For group-living animals to remain cohesive they must agree on where to travel. Theoretical models predict shared group decisions should be favoured, and a number of empirical examples support this. However, the behavioural mechanisms that underpin shared decision-making are not fully understood. Groups may achieve consensus of direction by active communication of individual preferences (i.e. voting), or by responding to each other's orientation and movement (i.e. copying). For example, African buffalo (Syncerus caffer) are reported to use body orientation to vote and indicate their preferred direction to achieve a consensus on travel direction, while golden shiners (Notemigonus crysoleucas) achieve consensus of direction by responding to the movement cues of their neighbours. Here, we present a conceptual model (supported by agent-based simulations) that allows us to distinguish patterns of motion that represent voting or copying. We test our model predictions using high-resolution GPS and magnetometer data collected from a herd of free-ranging goats (Capra aegagrus hircus) in the Namib Desert, Namibia. We find that decisions concerning travel direction were more consistent with individuals copying one another's motion and find no evidence to support the use of voting with body orientation. Our findings highlight the role of simple behavioural rules for collective decision-making by animal groups.