 A belief base \(K_i\) is a finite set of propositional formulas representing the explicit beliefs held by individual i. Each \(K_{i}\) is assumed to be consistent. \(\mathcal{K}\) denotes the set of all consistent belief bases. The postulates for merging consider a multi-set of belief bases (belief profile, or belief set, the terminology used in early papers) \(E = \{K_1, \ldots , K_{n}\}\). The reason for using multi-sets is that an element can appear more than once, thus allowing the representation of the fact that two or more agents can hold the same beliefs. This is needed to take into account the popularity of a piece of information, hence to define majority operators. To mark the distinction with the usual set union \(\cup\), the multi-set union is denoted by \(\sqcup\) and defined as \(\{\varphi\} \sqcup \{\varphi\} = \{\varphi, \varphi\}\). Two belief profiles are equivalent \((E_1\equiv E_{2})\) if and only if there exists a bijection f from \(E_1\) to \(E_{2}\) such that, for any \(B\in E_1\), we have that \(\models\land f(B)\leftrightarrow \land B\).