Online social network platforms have been, since their rise to prominence, considered as relevant gateways to study individual behaviors. One of those realms is politics, from massive movements and demonstrations to customary events like general elections or referendums in democratic countries. In this paper, we are interested in the behavior of politicians in the United Kingdom European Union membership referendum of June 2016, colloquially known as the “Brexit referendum”. In this case study we ask how, during the final weeks of the campaign, four political actors (Jeremy Corbyn, David Cameron, Boris Johnson, and Nigel Farage) used Twitter through their official accounts regarding this popular consultation and how that action was received by their followers. To be more precise, we ask if they predominantly appealed to emotions or to rational arguments, and what was, for each of them, the impact of their tweets. Our leading hypotheses were that: 1) the appeal to emotions prevailed over rationality, 1a) particularly in the case of “brexiters”; and 2) that appeal was more effective, 2a) and again that effectiveness was more significant for those that campaigned for “Leave”. We conclude that, while the first hypothesis (and its subsidiary) was not confirmed, the appeal to emotions and the debasement of the opposing views tended to have more relevance, thus confirming the second hypothesis (and particularly its subsidiary), which is consistent with the outcome of the referendum and may be a distressing hypothesis for democracy.