Searching for Paper on Voting for Amendements
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Hi All,
In something that I read a while ago (alas I forget exactly what), a result about voting for amendments to legislation was discussed. If I remember correctly, the general idea was that, if you are in control of the order in which amendments were voted on, you can thereby choose whether the final bill gets passed.
Does this sound familiar to anyone, and can anyone point me to the paper in which this is developed?
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So, in answer to my own question, it appears the reference is The Theory Of Committees And Elections by Duncan Black. Also perhaps relevant is Theory of Voting by Robin Farquharson, although I haven't got my hands on it yet.
Moreover the theorem is less powerful than what is stated above, and in a sense totally obvious. The theorem is, in modern terms: if there are a finite number of amendments to be voted upon, with no repeat votes on an amendment, and the last amendment winning, any amendment in the Smith set can win, by varying the order in which the amendments are voted for.
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Okay, so in my recent reading, I found a different result which sounds a lot more like the one I was hunting for here. The theorem is called the McKelvey–Schofield chaos theorem, the reference paper appears to be Intransitivities in multidimensional voting models and some implications for agenda control.
Anyway, for the statement of the theorem, I'll quote the Handbook of Social Choice and Welfare (Chap. 13, p.27):
Richard McKelvey has stated a famous theorem: Suppose the alternatives lie in an n-dimensional space (n > 1), we choose between alternatives by majority voting (as is standard in legislation), and there is no Condorcet winner. Given any two proposals, a and b, there exists a sequence of proposals, {a'_i}(i = 0, ..., n) such that a'_0 = a, a'_n = b, and a'_i defeats a'_{i+1} for all i = 0, ..., n−1. That is, by a suitably chosen agenda, any proposal can defeat any other if there is no Condorcet winner.