User:Lucasvb/Uncertainty in cardinal voting vs. ranked voting: Difference between revisions

Now, the assumptions here may seem strong, like normal distributions, overlaps and identical voters, but one can make an argument from the Central Limit Theorem using the means of voters opinions. Basically, if you got utilities at random from voters of each faction, and took the mean of many such set of samples, their means would likely follow a normal distribution, and this would fit the above analysis well. But that ''would'' involve aggregating cardinal utilities. However, you could do the same analysis under the <math>p(A>B) + p(B>A) = 1</math> ballot distribution alone, instead of <math>u_A(x)</math> and <math>u_B(x)</math>, which wouldn't have this problem.