Hey, great article, great topic! You missed one very interesting angle for the problem (speaking of games), namely Voting theory, which is an important part of

Hey, great article, great topic! You missed one very interesting angle for the problem (speaking of games), namely Voting theory, which is an important part of game theory! In voting theory, there is a concept called Kemeny ranking (Kemeny–Young method), which I believe is exactly what you are looking for. It is of course an NP-hard problem, but that shouldn't scare you away. In a voting setting, each movie would "vote" for a ranking of, say, the electric unit; i.e., the gaffer comes before the other people. When you have many movies, you have many votes that you want to combine in order to rank all the candidates, while minimizing inconsistencies. A seminal paper was published in the journal of the ACM, Aggregating inconsistent information: Ranking and clustering by Ailon, Charikar, and Newman. An important insight is that your directed graph is actually what we call a tournament; for every two vertices a and b, there is an edge either from a to b, or from b to a. In that case, you want to solve a well known and widely studied problem, namely Feedback Arc Set in Tournaments (FAST). Check out the paper in ISAAC by Karpinski and Schudy, Faster algorithms for feedback arc set tournament, Kemeny rank aggregation and betweenness tournament (it's on arxiv).