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α: calibrated so average coauthorship-adjusted count equals average raw count
Let V be a society whose members express weak preferences about two alternatives. We show simple representation formulae that are valid for all, and only, the elements of various classes of non-manipulable social choice functions on V. We represent the entire class of the non-manipulable social choice functions, and various of its subclasses corresponding to further properties. We focus mainly on anonymity. Efficiency and neutrality up to one voter are also considered. As a consequence of the representation formulae, the cardinalities of some of these classes are also established. Notably, we show that the number of anonymous and non-manipulable social choice functions on V is 2n+1 if V contains n members.