Source-linked AI summary
Argumentation for Common Ground: Finding Zones of Possible Agreement between Individuals in Conflict
Elisa Cavatorta, Antonio Rago
TL;DR
The paper asks how negotiators can identify common ground when agreement acceptability depends on contested narratives and citizens’ subjective reasoning. It builds and merges quantitative bipolar argumentation frameworks to represent those views and identify ZOPAs, finding theoretical support and reasonable empirical correlation in the Israeli-Palestinian case. The authors conclude that argumentation has potential for assisting negotiators, while noting that scaling and empirical validation remain future work.
Problem
Peace-agreement acceptance depends on citizens’ subjective reasoning about clauses, outcomes, grievances, and risks, creating a need to identify common ground amid contested narratives.
Method
The paper develops QBAFs for each side’s reasoning, evaluates them with gradual semantics, and merges them to identify mutually acceptable agreements.
Results
The framework identifies ZOPAs theoretically and shows reasonable correlation with existing survey data in preliminary Israeli-Palestinian experiments.
Takeaways & Limitations
Argumentation has potential to assist negotiators and conflict-resolution teams in mapping feasible common ground grounded in citizens’ reasoning.
Takeaways & Limitations
The approach evaluates all possible agreements, leaving efficient scaling methods for future work, and its threshold-based ZOPA variants lack formal-guarantee analysis.
Abstract
from arXiv · showhide
How can common ground between societies in conflict be identified when citizens' acceptability of peace agreements is shaped by contested narratives? Such acceptability is mediated not only by the clauses that agreements include or exclude, but crucially by citizens' subjective reasoning concerning agreements' clauses. In this paper, we leverage computational argumentation to introduce a novel approach to identifying mutually acceptable agreements among individuals in conflict, i.e. a Zone of Possible Agreement (ZOPA). First, we introduce a quantitative bipolar argumentation framework tailored to represent each side's reasoning about peace agreements. We then show how merging these frameworks can enable negotiators to identify peace agreements that are mutually acceptable. To evaluate our approach under conditions of real-world relevance, we focus on the Palestinian-Israeli conflict, where long-standing policy, practitioner and public interest underscores the demand for methods capable of analysing polarised public reasoning. We show how our framework identifies a ZOPA through theoretical analysis and preliminary experiments using survey data from both existing work and retrieved by a large language model. The results illustrate how argumentation can empower negotiators and conflict-resolution teams in mapping feasible ZOPAs grounded in citizens' reasoning.
1 Introduction
The paper addresses how contested narratives and subjective reasoning shape public acceptance of peace agreements. It proposes computational argumentation as a way to represent these views and identify mutually acceptable agreements.
- Public acceptance depends on agreement provisions as well as narratives about outcomes, grievance reduction, and perceived risks.
- Computational argumentation represents knowledge and resolves conflicts, but its technologies have not previously been deployed in real-world conflict resolution.
- The framework introduces QBAFs tailored to conflicting individual reasoning about peace agreements and theoretically evaluates their suitability.
- Merging citizens’ QBAFs indicates ZOPAs, with formal guarantees and preliminary experiments using existing survey data and LLM-retrieved survey evidence.
2 Preliminaries
The preliminaries define QBAFs as quantitative representations of arguments, their relations, and intrinsic acceptability, then use gradual semantics to evaluate argument strength.
- A QBAF contains arguments, directed attack and support relations, and base scores in [0,1] representing intrinsic acceptability.
- Gradual semantics assigns each argument a strength in [0,1] representing its acceptability within a QBAF.
- The framework compares attacker and supporter strengths while discounting arguments assigned zero strength.
- Balance requires an argument’s strength to remain at or below its base score when attackers outweigh supporters, and vice versa.
3 Representing Citizens’ Reasoning on Peace Agreements with QBAFs
This section constructs QBAFs that encode agreements, clauses, and citizens’ reasoning, then establishes properties needed for intuitive agreement rankings. The framework evaluates all possible agreements while leaving scaling improvements for future work.
