Many evolutionary game theory papers have obtained their results when the bounded rationality which creates change vanishes. In our first chapter we consider whether such results are actually a good reflection of a population whose bounded rationality is small yet persistent. Our model consists of a two type population with three stable equilibria. Firstly we find that results from the standard vanishing noise approach can be very different from those obtained when noise is small but constant. Secondly when the results differ the small and persistent noise approach selects an equilibrium with a co-existence of conventions. Our second chapter generalises the model of our first chapter to a population of many player types and several stable equilibria. Firstly we produce the characteristics of the long run equilibria under vanishing noise analysis. Secondly we find that the introduction of a small neutral group into a divided society can produce a welfare improving switch in the long run equilibrium towards social co-ordination. Our third chapter combines the model of the second chapter with the message of the first. We show numerically that the long run location of a heterogenous population with extremely low levels of bounded rationality can be completely different to the equilibria selected through vanishing noise analysis. We also show that such an event is not a rare occurrence and find that over a third of populations are misrepresented by stochastic stability. Our final chapter conducts a review of the literature on social threshold models. We give a thorough description of each paper and discuss the main assumptions that drive the key results.