Abstract

There are two important aspects of any democratic decision: aggregation of preferences and deliberation about preferences. They are essential and complementary components of any decision making process. While the well-studied process of aggregation focuses on accumulating individual preferences without discussing their origin [4], deliberation can be seen as a conversation through which individuals justify their preferences, a process that might lead to changes in their opinions as they get influenced by one another. Till now, there has been a lot of work on the ‘aggregation’ aspect (e.g., [12, 14, 6]). However, some recent work has focussed on the deliberation aspect as well [8, 9, 10, 15]. Sometimes, deliberation does not lead to unanimity in preferences, but the discussion can lead to some ‘preference uniformity’ (see how deliberation can help in bypassing social choice theory’s impossibility results in [5]), which might facilitate their eventual aggregation. In addition, the combination of both processes provides a more realistic model for decision making scenarios. In light of this status quo, our focus is on the formal study of achieving such preference uniformities, e.g., single-peaked, single-caved, single-crossing, value-restricted, best-restricted, worst-restricted, medium-restricted, or group-separable profiles. In this short abstract we provide our preliminary ideas towards achieving singlepeakedness of preference profiles via deliberation. In what follows, we define two preference upgrade operators based on [8, 9] and provide a preliminary discussion on how single-peaked preference profiles can be achieved through such operations. We will delve into the details of the logical language in the main paper.