Search algorithms explore a finite space of solutions Ω. An algorithm basically selects a solution in Ω, examines the solution, and decides which solution to select next. It repeats this until it has made Q selections. It is crucial to the arguments of Dembski and Marks that search algorithms have the capacity for randomizing their decisions. To randomize a decision is to base it, at least in part, on inputs from a random source. (Think of flipping a fair coin repeatedly and feeding the sequence of outcomes into a computer program. The inputs would permit the program to randomize its decisions.)
Dembski and Marks believe that people search for search algorithms in a higher-order space Ω2. They write,
Let Ω2 be the finite space of all search algorithms on the search space Ω.The word I've emphasized is wrong, wrong, and wrong. The set of all randomized search algorithms is infinite, not finite. Section III.A and the "proof" of Equation (7) in Appendix B are based on a false premise.
Consider making just one randomized decision between alternative solutions ω1 and ω2 in Ω, with the probability of choosing ω1 equal to p. The set of all possible values for p is infinite, and therefore the set of all randomized algorithms for making the decision is infinite.
Some technical details
For a fixed representation of randomized algorithms (e.g., probabilistic Turing machines reading i.i.d. uniform bits from an auxiliary tape), the set of probabilities p possible in a randomized dichotomous decision is countably infinite. There is no upper bound on the size and running time of the randomized decision algorithm.
The set of probabilities [0, 1] is uncountably infinite. Thus, while every randomized search algorithm implements a random search process, vanishingly few random search processes correspond to randomized search algorithms. Relatively few randomized search algorithms are fast enough and small enough to solve a problem in practice. We humans necessarily prefer small randomized search algorithms that make decisions rapidly.