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Argumentation for Common Ground: Finding Zones of Possible Agreement between Individuals in Conflict

This paper proposes a computational argumentation framework that models citizens' subjective reasoning about peace agreements to identify a mutually acceptable Zone of Possible Agreement (ZOPA), demonstrating its efficacy through theoretical analysis and experiments on the Palestinian-Israeli conflict.

Original authors: Elisa Cavatorta, Antonio Rago

Published 2026-08-18

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Elisa Cavatorta, Antonio Rago

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Peace is rarely a simple matter of signing a document; it is a fragile construct built on whether ordinary people believe the terms are fair. When two societies are locked in conflict, the path to a lasting agreement often stalls not because the leaders cannot agree on the text, but because the citizens on both sides are convinced by different stories about what that text means. A clause that looks like a victory to one group may feel like a surrender to another, and these subjective narratives are often too complex, too emotional, and too contradictory to be mapped by traditional surveys or simple polls. This is where a branch of artificial intelligence known as computational argumentation steps in. Rather than just counting votes, this field attempts to model the actual logic people use to reach their conclusions, treating every reason for or against a policy as a distinct piece of a larger puzzle. By understanding how these pieces attack or support one another, researchers can move beyond asking "what do you want?" to understanding "why do you believe this is right?"

In a new study, researchers at King's College London have applied this logic to the deeply polarized conflict between Israelis and Palestinians, creating a digital tool designed to find the "Zone of Possible Agreement." This zone represents the specific set of peace deals that both sides might actually accept, not because they are perfect, but because they are the least objectionable options given the complex web of reasons each citizen holds. The team did not simply ask people to rank a list of potential treaties. Instead, they built a system that takes the specific reasons people give for supporting or rejecting a clause—such as a freeze on settlement building or the recognition of a state—and weaves them into a structured network. In this network, every reason is an argument, and the connections between them show how one belief supports or undermines another.

The researchers began by constructing these networks for individual citizens, or groups of citizens, based on their stated preferences and the reasoning behind them. They treated the peace agreement itself as a collection of possible clauses, where each clause is a potential change to the current situation. If a citizen supports a clause, that support acts as a boost to any agreement containing it; if they oppose it, that opposition acts as a drag. Crucially, the system also accounts for the reasoning that leads to those positions. For instance, a person might oppose a clause not because of the clause itself, but because of a specific fear about its consequences, which in turn might be supported or weakened by other facts they believe. By assigning a strength to each of these reasons, the system can calculate an overall "score" of acceptability for every possible combination of clauses, effectively simulating how a person would feel about a complex deal based on the sum of their individual beliefs.

To find common ground, the researchers then merged the networks of opposing sides into a single, combined map. This is where the method reveals its power. Even when two groups appear to be in total disagreement, with one side supporting every clause the other rejects, the merged map can still identify a middle path. The system looks for agreements where the collective weight of support from both sides outweighs the collective weight of opposition. In their analysis, the researchers found that this approach could identify specific deals that were more acceptable than others, even when the surface-level preferences seemed irreconcilable. The key insight was that the strength of the reasoning mattered more than the simple binary of "for" or "against." An agreement might survive the merger if the reasons supporting it were strong enough to overcome the objections, even if those objections were numerous.

The team tested this framework using real data from previous surveys involving thousands of Israeli and Palestinian respondents, as well as data retrieved from recent public opinion reports using large language models to extract specific reasoning. In the first test, they compared the system's rankings of peace deals against the actual preferences recorded in the survey data. The results showed a clear correlation, suggesting the model could accurately predict which deals the public would find most acceptable. In the second test, using the language model to pull reasoning from news reports, the system successfully identified that clauses with the strongest combined support from both sides ended up in the most "acceptable" deals, while those with the most negative reasoning were excluded. This demonstrated that the tool could work even without direct access to raw survey data, provided it could access the public arguments being made.

The study does not claim to have solved the conflict or to have found a perfect peace treaty. Instead, it offers a new way for negotiators to see the landscape of public opinion. By visualizing the underlying arguments, mediators can see exactly where the friction lies and which compromises might actually hold up under scrutiny. The research suggests that by focusing on the strength of the reasoning rather than just the count of supporters, it is possible to find a zone of agreement that was previously invisible. This approach provides a way to navigate the messy, subjective reality of human conflict, turning the chaotic noise of public opinion into a structured map that points toward a feasible future.

Technical Summary: Argumentation for Common Ground in Conflict Resolution

Problem Statement
Sustainable peace agreements rely on public acceptability, which is mediated not merely by the specific clauses included in an agreement, but by the subjective narratives and reasoning citizens employ to evaluate those clauses. In polarized conflicts, such as the Israeli-Palestinian one, citizens often hold contested narratives that make identifying a "Zone of Possible Agreement" (ZOPA)—a set of mutually acceptable agreements—difficult. While computational argumentation has been applied to opinion modeling and forecasting, it has not yet been deployed for real-world conflict resolution to map feasible ZOPAs grounded in citizens' reasoning. The core challenge is to systematically represent and merge conflicting individual reasoning to identify agreements that satisfy both parties.

Methodology
The authors propose a novel approach utilizing Quantitative Bipolar Argumentation Frameworks (QBAFs) to model and merge the reasoning of conflicting parties.

