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Derivation of proposition 1:
* <math>z_{i}>\delta\bar{V}</math>. <math> b_{i}-T/n\geq\bar{V} \implies b_{i}\geqTgeq T/n+\delta\bar{V}<\math>.
* Proposal will be accepted if <math>(n-1)/2</math> members vote yes, therefore proposals will be of the form of: Keep <math>B-\frac{n-1}{2}(\frac{T}{n+\delta\bar{V}}. Give <math>T/n +\delta\bar{V}</math to <math>(n-1)/2</math> others, and the rest zero.
* <math>\bar{V}</math>=P(selected)E[Value of being selected|p^{\ast})+P(not selected)(value of not being selected).
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