For a number of existing algorithms, we observe that the restriction to ordinal information does not represent any additional obstacle. They maintain their competitive ratios even in the ordinal model. For bipartite matching and independent set in graphs with bounded independence, we give new algorithms that obtain constant competitive ratios in the ordinal model. Moreover, we show that ordinal variants of the submodular matroid secretary problems can be solved using algorithms for the linear versions by extending a result from (Feldman and Zenklusen 2015).
Finally, in the matroid secretary problem we provide a lower bound of Ω( n/(log n)) for algorithms that are oblivious to the matroid structure, where n is the total number of elements. This contrasts an upper bound of O(log n) in the cardinal model, and it shows that the technique of thresholding is not sufficient for good algorithms in the ordinal model.