5 problems

Quantitative approximate polymorphism conjecture. The dependence between $\epsilon$ and $\delta$ in the Alekseev--Filmus theorem can be improved to polynomial or even linear.

Quantitative sumset conjecture. For every $\delta>0$,

Fix $\epsilon>0$. For each $m$, let $\delta$ be the probability lower bound supplied by the lemma for a neutral, independent-of-irrelevant-alternatives generalized social welfare f…

Let $m>3$ be the number of alternatives, and let the quantitative Gibbard–Satterthwaite theorem refer to a bound on the manipulation power of a social choice function in terms of i…

Let a generalized social welfare function (GSWF) on three alternatives satisfy the independent conditions of Arrow's theorem, and let $\epsilon>0$. Suppose that the probability of…