Social influence plays an important role in human behavior and decisions. The sources of influence can be generally divided into external, which are independent of social context, or as originating from peers, such as family and friends. An important question is how to disentangle the social contagion by peers from external influences. While a variety of experimental and observational studies provided insight into this problem, identifying the extent of social contagion based on large-scale observational data with an unknown network structure remains largely unexplored. By bridging the gap between the large-scale complex systems perspective of collective human dynamics and the detailed approach of the social sciences, we present a parsimonious model of social influence, and apply it to a central topic in political science -- elections and voting behavior. We provide an analytical expression of the county vote-share distribution in a two party system, which is in excellent agreement with 92 years of observed U.S. presidential election data. Analyzing the social influence topography over this period reveals an abrupt transition in the patterns of social contagion -- from low to high levels of social contagion. The results from our analysis reveal robust differences among regions of the United States in terms of their social influence index. In particular, we identify two regions of 'hot' and 'cold spots of social influence, each comprising states that are geographically close. These results suggest that social contagion effects are becoming more instrumental in shaping large scale collective political behavior, which is at the core of democratic societies.