There are many problems with your criteria table.
1. No deterministic non-delegative party agnostic proportional voting method that assigns each winner one equally weighted seat passes the favorite betrayal criteria because of free riding. While it may be theoretically possible for a proportional voting method of this type to pass FBC if you allow individual candidates to win more then one seat, there has yet to be a non deterministic non-delegative party agnostic proportional voting method that does so so if you want to assert that your method does do this you need to back it up with proof.
- I think we are using different definition of Favorite Betrayal. Free riding does not come into play. The criteria is about what a voter can do not what they might do. If you look at what is given on the Favorite betrayal criterion page that is consistent with what I was using. Ill take it out. --Dr. Edmonds (talk) 17:32, 10 February 2020 (UTC)
2. Different versions of proportional approval voting are the only non-deterministic non-delegative party agnostic approval ballot proportional voting methods that pass the consistency criterion. I've proved this on my own using hand-drawn ternary plots but I've also seen a an academic paper proving something similar to this (I'll have to find the paper). I might be wrong but this is also a big claim that needs to be proved to be accepted.
- I thought this followed from monotonicity and score ballots. Ill take it out. --Dr. Edmonds (talk) 17:32, 10 February 2020 (UTC)
3. Reversal symmetry: I'm not sure if this criteria continues to be desirable in multi winner elections, though if it is, you again have not provided any proof that your method passes it.
- Which criterion? Consistency? Maybe I was more thinking of Partitionable --Dr. Edmonds (talk) 17:32, 10 February 2020 (UTC)
- User:Dr. Edmonds I forgot to state the criteria I was talking about here - Reversal symmetry. Consistency on the other hand (where if you partition the electorate into multiple groups that all elect the same set of winners, the electorate overall should also elect that same set of winners) is (in my view) definitely a desirable criteria for both single and multi-winner elections. ParkerFriedland (talk) 01:23, 11 February 2020 (UTC)
- User:Dr. Edmonds Why I don't think reversal symmetry is desirable in multi-winner proportional methods: if 25% of voters approve D, 25% approve R, 25% approve I and D, and 25% approve I and R, then D and R should win (since all candidates are approved by 50% of voters so the total utility will be the same but if you elect D and R all voters will have approved of at-least one candidate). If you reverse all the ballots then D and R should still win because the votes are exactly the same. Reversal symmetry would instead require all the possible results to be tied with one another because if any one result won, reversing the results would force one of the other two to be the resulting outcome (or for the resulting outcome to be the other two possible results tied with each other) which is impossible because both the reversed and unreserved cases of these ballots are identical. Thus reversal symmetry is (in my view) clearly not desirable in multi-winner methods when proportionality is desired. ParkerFriedland (talk) 03:10, 11 February 2020 (UTC)
4. As you said yourself, vote unitary isn't a criteria but a class of voting methods. It's not a criteria so we shouldn't treat it as one.
- It is either a extra criteria on Monroe or it is its own thing. I am happy either way. Ill take it out. --Dr. Edmonds (talk) 17:32, 10 February 2020 (UTC)
I apologize if I sound a bit harsh. I've also recently criticized these unsubstantiated assertions for another method (https://electowiki.org/wiki/Talk:Distributed_Score_Voting).
Perhaps you should wait to post a criteria table until I finish my automatic criteria checker (I'm going to reuse a lot of the code for the ternary plots I'm making to do that as well). ParkerFriedland (talk) 06:01, 10 February 2020 (UTC)
- OK ParkerFriedland I will leave some of the criteria still in there. I will add to this as I compile work. I will add proofs when I get them. Please do not nuke the whole table. You can add citation needed if you think it is worth doubting. --Dr. Edmonds (talk) 17:32, 10 February 2020 (UTC)
FBC discussion[edit | edit source]
- - Strictly speaking, it hasn't been proven that free riding is an unavoidable fact of any proportional method, just that the Droop proportionality criterion implies some degree of vulnerability to Hylland free riding. There could be other proportionality measures (e.g. ones that only hold for dichotomous ballots like Approval, or ones based on divisor methods or other quotas than Droop) that would pass FBC -- we don't know. Thus, while the extrapolation you do in your first point might well be true, you don't currently have the proof to do it.
- Perhaps this is forced by both proportionality and the Pareto condition. Consider the fallowing election example where 50% of the voters lean Democratic and 50% lean Republican, however 100% of voters prefer the Independent to both the Democrat and the Republican. If all voters honestly approve of both their first and second choices, then the election result should be IR or ID since both results are strictly better then DR (if ID or IR is not elected, then the method fails the multi-winner version of the pareto condition: if at-least one voter expresses a preference between X and Y and every voter that does expresses a preference between X over Y prefers X, then if Y is elected, X must also be elected). Suppose that ID won (we can repeat the fallowing argument with the D's and R's swaped if R won): Then if 99.999...% of the R voters betrayed their favorite I (and at-least one R voter didn't betray I and voted IR) then proportionality would force R to win a seat, making the result IR or DR. However since IR pareto beats RD because of the one R voter that prefers I to D (all other voters don't express a preference between I and D). This result is strictly better from the perspective of the Republican voters, thus they got a better result by betraying their favorite. Since Edmond's method can be conducted with approval ballots, it must fail either pareto or favorite betrayal. So which is it User:Dr. Edmonds ? You said that your method passed both Pareto and FBC. ParkerFriedland (talk) 15:51, 10 February 2020 (UTC)
- - "Desirable" is a very subjective thing, and whether it's desirable for a method to pass or fail a criterion has no bearing on whether it actually does pass or fail that criterion. Since it's subjective, you should clarify what you mean by it, and back that up. If you mean e.g. "the method says it's proportional, but consistency (or whatever criterion) is incompatible with Droop proportionality and no other proportionality criterion has been given" then that's what you should say, because it says what is wrong.