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.

翻译：给定若干个体对公共政策倡议相关提案的明确偏好，其中某些提案可能被判定为比其他提案更具“分歧性”。在设计支持数字民主倡议的在线参与平台以促进公民对此类提案的审议时，我们可能希望为这些平台配备检索当前讨论中最具分歧性提案的功能。此类服务将有助于分析审议进展，并将讨论引导至仍需进一步辩论的议题。在此应用场景的指导下，我们探索了基于个体对提案的明确偏好来定义“选择最具分歧性提案集合”这一概念的可行路径。随后，运用社会选择理论中常见的公理化方法，我们证明了在满足某些看似温和的规范性要求的前提下，选择最具分歧性提案的任务面临若干根本性困难。