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\item $\Atoms = \set{p_1,\dots,p_m}$ is a finite set of issues, 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., $\set{\neg, \wedge}$).  We denote with $\D= \{B \{O  \mid B: \I O: \Atoms  \to \{0,1\}\}$ the set of all possible assignments of truth values to the set of issues $\Atoms$ and call an element $O\in\D$ an \emph{opinion}. Thus, $O(p)=0$ (respectively, \mbox{$O(p)=1$}) indicates that opinion $O$ rejects (respectively, accepts) the issue $p$. Syntactically, the two opinions correspond to the truth of the literals $p$ or $\neg p$. For $p \in \Atoms$ we write $\pm p$ to denote one element from $\set{p, \neg p}$. An \emph{opinion profile} $\O=(O_1,\dots,O_n)$ records the opinion, on the given set of issues, of every individual in $\N$. Given a profile $\O$ the $i^{\mathit{th}}$ projection $\O_i$ denotes the opinion of agent $i$ in profile $\O$. We also denote by $\O(p)=\{i \in \N \mid \O_{i}(p)=1\}$ the set of agents accepting issue $p$ in profile $\O$.  \subsection{Binary Aggregation and Binary Influence}