Davide Grossi edited section_Binary_Aggregation_and_DeGroot__.tex  about 8 years ago

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A binary aggregation structure (\emph{BA structure}) is a tuple $\S = \tuple{\N,\Atoms}$ where:  \begin{itemize}  \item $\N = \set{1,\dots,n}$ is a finite set individuals s.t. $|\N|= n \in \mathbb{N}$;  \item $\Atoms = \set{p_1,\dots,p_m}$ is a finite set of issues, issues ($|\Atoms|= m \in \mathbb{N}$),  each represented by a propositional atom. \end{itemize}  We denote with $\L$ the propositional language constructed by closing $\Atoms$ under a functionally complete set of Boolean connectives (e.g., $\set{\neg, \wedge}$).  An {\em opinion} $O: \Atoms \to \{0,1\}$ is an assignment of truth values to the set of issues $\Atoms$