the Wikipedia PAV article. The example had wrong logic in it. I have now corrected the example. Though PAV and SPAV do occasionally yield different result due to ties in small sample sets, most of the time, it empirically seems that the results are the same, so I do think that there could be a legitimate argument to merge the two articles, but I acknowledge that due to the possibility of a difference, there is certainly less importance to a merge. Dhalsim2 ( talk) 01:52, 12 July 2018 (UTC) reply

I'm glad we agree they are different, and I think should not be merged. I'd love to see more research on the question of when the results are the same vs different, but that should be published somewhere outside of Wikipedia. ★NealMcB★ ( talk) 03:36, 21 January 2019 (UTC) reply

The two don't agree, regardless of ties. SPAV is a greedy approximation algorithm for PAV that elects candidates one at a time. The greedy strategy elects a potentially very different slate of candidates from PAV.

That being said, I think the two systems are procedurally similar enough to be described in one article. SPAV is a strategy for calculating PAV, which suggests the two articles should be merged, probably with a section that explains SPAV. Otherwise, we'd be forced to spin off a dozen different articles, one for every integer linear programming algorithm you could use to approximate PAV.

As precedent, Kemeny–Young doesn't have separate articles describing every possible approximation method. Closed Limelike Curves ( talk) 04:03, 16 February 2024 (UTC) reply