Honeybee swarms are faced with a challenging task: how to decide on a new home. The way in which such a decision is made is a prime example of decentralised decision-making: only a small subset of bees in the swarm are involved in the process, each acting upon local information. Previous work has used individual-based simulations to unravel how the behaviour of the bees engaged in decision-making results in the swarm collectively choosing the best possible nest site. Here we explore how the size of the swarm affects the accuracy of the decision-making process when the presence of a certain number of bees at one nest site (quorum) is used to end the deliberations. As soon as a quorum is reached bees involved in the decision-making process indicate to the other bees on the swarm that a decision has been made and the swarm will prepare for lift-off. Assuming a fixed quorum size, we show that the larger the swarm, the less likely it will be able to select the best nest site as the quorum will be reached early in the process. We also show that the speed of the decision-making process is reduced in small swarms especially when only sites of mediocre quality have been discovered. Our results therefore indicate that large swarms will often make sub-optimal decisions while small swarms will require more time to select a nest site but that small swarms select, on average, better quality sites.