Putting the group back into unions: A social psychological contribution to understanding union support

Industrial relations research that attempts to grapple with individuals' union-related sentiments and activities often draws on one of two traditions of psychological research—the individual-level factors tradition (for example, personality and attitude-behaviour relations) and the social context tradition (for example, frustration-aggression and relative deprivation). This paper provides an overview of research conducted from within these traditions to explain union-related phenomena and identifies some of the limitations that arise as a consequence of a shared tendency to treat people in an atomistic fashion. The paper argues for an understanding of the psychological processes that underpin group-based action. To this end, it elaborates a theoretical framework based on social identity theory and self-categorisation theory that would allow us to examine the dynamic interplay between the individual, their cognitions and their environment. The paper concludes with a brief discussion of a specific case of union mobilisation, to indicate how this theoretical framework might aid empirical analysis.

Pseudo-randomness of round-off errors in discretized linear maps on the plane

We analyze the sequences of round-off errors of the orbits of a discretized planar rotation, from a probabilistic angle. It was shown [Bosio & Vivaldi, 2000] that for a dense set of parameters, the discretized map can be embedded into an expanding p-adic dynamical system, which serves as a source of deterministic randomness. For each parameter value, these systems can generate infinitely many distinct pseudo-random sequences over a finite alphabet, whose average period is conjectured to grow exponentially with the bit-length of the initial condition (the seed). We study some properties of these symbolic sequences, deriving a central limit theorem for the deviations between round-off and exact orbits, and obtain bounds concerning repetitions of words. We also explore some asymptotic problems computationally, verifying, among other things, that the occurrence of words of a given length is consistent with that of an abstract Bernoulli sequence.