- The proposed QBAF represents agreements, clauses, and reasoning as arguments connected by attacks and supports.
- Endorsed clauses support agreements containing them and attack agreements omitting them, with the opposite relations for non-endorsed clauses.
- Agreement arguments receive neutral base scores of 0.5, and the paper restricts analysis to acyclic QBAFs without circular reasoning.
- The approach evaluates all possible agreements, although the number of agreements is combinatorial in the number of clauses.
- Monotonicity implies that agreements with more endorsed and fewer non-endorsed clauses become more acceptable.
- Balance, monotonicity, and duality are identified as essential properties, with DF-QuAD and QEM satisfying the requirements at this stage.
4 Merging QBAFs to Find ZOPAs
The paper merges citizens’ QBAFs into one graph whose strength-based rankings identify agreements supported by collective reasoning as a ZOPA. The construction preserves citizen-specific reasoning and provides theoretical guarantees, while experiments illustrate compromise-based common ground and expose scope limitations.
- Merged representation: Merging citizens’ QBAFs preserves their arguments, relations, and base scores while sharing the candidate-agreement layer.Clause and reasoning arguments remain individual-specific and disjoint, enabling provenance tracing back to the citizen who supplied the reasoning.
- ZOPA criterion: An agreement enters the ZOPA when its merged-QBAF strength exceeds the neutral base score of 0.5.Equivalently, under balance and strict monotonicity, its attackers are weaker than its supporters.
- Illustrative result: In the Figure 2 example, the ZOPA is {P3,P4}, with P4 ranked as the most mutually acceptable agreement despite mixed clause endorsement.P4 is supported by stronger reasoning, illustrating how compromise in narratives can generate common ground.
- Theoretical guarantees: When citizens disagree equally on every clause, the ZOPA is empty because every agreement receives balanced support and attack.Conversely, shared endorsement ranks the agreement containing exactly those clauses highest and places it inside the ZOPA.
- Theoretical guarantees: Balance, monotonicity or strict monotonicity, and duality characterize suitable gradual semantics; QEM qualifies, whereas DF-QuAD fails strict monotonicity.The merged framework therefore supports intuitive ZOPA guarantees under the selected semantics.
5 Empirical Evaluation
The empirical evaluation tests the merged QBAF against existing survey data and LLM-retrieved polling arguments in the Israeli-Palestinian context. Results show encouraging agreement with measured preferences and an interpretable relationship between clause reasoning and ZOPA inclusion.
- 5.1 Survey Data from Existing Work: The first experiment compares the merged QBAF with a 64-agreement rank-ordering task using balanced Israeli and Palestinian samples of 1,152 respondents each.Clause arguments are populated from 16 causal estimates of clause preferences.
- 5.1 Survey Data from Existing Work: 0.448 Spearman ρ and 0.293 Kendall τ quantify the correlation between argumentative and empirical rankings across the 64 agreements.Both reported significance values are p = 0.000.
- 5.1 Survey Data from Existing Work: 0.873 precision and 0.982 recall result when comparing agreements above the status quo under pooled-majority preferences and the merged QBAF.The pooled majority places 56 of 64 deals above the status quo, while the merged QBAF places 63 above it; the authors note that this target is easy.
- 5.2 Retrieved Data from LLMs: The second experiment uses an LLM pipeline to retrieve reasoning arguments from published nationally representative survey reports, producing agreement rankings and clause-level strengths for negotiators.The pipeline is intended to provide relevant information without costly fieldwork, with every candidate argument manually validated against its source document.
- 5.2 Retrieved Data from LLMs: 29 validated reasoning arguments were retrieved from seven opinion-poll reports published in 2024-2025: 14 for Israelis and 15 for Palestinians.Israeli arguments included 2 supporting and 12 opposing changes; Palestinian arguments included 11 supporting and 4 opposing changes.
- 5.2 Retrieved Data from LLMs: Clauses with stronger endorsement than opposition appeared in more ZOPA agreements, while the reverse pattern held for clauses with more negative combined reasoning.Clause 5 appeared in the most ZOPA agreements, Clause 7 in the next most, and Clause 2 in the fewest.
