Filtrations,values and voting discipline

Replication and condensation of games are shown to be partially reciprocal procedures, in which partnerships play an important role. Two extensions are studied: filtrations, that form partial replications by introducing any given set of partnerships while the quotient game is kept invariant, and partial condensations; they inherit full compatibility properties. The weighted Shapley value and the coalitional value, respectively associated with these procedures, are shown to exhibit some kind of parallelism, and their behavior under both extensions is also studied. When applied to simple games these values give a measure of the effect of voting discipline within parliamentary bodies. Some final examples, including two Spanish regional parliaments, illustrate both stable and unstable situations.