On the Difficulty of Measuring Divisiveness of Proposals under Ranked Preferences

Given the stated preferences of several people over a number of proposals regarding public policy initiatives, some of those proposals might be judged to be more ``divisive'' than others. When designing online participatory platforms to support digital democracy initiatives enabling citizens to deliberate over such proposals, we might wish to equip those platforms with the functionality to retrieve the most divisive proposals currently under discussion. Such a service would be useful for analysing the progress of deliberation and steering discussion towards issues that still require further debate. Guided by this use case, we explore possibilities for providing a clear definition of what it means to select a set of most divisive proposals on the basis of people's stated preferences over proposals. Then, employing the axiomatic method familiar from social choice theory, we show that the task of selecting the most divisive proposals in a manner that satisfies certain seemingly mild normative requirements faces a number of fundamental difficulties.