Opinion Mining is the subject of vast research literature, dealing with the automatic extraction and classification of people's opinions from sources such as reviews and social media. Recently, the focus is shifting towards the analysis of more and more subjective phenomena, such as hate speech and the public discourse on controversial topics like Brexit or gender policies. In these contexts, the traditional techniques to study the relationship between language, opinions and personal beliefs show their limitations. As important assumptions about language and truth crumble, the need emerges of a new paradigm to frame the computational analysis of opinions on highly subjective, polarizing topics. I propose a novel set of statistical tools that leverage and disentangle the disagreement in order to gain better insight on controversial social phenomena.