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Are convex combinations of 0-1 Pareto efficient vectors efficient?

Let $Y$ be any subset of $\{0,1\}^n$ for $n\geq3$. A vector $\alpha\in$ $Y$ is Pareto efficient if there is no $\beta\in$ $Y$ such that $\beta_i$ $\geq$ $\alpha_i$ for each $i\in\{1,...,n\}$ and $\bet …
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