Sentence:  We demonstrate that for any power index satisfying a number of standard properties, the index of a player in the <WSD>multicameral</WSD> game can be smaller (or greater) than in all the chamber games; this can occur even when the players are ordered the same way by desirability relations in all the chamber games. 
Meaning of the word marked with <WSD> tags:  Involving three or more special interest groups or viewpoints.