Cooperative game theory methods for determining text complexity

We propose a method for estimating the complexity of texts based on the methods of cooperative game theory. The players in this game are the lengths of words in the text. The game itself is represented as a voting game in which the value of a player is determined by the number of coalitions in which the player is key. The ranks of the players are formed by computing the Shepley — Schubik value or the Banzaf index in a voting game with a given voting threshold. Thus, a vector of Shepley — Schubik or Banzaf values is assigned to each text. After that, the vector space is used to rank the texts in terms of complexity based on the expert evaluations obtained in this domain.