Newcomers to a social network show preferential attachment, a tendency to befriend those with many friends. Here, we show that preferential attachment is equivalent to a form of ‘probability matching’ commonly found in studies of decision-making. This equivalence, whereby newcomers probability match to a social signal akin to popularity, marries network science to the study of decision-making and raises new questions about how individual psychology impacts the social structure of groups. We asked people to view a visualization of a social network and to select group members whom they would like to meet and befriend. People varied in how strongly they weighed popularity and this was mildly correlated with aspects of their personality. Individual differences in preferential attachment affect the structure and connectivity of the network that emerges.