Talk:Sequentially Spent Score: Difference between revisions
Is this proof valid?
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(Is this proof valid?) |
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: - 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. [[User:ParkerFriedland|ParkerFriedland]] ([[User talk: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.
: - That said, I'm inclined to think that every criterion compliance statement should either be accompanied by a proof or a reference to a source that contains a proof. It's easy to think that a method "obviously" passes some criterion when it doesn't. [[User:Kristomun|Kristomun]] ([[User talk:Kristomun|talk]]) 12:38, 10 February 2020 (UTC)
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