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 Jan 22 awarded Notable Question Oct 29 awarded Commentator Oct 29 comment How to do a statistically sound ranking using varying numbers of likes/dislikes? True, hence I was rather aiming for the Bayesian approach of the accepted answer. Oct 29 comment How to do a statistically sound ranking using varying numbers of likes/dislikes? Actually, I found my question answered (for the most part) at [this CrossValidated question][1]. [1]: stats.stackexchange.com/questions/15979/… Oct 26 comment How to do a statistically sound ranking using varying numbers of likes/dislikes? Also, thinking about it, wouldn't most (simple) models of a user's voting behavior pretty much boil down to a simple "likes to dislikes ratio" test? E.g., model $\Pr[like\ x_i]=\delta_i$, $\Pr[dislike\ x_i]=\epsilon_i$, and $\Pr[ignore\ x_i]=1-\delta_i-\epsilon_i$ with like hypothesis $H_0: \delta_i>\epsilon_i$ and dislike hypothesis $H_1: \epsilon_i>\delta_i$? Oct 26 comment How to do a statistically sound ranking using varying numbers of likes/dislikes? Thanks for your answer. If I understand correctly you propose a likelihood test to decide whether a particular item is generally liked ($H_0$) or disliked ($H_1$). I agree that this should be possible. However, I do not see how this helps to rank all items accordingly. Do you suggest ranking by likelihood ratios? If so, can you point me to some literature that discusses why such an approach avoids the fallacies given in the opening post? Oct 25 comment How to do a statistically sound ranking using varying numbers of likes/dislikes? A possible answer would be highly appreciated. ;) Oct 25 comment How to do a statistically sound ranking using varying numbers of likes/dislikes? @Seyhmus Güngören: Do you mind to elaborate? Oct 25 asked How to do a statistically sound ranking using varying numbers of likes/dislikes? Jul 28 awarded Yearling May 30 awarded Popular Question Mar 21 awarded Nice Answer Oct 8 awarded Enlightened Oct 8 awarded Nice Answer Oct 6 awarded Taxonomist Jul 29 awarded Yearling Aug 27 comment Positive definite Hessians from strictly convex functions A proof of Conjecture 2 in dimension d=1: Assume such an open interval exists, that is, there is a (closed, non-empty) interval $[a,b]$ such that $f''(t)=0$ for all $t \in [a,b]$. By Taylor expansion, we find $f(b) = f(a) + f'(a)\cdot(b-a)$. Let $c=(a+b)/2$. Again using Taylor expansion, we find $f(c) = f(a) + f'(a)\cdot(c-a) = f(a) + f'(a)\cdot(b-a)/2$. Hence, $(f(a)+f(b))/2 = f(c)$, which contradicts the strict convexity of $f$. Aug 27 comment Positive definite Hessians from strictly convex functions Thanks, this is a very convincing counter example. (I wasn't even aware that there are nowhere dense sets of positive Lebesgue measure.) I took the liberty of updating my question. Aug 27 revised Positive definite Hessians from strictly convex functions added 23 characters in body; edited tags Aug 26 awarded Student