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Conflict is one of the most important phenomena of social life, but it is still largely neglected by the computing community. This work proposes an approach that detects common conversational social signals (loudness, overlapping speech, etc.) and predicts the conflict level perceived by human observers in continuous, non-categorical terms. The proposed regression approach is fully Bayesian and it adopts automatic relevance determination to identify the social signals that influence most the outcome of the prediction. The experiments are performed over the SSPNet Conflict Corpus, a publicly available collection of 1,430 clips extracted from televised political debates (roughly 12 hours of material for 138 subjects in total). The results show that it is possible to achieve a correlation close to 0.8 between actual and predicted conflict perception.