Green and Laffont (1979: 44)
have pointed out that there is essentially only one demand-revealing (DR) mechanism, to which the varied proposals in the literature must be reducible. But the relation among versions of DR is often obscure. This note gives a geometrical treatment of the underlying mechanism, presented in a way that brings out the connection between the two bestknown proposals: Tideman and Tullock's (1976) presentation of the Clarke (1971) mechanism, hereafter TT; and , hereafter GL. It turns out that GL differs only in a rather trivial way from TT. In particular, the often-noted Nash vs. dominant equilibrium distinction between the two turns out to be an illusion, as does the GL claim to provide a budget balance.while preserving incentive-compatibility.
Throughout the discussion here I ignore the more fundamental issues raised in my 'Thought Experiment on Demand-Revealing'Mechanisms' . Further, it is sufficient for our purpose to treat the case in which there are large numbers of voters, so that the term in brackets in Groves and Ledyards's Equation 4.3c can be harmlessly simplified to (ms-rh) 2 -o -2, where rn~ is the message of voter i, rh is the mean across all messages, and o.2 is the variance among all the messages. 1,2