Pre-transitive balance mechanisms for signed networks

The fundamental empirical structural balance hypothesis claims that human s igned networks tend towards balance over time. Balance theorists assume tha t there is a balance theoretic mechanism whose cumulative effect drives the evolution of signed social structures towards balance. In previous work, w e used a line index of imbalance to measure the imbalance of a network thro ugh time. Consistent with balance theory, we found a steady movement toward s balance in the well known "Newcomb data". The balance mechanisms were, at best, implicit in that earlier analysis and our use of the line index of i mbalance meant that we ignored triples. Here, we consider triples with the simple hypothesis that balanced triples exist at all times and, that throug h time, the balanced triples become more frequent while the imbalanced trip les become less frequent. We examine pre-transitive balance conditions defi ned in terms of the (i --> j, j --> k) ties and count the frequencies of th e completion tie (i --> k) for each of the combinations of tie signs in the pre-transitive condition. The basic structural balance theoretic hypothese s ate supported - but only partially. Worse, from a balance theoretic viewp oint, there are triples For which the fundamental structural balance hypoth esis is contradicted. We construct three substantive arguments to account f or the exceptions and end with a plea for the collection of much more appro priate data in order to disentangle multiple mechanisms.