A Consensus Achieving Process for Group Preference

Cover A Consensus Achieving Process for Group Preference
A Consensus Achieving Process for Group Preference
Samuel Edwin Bodily
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If consensus is achieved the weights of the SUF U= l. L^ a. U, (6) are given by a = a W and Y . ", a. = 1. (7) — — = ^1=1 1 (Note: We must use equation (7b) because one of the n equations in (7a) is redundant. ) -11- Consider two examples; Example 1 . Suppose w = 2/3 1/3 1/3 2/3 1/100 1/100 98/100 We have the equations, a) 2/3 a^ + 1/3 a^ + l/lOO a^ = a^ b) 1/3 a^ + 2/3 a^ + 1/100 a^ = a^ c) d) 98/100 a^ = a^ ^1 -^ ^2 -^ ^3 = ^ W Clearly c) is solved by a = 0, with the other equations giving a..... = a = 1/2. Then a = [. 5, . 5, 0] and the utility function of the third individual does not affect the surrogate utility function. We expected this to happen since individual three is transient. Example 2 . Suppose 2/3 1/3 1/3 2/3 Individuals one and two communicate with each other and reach a consensus 1/2 u + 1/2 u and individuals three and four communicate with each other and achieve a consensus 1/3 u + 2/3 u . However, the entire group does not achieve a consensus, since there are two communicating chains.

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