6 Related Work
The paper situates its contribution within gradual semantics and computational argumentation. Although related methods support negotiation and persuasion, the authors identify an unfilled application space for gradual argumentation in real-world peace agreements.
- Gradual Semantics: Related gradual-semantics research includes frameworks with attack relations, support relations, or no base scores, alongside extensive analyses of their behavior.The surveyed analyses include applications to uncertainty, incomplete information, explainable AI, fraud detection, and judgmental forecasting.
- Negotiation and Persuasion: Existing argumentation approaches have been deployed in negotiation and automated persuasion, but none of those approaches use gradual argumentation.This contrast highlights a potential cross-fertilization between negotiation research and the paper’s approach.
7 Conclusions
The paper concludes that merged QBAFs can represent opposing citizens’ reasoning and reveal evidence-grounded ZOPAs, with preliminary Israeli-Palestinian evaluations showing reasonable correlation and deployment potential. Future work must address respondent-level reasoning, scalability, and principled base-score elicitation.
- Conclusions: The tailored QBAF represents citizens’ reasoning about peace agreements, while merging opposing parties’ QBAFs reveals ZOPAs grounded in evidence-based reasoning.The framework is presented as a way to identify feasible common ground amid polarized public discourse.
- Conclusions: Theoretical analysis supports intuitive agreement rankings for gradual semantics satisfying balance, strict monotonicity, and duality.The empirical evaluation uses both existing survey data and LLM-retrieved data in the Israeli-Palestinian conflict.
- Future Work: Future evaluations should use reasoning elicited from survey respondents or structured interviews and develop efficient methods for merging thousands of individual QBAFs.The authors also identify principled base-score elicitation as a methodological priority.
- Future Work: Future extensions could model conditional dependencies between clauses and derive base scores from respondent preferences converted into quantitative values.The paper mentions set-attacks, set-supports, and preference-based approximation as possible extensions.
Supplementary Material
The supplementary material provides additional definitions and proofs supporting the paper’s theoretical work.
- The supplementary material contains additional definitions and proofs for the theoretical analysis.
Additional Definitions
The paper formalizes reasoning chains through paths over attack and support relations, and defines gradual semantics for evaluating arguments. It presents DF-QuAD and QEM as quantitative evaluation schemes.
- Paths: A path connects two arguments through a sequence of attack or support relations.Paths are represented as sets of relation pairs and may contain any positive number of steps.
- Gradual semantics: DF-QuAD evaluates each argument from its initial strength together with aggregated attack and support influences.The aggregation operator combines values recursively, with empty, singleton, and multi-value cases defined explicitly.
- Gradual semantics: QEM assigns each argument a score by adjusting its initial strength according to the summed strength of supporting arguments.The displayed formulation also includes a corresponding adjustment based on opposing influence.
Proofs
The proofs establish how argument strength and preference relations determine membership in the ZOPA. They also characterize cases where the ZOPA is empty, including total disagreement.
- Duality: Under duality, paired arguments with reversed attack and support relations receive complementary strengths.For such arguments, the evaluated strength of one equals 1 minus the evaluated strength of the other.
- Monotonicity: Monotonicity guarantees that an argument with a larger support set is evaluated at least as strongly as one with a smaller support set.The proof assumes the arguments have the same combined clause set and initial strength.
- ZOPA membership: A proposal belongs to the ZOPA when its aggregate support exceeds its aggregate attack, and is excluded when attack is at least as large as support.This criterion is derived under balance and strict monotonicity assumptions.
- ZOPAs under total disagreement: Under total disagreement, every proposal has balanced evaluation at 0.5, so no proposal belongs to the ZOPA.The result follows from duality and the definition of ZOPA membership.
- Preference and membership: When one proposal has strictly more support than attack while another has the reverse pattern, monotonicity yields a strict preference between them and distinguishes their ZOPA membership.The proof compares attack and support sets while holding the relevant initial strengths equal.