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We consider generalizations of the classical secretary problem, also known asthe problem of optimal choice, to posets where the only information we have isthe size of the poset and the number of maximal elements. We show that, giventhis information, there is an algorithm that is successful with probability atleast $\frac{1}{e}$. We conjecture that if there are $k$ maximal elements and$k \geq 2$ then this can be improved to $\sqrt[k-1]{\frac{1}{k}}$, and provethis conjecture for posets of width $k$. We also show that no better bound ispossible.

The secretary problem on an unknown poset