A4MONG the many problems raised by the X'Wactual construction of empirical input-output tables two key issues are often singled out: (1) what industrial classification scheme should be adopted and (2) how the data should be structured. Actually, these problems of industry definition and data structuring are two facets of a more fundamental problem: Given external constraints on data gathering (availability and format) which make the industry concept mostly unobservable, how can we best group the available data into an input-output table. Ideally, each industry would be defined by a single well-defined product and a separate industry should be used for different, but possibly 6closely related, products.1 A widely accepted notion of best grouping is one which minimizes the bias, i.e., the difference between the gross output forecast obtained with a disaggregated table and the forecast obtained with an aggregated table, for any final demand bill. Historically, a theoretical condition for zero aggregation bias was first derived by Hatanaka (1952).2 Briefly stated, let A denote the (n x n) disaggregated direct coefficient matrix; x denote the n-dimensional column vector of gross outputs; y denote the n-dimensional column vector of final demands; I denote the (n X n) unit matrix; S denote the aggregation operator where S is (M X n) and reads

This paper shows that no nondictatorial voting procedure exists that induces each voter to choose his voting strategy solely on the basis of his preferences and independently of his beliefs concerning other voters' preferences. This necessary dependence between a voter's beliefs and his choice of strategy means that a voter can manipulate another voter's choice of strategy by misleading him into adopting inaccurate beliefs concerning other voters' beliefs. CONSIDER A VOTING SITUATION, as in a committee. Each rational member has preferences over the alternatives being considered and beliefs concerning the other members' preferences. The question we consider in this short paper is: can a voting procedure be constructed such that each member's vote depends only on his preferences, not on his beliefs concerning other individual preferences. We show, by an application of Gibbard [6] and Satterthwaite's [11] impossibility theorem for strategy-proof voting procedures, that such a voting procedure does not exist. Moreover, we show that this necessary lack of independence between a member's beliefs and his choice of voting strategy makes him vulnerable to possible manipulation by other members. Specifically, consider members one and two. Since member one partially bases his vote on what he believes member two is seeking, member two may deliberately mislead member one into adopting a false belief concerning member two's preferences. As a consequence of this inaccurate belief, member one may decide to vote in a manner that is, in fact, unfavorable to himself and favorable to member two. Derivation of these results depends critically on the possibility that members may be uncertain concerning other members' preferences. This assumption is reasonable because the purpose of legislative bodies is to reconcile conflicting preferences. If preferences were generally known with certainty, then, as Wilson [14, p. 310] has pointed out, the need for a legislative body would vanish because preferences could be aggregated directly. Therefore, a realistic analysis of voting behavior must accept that a member's true preferences are private. Our results are consistent with the work that other researchers have reported. Dummett and Farquharson [3, pp. 34-35] and, to a lesser extent, NVilson [14] assumed the validity of our results. Harsanyi [7] in discussing bargaining situations where the two opponents are uncertain concerning the other's preferences argued that the decisive element may not be the actual preferences of the two individuals involved, but rather the societal stereotypes (beliefs) concerning their preferences. Schelling (12, e.g., Ch. 3] in his insightful discussion of bargaining strategy dwells extensively on the same theme.