Many natural and artificial decision-making systems face decision problems where there is an inherent compromise between two or more objectives. One such common compromise is between the speed and accuracy of a decision. The ability to exploit the characteristics of a decision problem in order to vary between the extremes of making maximally rapid, or maximally accurate decisions, is a useful property of such systems. Colonies of the ant Temnothorax albipennis (formerly Leptothorax albipennis) are a paradigmatic decentralized decision-making system, and have been shown flexibly to compromise accuracy for speed when making decisions during house-hunting. During emigration, a colony must typically evaluate and choose between several possible alternative new nest sites of differing quality. In this paper, we examine this speed-accuracy trade-off through modelling, and conclude that noise and time-cost of assessing alternative choices are likely to be significant for T. albipennis. Noise and cost of such assessments are likely to mean that T. albipennis' decision-making mechanism is Pareto-optimal in one crucial regard; increasing the willingness of individuals to change their decisions cannot improve collective accuracy overall without impairing speed. We propose that a decentralized control algorithm based on this emigration behaviour may be derived for applications in engineering domains and specify the characteristics of the problems to which it should be suited, based on our new results.