Ranking graphs through hitting times of Markov chains
Emilio De Santis · Random Structures and Algorithms · 2021
Abstract In the present paper we show that for any given digraph , that is, an oriented graph without self‐loops and 2‐cycles, one can construct a 1‐dependent Markov chain and n identically distributed hitting times T1, … , Tn on this chain such that the probability of the event Ti > Tj, for any i, j = 1, … , n, is larger than if and only if . This result is related to various paradoxes in probability theory, concerning in particular non‐transitive dice.