Before revision:  We give an asymptotic answer to the open question for a wide range of commonly-studied voting rules under a model that is much more general and realistic than i.i.d. models including IC--the smoothed social choice framework Xia20 , which was inspired by the celebrated smoothed complexity analysis ST09 . We prove dichotomy theorems on the smoothed likelihood of ties under a large class of voting rules .
After revision:  We give an asymptotic answer to the open question for a wide range of commonly-studied voting rules under a model that is much more general and realistic than i.i.d. models including IC--the smoothed social choice framework Xia20 , which was inspired by the celebrated smoothed complexity analysis by Spielman and Teng . We prove dichotomy theorems on the smoothed likelihood of ties under a large class of voting rules .