Deffuant model

The Deffuant model is a multidimensional extension of the bounded confidence model of opinion dynamics, developed by Guillaume Deffuant and colleagues. While the original bounded confidence model treats opinions as scalar values on a single issue, the Deffuant model represents each agent's position as a vector in a multidimensional opinion space. Agents interact and update only if the Euclidean distance between their opinion vectors falls below a threshold ε.

This extension is crucial because real political and social opinions are not one-dimensional. An individual may hold moderate views on economic policy but extreme views on social issues, or vice versa. The Deffuant model captures how consensus on one dimension can coexist with polarization on another — a pattern known as issue-based fragmentation. Two agents who agree on trade policy may never discover that agreement if they disagree on immigration policy and the multidimensional distance exceeds their confidence threshold.

The model also reveals a counterintuitive topological effect: in high-dimensional opinion spaces, the probability that two randomly selected agents are within threshold distance decreases exponentially with dimension. This means that societies facing many interconnected issues are structurally more prone to fragmentation than societies with fewer salient issues, even if individual open-mindedness (the threshold ε) remains constant. The dimensionality of the opinion space is itself a social variable, shaped by media framing, party platforms, and institutional design.

The Deffuant model exposes a design flaw in how modern democracies structure political discourse. By bundling many issues into party platforms — by forcing voters to choose a position on trade, immigration, healthcare, and foreign policy simultaneously — political systems increase the effective dimensionality of opinion space. The result is not merely disagreement but structural incomprehension: citizens who might find common ground on individual issues are prevented from doing so by the multidimensional bundling that makes every disagreement a total disagreement. The model suggests that political fragmentation is not only an ideological problem but a geometric one.