Optimal selection of thek best of a sequence withk stops

We first consider the situation in which the decision-maker is allowed to have five choices with purpose to choose exactly the five absolute best candidates fromN applicants. The optimal stopping rule and the maximum probability of making the right five-choice are given for largeN ε<Emphasis Type="Bold">N, the maximum asymptotic value of the probability of the best choice being lim<Subscript> N→∝ </Subscript> <Emphasis Type="BoldItalic">P (win) ≈ 0.104305. Then, we study the general problem of selecting thek best of a sequence withk stops, constructing first a rough solution for this problem. Using this suboptimal solution, we find an approximation for the optimal probability values<Emphasis Type="BoldItalic">P <Subscript>k</Subscript> of the form<Equation ID="E1"> <EquationSource Format="TEX"> $$P_k \approx \frac{1}{{(e - 1)k + 1}}$$ </EquationSource> </Equation> for any k ε<Emphasis Type="Bold">N. Copyright Physica-Verlag 1997