Decisions reached through consensus are often more accurate, because they efficiently utilize the diverse information possessed by group members [1-3]. A trust in consensus decision making underlies many of our democratic political and judicial institutions , as well as the design of web tools such as Google, Wikipedia, and prediction markets [5, 6]. In theory, consensus for the option favored by the majority of group members will lead to improved decision-making accuracy as group size increases [2, 4]. Although group-living animals are known to utilize social information [7-10], little is known about whether or not decision accuracy increases with group size. In order to reach consensus, group members must be able to integrate the disparate information they possess. Positive feedback, resulting from copying others, can spread information quickly through the group, but it can also result in all individuals making the same, possibly incorrect, choice [8, 11, 12]. On the other hand, if individuals never copy each other, their decision making remains independent and they fail to benefit from information exchange . Here, we show how small groups of sticklebacks (Gasterosteus aculeatus) reach consensus when choosing which of two replica fish to follow. As group size increases, the fish make more accurate decisions, becoming better at discriminating subtle phenotypic differences of the replicas. A simple quorum rule proves sufficient to explain our observations, suggesting that animals can make accurate decisions without the need for complicated comparison of the information they possess. Furthermore, although submission to peers can lead to occasional cascades of incorrect decisions, these can be explained as a byproduct of what is usually accurate consensus decision making.