Penrose's square-root rule and the EU Council of Ministers: significance of the quota

Abstract
In a two-tier decision-making system such as the EU Council of Ministers, if the number of constituencies (member-states) is sufficiently large (say, 15 or more), Penrose’s Square-Root rule can be implemented to a high level of approximation by a simple weighted decision rule at the top level (the Council) with any given quota q smaller than the total weight. This leaves one degree of freedom: the value of q as a free parameter, to be determined by some additional condition. I propose to survey and discuss critically the most important considerations for fixing this value – some of which have actually been used by theoreticians or practitioners: efficiency, transparency, sensitivity (total voting power of citizens), mean majority deficit, giving certain ‘privileged’ coalitions blocking status. Some of these considerations are reasonably compatible; others less so. Some kind of compromise is clearly needed. But which? This is essentially a political matter; but a political decision ought to be made in a theoretically enlightened way.
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