A linear order L on a set X is a linear extension of partial order P on X if PℝL. ℒ(P) denotes the set of all linear extensions of P, and ℒ(x,y) denotes the subset of ℒ(P) for which xLiy if L∈ℒ(x,y). A linear extension majority (LEM) relation M is defined by xMy if ’ℝℒ(x,y)∈’ℝℒ(y,x). A LEM cycle exists on P if xMy, yMz and zMx for some x,y,z∈X. Similarly, M' on X is defined by xM'y if ’ℝℒ(x,y)∈’ℝℒ(y,x) for xℝy. A LEM quasi-cycle exists if xM'y,yM'z and zM'x for some x,y,z∈X and the equality part of the M' definition holds for exactly one of the pairs in the triple. A Monte-Carlo simulation study is conducted to obtain estimates of the relative frequency with which LEM cycles and LEM quasi-cycles are observed.
