Need help in understanding

what is W(x) or UI (w) in a.

What is the formula talking about in b.

Lemma 4.1: Nash equilibrium of plurality rule voting game Let G = (N,X,[u,;)geN) be a plurality rule voting game, let x be a Nash equilibrium of G, and let W(x) be the set of winning alternatives for x. a. If x;- is either a vote for an alternative outside W(x] or abstain, then u ;(w] is the same for all w e W(x] (i is indifferent between all winning alternatives). . If for some a e W[x] the action x;- is a vote for a, then u;(b] Z Ug[Z)/|W[)C)l foralleW[x)\\{a} zEW(x] and hence either Liz-(a) > u;(b] for all b E W(x)\\{a} (i prefers a to each of the other winning alternatives) or 11,151): Iii-(LU) for all w 6 W05] (1' is indifferent among all the winning alternatives)