Representation (QBAF Construction):
- The framework models a citizen's reasoning as a QBAF $\langle X, A, S, \tau \rangle$ $⟨ X, A, S, τ ⟩$ , where $X$ $X$ contains three types of arguments:
  - Agreement Arguments ( $X_P$ ): Representing specific peace agreements (subsets of clauses).
  - Clause Arguments ( $X_C$ ): Representing individual clauses (changes to the status quo) and their endorsement or rejection by the citizen.
  - Reasoning Arguments ( $X_R$ ): Representing the underlying narratives or justifications for supporting or opposing clauses.
- Relations: Attacks ( $A$ ) and Supports ( $S$ ) are defined based on the citizen's stance. For instance, a clause argument representing an endorsed clause supports agreement arguments containing that clause and attacks those that do not.
- Base Scores ( $\tau$ ): Agreement arguments are assigned a neutral base score of 0.5. Clause and reasoning arguments are assigned base scores reflecting their intrinsic acceptability or prevalence.
- Gradual Semantics: A gradual semantics function $\sigma$ is applied to compute the strength (acceptability) of each argument in $[0, 1]$ , accounting for the interplay of attacks and supports.
Merging for ZOPA Identification:
- To find common ground, the QBAFs of multiple citizens (e.g., an Israeli and a Palestinian) are merged into a single framework $Q^*$ .
- The merging process takes the union of all arguments and relations while preserving the specific reasoning and clause arguments of each individual. The agreement layer remains shared.
- The ZOPA is defined as the set of agreements in the merged framework whose computed strength exceeds the neutral threshold of 0.5 ( $\sigma(Q^*, p_k) > 0.5$ ).
Theoretical Constraints:
- The authors analyze which properties of gradual semantics are necessary for intuitive behavior in this context. They establish that Balance, (Strict) Monotonicity, and Duality are essential.
- Balance ensures that if attacks outweigh supports, the strength drops below the base score.
- Monotonicity ensures that increasing support or decreasing attacks increases strength.
- Duality ensures symmetry in mirrored scenarios (e.g., if one side's reasoning is the exact inverse of another's, their strengths should sum to 1).
- The paper identifies QEM (Potyka 2018) as a suitable semantics because it satisfies all three properties, including strict monotonicity, whereas DF-QuAD fails strict monotonicity.

Key Contributions

Novel Framework: Introduction of tailored QBAFs to represent conflicting individual reasoning regarding peace agreements, distinguishing between agreement, clause, and reasoning arguments.
Theoretical Guarantees: Proof that merging QBAFs with gradual semantics satisfying balance, monotonicity, and duality intuitively represents individual views and guarantees that the resulting ZOPA reflects agreements supported by the collective reasoning of both sides.
Formal Definition of ZOPA: A formal mechanism to identify the ZOPA as a subset of agreements where the merged reasoning yields a strength greater than the neutral baseline.
Empirical Validation: Preliminary experiments applying the framework to the Israeli-Palestinian conflict using two data sources:
1. Survey Data: Re-analyzing data from Cavatorta, Groom, and Sher (2025) involving 1,152 Israelis and 1,152 Palestinians.
2. LLM-Retrieved Data: Using a Large Language Model (Opus 4.7) to extract reasoning arguments from nationally representative opinion poll reports, manually validated for accuracy.

Results

Survey Data Correlation: When applied to the existing survey data, the argumentative ranking generated by the merged QBAF showed a statistically significant correlation with the empirical ranking of agreements (Spearman $\rho = 0.448$ , Kendall $\tau = 0.293$ ). In terms of identifying agreements above the status quo, the model achieved a precision of 0.873 and recall of 0.982 against the pooled majority ground truth.
LLM Data Insights: The experiment using LLM-retrieved reasoning demonstrated that the framework could identify ZOPAs consistent with the strength of reasoning. For example, clauses with strong positive combined reasoning (e.g., mutual amnesty, Clause 7) appeared in more ZOPA agreements, while clauses with strong negative reasoning (e.g., recognition of Israel as a Jewish state, Clause 2) appeared in fewer. The mutually endorsed change (Clause 5) was correctly identified as being in the most ZOPA agreements.
Theoretical Findings: The analysis confirmed that without strict monotonicity, the framework could fail to intuitively rank agreements in cases of partial consensus. The QEM semantics successfully handled the merging of opposing views to reveal compromise solutions (e.g., Agreement $P_4$ in the illustrative example) that were not obvious when viewing individual frameworks.

Significance and Claims
The paper claims that computational argumentation offers a viable tool for conflict-resolution teams and negotiators to map feasible ZOPAs grounded in citizens' reasoning, rather than just policy provisions. By leveraging the reasoning behind narratives, the method can reveal common ground that might be inaccessible through traditional analysis.

The authors position this work as a foundational step, noting that while the approach shows encouraging correlation and suitability for real-world deployment, it is a preliminary evaluation. They emphasize that the framework supports the identification of ZOPAs even in deeply polarized contexts, provided the underlying reasoning is accurately captured. The work does not claim to solve the conflict but to provide a structured, evidence-based method for visualizing and analyzing the space of possible agreements. Future work is suggested to include scaling to larger populations, developing protocols for base score elicitation, and exploring more complex argumentation formalisms (e.g., set-attacks, probabilistic argumentation).

Technical Summary: Argumentation for Common Ground in Conflict Resolution

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