Jackson and Sonnenschein (2006) show that by linking collective decisions the incentive costs can become negligible and, at the limit, ex-ante efficiency can be achieved. In a voting situation this implies that the agents` intensity of preferences can be taken into account even in the absence of monetary transfers. Rather than considering a limiting result we want to analyse what can be achieved while we consider a finite number of linked decisions. We first characterise the set of implementable mechanisms and show that ex-ante efficiency can never be achieved. We then proceed to relax the efficiency requirement and prove that, even when we just require unanimity, the mechanism cannot be sensitive to the agents` intensity of preference.
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