On Middle Grounds for Preference Statements

2025-08-13

AI Summary

This paper addresses the challenge of formally reconciling conflicting stakeholder preferences in group decision-making. Methodologically, it introduces a logic-based Middle Position framework, defining an attribute-driven preference statement model that integrates both hierarchical and lexicographic preference structures, and provides a general formal definition of the Middle Position. Theoretically, it characterizes necessary and sufficient conditions for existence and uniqueness, revealing its intrinsic properties—namely, potential non-existence or multiplicity of solutions. Algorithmically, it devises efficient procedures to decide existence and construct Middle Positions when they exist. The primary contributions are: (i) establishing the first rigorous logical foundation for the Middle Position within preference logic; (ii) providing a verifiable and computationally tractable approach to consensus modeling; and (iii) delivering formal support for ethical deliberation—such as in trolley-problem scenarios—and negotiation systems requiring principled preference aggregation.

Technology Category

• Knowledge Representation and Reasoning: Preferences
• Multiagent Systems: Agreement, Argumentation & Negotiation
• Machine Learning: Learning Preferences or Rankings

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness and ethical considerations in crowd work and in human-in-the-loop AI systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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.

Problem

• Investigating logic-based expression of conflicting stakeholder opinions
• Defining formal notion of middle ground between conflicting preferences
• Developing algorithms to find consensus in hierarchical preference statements

Innovation

• Logic-based framework for conflicting opinions
• Hierarchical lexicographic preference statement modeling
• Algorithms for middle ground existence determination