A Game-Theoretic Perspective on the Notion of Argument Strength in Abstract Argumentation

This paper is concerned with the problem of quantifying the strength of arguments in controversial debates, which we model as abstract argumentation frameworks [Dung, 1995]. Standard approaches to abstract argumentation provide only a qualitative account of the status of arguments, whereas numerical measures of argument strength might provide a more precise evaluation of their individual status. Intuitively, the strength of an argument in a debate essentially depends on how a proponent of that argument would defend himself against the criticisms of someone opposed to the argument. Since there can be many ways of defending and attacking an opinion, we essentially conceive argument strength as an equilibrium resulting from the interactions taking place between the opinions that a proponent and an opponent of the argument could a priori embrace. More formally, we define argument strength in terms of the value of a repeated two-person zero-sum strategic game with imperfect information. Then, using the game-theoretic properties of such games and notably the von Neumann minimax theorem [Neumann, 1928], we establish and illustrate the main properties of this new argument strength measure.