Agreementsshape

Agreementsshape is a term used in theoretical social science and network analysis to describe the geometric representation of agreement among a set of agents on multiple issues. It captures how consensus forms and propagates by mapping individual stances into a multi-dimensional space and considering the resulting shape.

Construction: For each agent i, define x_i in [0,1]^n where n is the number of issues; each component x_i_j reflects the degree of agreement with issue j. The agreementsshape is typically taken as the convex hull of the set {x_i} or the smallest polytope that contains all substantially aligned vectors. Weighting by confidence or influence can alter the shape.

Interpretation: Vertices correspond to representative positions; facets reflect constraints or common viewpoints; the size and geometry indicate the level of overall agreement, dispersion, and the presence of subgroups. The projection of the shape into lower dimensions can aid visualization.

Computation: computed from data with standard convex-hull algorithms; can incorporate thresholds to separate core consensus from fringe opinions; dimensionality reduction (PCA, t-SNE) can help interpret.

Applications and limitations: used to analyze committee decisions, online opinion dynamics, and policy formation; sensitive to scale and metric; does not capture temporal dynamics unless used iteratively.

See also: convex hull, consensus theory, opinion dynamics; references to general convex analysis and network science.