On Middle Grounds for Preference Statements

TL;DR

This paper explores a formal logic-based framework for representing conflicting stakeholder opinions using preference statements, analyzing the existence and uniqueness of middle grounds, and providing algorithms for their identification.

Contribution

It introduces a formal framework for middle grounds in preference statements, with theoretical results on their existence, uniqueness, and algorithms for decision-making.

Findings

Middle grounds may not always exist for preference statements.

Middle grounds may not be unique, leading to multiple solutions.

Algorithms are provided to decide existence and find middle grounds.

Abstract

In group decisions or deliberations, stakeholders are often confronted with conflicting opinions. We investigate a logic-based way of expressing such opinions and a formal general notion of a middle ground between stakeholders. Inspired by the literature on preferences with hierarchical and lexicographic models, we instantiate our general framework to the case where stakeholders express their opinions using preference statements of the form I prefer 'a' to 'b', where 'a' and 'b' are alternatives expressed over some attributes, e.g., in a trolley problem, one can express I prefer to save 1 adult and 1 child to 2 adults (and 0 children). We prove theoretical results on the existence and uniqueness of middle grounds. In particular, we show that, for preference statements, middle grounds may not exist and may not be unique. We also provide algorithms for deciding the existence and finding middle grounds.