Representations of votes based on pairwise information: Monotonicity versus consistency

Representations of votes, such as the scorix, the votrix or the beatpath matrix, are common tools in social choice theory. They gather the most relevant information given by the voters and are key elements in most of the existing ranking rules. The goal of this paper is twofold. First, the most relevant representations of votes based on pairwise information are revisited. Second, three properties (consistency, pseudo-monotonicity and monotonicity) of these representations of votes are introduced. Although similar notions to that of consistency have been analysed in social choice theory since the eighteenth century, pseudo-monotonicity and monotonicity have only called the attention of the research community in recent years.