Does the β-measure make empirical sense? A vignette experiment on humans’ judgment of social dominance

Dominance hierarchies play an important role in governing the social interactions of humans and other species of social animals. In a social group, dominance relations can be inferred from the directed network of matchups between actors. Methodologists have proposed different ways to measure social dominance in directed networks. One such measure, the “β-measure” (van den Brink and Gilles, 2000), emphasizes the quality of defeated opponents in a way that an actor is seen as being more dominant when s/he defeats opponents who are more rarely defeated. While insightful in theory, the validity of the measure in people's perception remains questionable, considering the cognitive complexity imposed by this measure, compared to a simpler measure that merely counts the number of defeated opponents. We conducted a vignette experiment with human subjects (professional athletes) to test their judgments of the dominance relation in a hypothetical tournament. Fitting our parametric model to peoples’ evaluations in the experiment, we found strong evidence in support of the β-measure: Although, in general, contestants who win more in the tournament are regarded as being more dominant, the contents of the winning records matter, such that those who beat more victorious opponents are further regarded as more dominant than those who defeat less victorious opponents. We also found a gender difference, in that men have a stronger propensity than women to adopt the β-measure when judging social dominance.