In despotically driven animal societies, one or a few individuals tend to have a disproportionate influence on group decision-making and actions. However, global communication allows each group member to assess the relative strength of preferences for different options amongst their group-mates. Here, we investigate collective decisions by free-ranging African wild dog packs in Botswana. African wild dogs exhibit dominant-directed group living and take part in stereotyped social rallies: high energy greeting ceremonies that occur before collective movements. Not all rallies result in collective movements, for reasons that are not well understood. We show that the probability of rally success (i.e. group departure) is predicted by a minimum number of audible rapid nasal exhalations (‘sneezes’), within the rally. Moreover, the number of sneezes needed for the group to depart (i.e. the quorum) was reduced whenever dominant individuals initiated rallies, suggesting that dominant participation increases the likelihood of a rally’s success, but is not a prerequisite. As such, the ‘will of the group’ may override dominant preferences when the consensus of subordinates is sufficiently great. Our findings illustrate how specific behavioural mechanisms (here, sneezing) allow for negotiation (in effect, voting) that shapes decision-making in a wild, socially complex animal society.