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 ST09 . We prove dichotomy theorems on the smoothed likelihood of ties under positional scoring rules, edge-order-based rules, and some multi-round score-based elimination rules, which include commonly studied voting rules such as plurality, Borda, veto, maximin, Copeland, ranked pairs, Schulze, STV, and Coombs as special cases. We also complement the theoretical results by experiments on synthetic data and real-world rank data on Preflib .