Therefore, all other honest players Pk will accept P ’s gradecast Sample Clauses

Therefore, all other honest players Pk will accept P ’s gradecast with confidence at least 1, which means that P ∈ viewk(C) for all honest Pk. ⊇ A few more general facts about the views are worth noting. First of all, note that viewj(Ck) viewj(Ck) for all honest players Pj and committees Ck – this follows trivially from the definition of a view (and an extended view). Secondly, it is quite possible that for two different honest players Pj and Pj' , and committee Ck, viewj(Ck) and viewj' (Ck) are different. This is because the faulty players may present conflicting values to two different honest players (An analogous statement is true for view’s of two honest players). Since the good players choose their committee uniformly at random, the expected number of good players that chose each committee is ( 3 + ϵ)a log n. A simple application of Xxxxxxxx bound followed by a union bound shows that, with high probability, every committee has at least 3 a log n good players.