A self-organizing list problem is characterized by a sequential list of n items subject to a reordering policy. Each item has an unknown probability of being requested. At the beginning of each time period, an item is requested and the list is searched sequentially from the first position. The list is then reordered according to the reordering policy. The cost is taken to be the position where the requested item is found. The steady state costs and probabilities under the transposition, move-to-front, and move-to-back policies are discussed. A randomized policy is a policy which, when an item is requested and found at position i, moves that item to position j with some probability$$a\sb{ij},\ {\sum\limits\sbsp{j=1}{i}}\ a\sb{ij} = 1,$$leaving the relative ordering of others unchanged. When only one item has a different request probability, randomized policies are used to show that the steady state cost under the move-i-position policy is stochastically smaller than that under the move-(i + 1)-position policy. This partially supports the conjecture of Gonnett et. al. (1981). Sufficient conditions are obtained to determine if the steady state cost under a randomized policy is stochastically smaller than that of another randomized policy. Under a subclass of randomized policies, the steady state cost of one list is stochastically smaller than that of another, if its request probabilities majorize those of another list. This majorization of the request probabilities is also analyzed in transience. A related problem to the self-organizing list problem is called the processor problem, where a sequential list containing an ordering of n processors is considered. Each processor has an unknown probability that it will successfully process a given job. The results obtained are parallel to those obtained in the self-organizing list problem. Simulations are made and the effective variance reduction techniques are proposed for both the self-organizing list and processor problems.