
\section{Related work} 
One of the noted shortcomings of the CBP is that it is susceptible to path-dependence \cite{Nash2003}.  Path-dependent decisions are decisions whose outcome depends on the order in which propositions are considered.  
For any proposition, the collective judgment on it is decided by majority rule (or by any other suitable aggregation rule) unless this conflicts with the collective judgments of  previously aggregated propositions. In the latter case, the collective value of that proposition is deduced by logical implication from the previously aggregated propositions. List \cite{List2004} provided necessary and sufficient conditions for path-dependence. Furthermore, in \cite{DietrichList2007b} it has been shown that the absence of path-dependence is equivalent to strategy-proofness.

 
Here we propose a complete CBP without assuming any order over the premises. We aimed at a procedure that treats all premises in an even-handed way. The absence of full manipulability is coherent with the results of \cite{DietrichList2007b}.
 


Non-manipulability is one of the advantages of CBP over PBP. The question of manipulability under operators used for merging of propositions has been treated extensively in \cite{KEM2007}. There, Everaere \textit{et al.} explore a broad spectrum of manipulability for various merging operators over complete and incomplete sets of beliefs. Our work uses results from \cite{KEM2007} on complete sets of beliefs under model-based merging operators that use the sum of the distances between belief bases. 