A Pseudomodel of the Small World Problem

A model is presented of the decision-making process used by intermediaries in small world experiments in the United States. This involves allocating each of the population of the U.S. to one of 16 categories; the membership of each population is a function of the target in the small world experiment. This is shown to be equivalent, for modeling purposes, to a Markov process with 16 states.The Markov transition probabilities are derived partly from reverse small world data and partly by guesswork, but using as few disposable parameters as possible (3). Statistics of chain lengths from various types of starter (e.g., those far from the target, those in the target's occupation, etc.) are derived, and compare favorably with observations. The possibility of incompleted chains is included by allowing a constant probability of loss at every step in the chain. Again, there is good agreement with most observations.How such a model might be validated by suitable observations is discussed; in particular, a set of experiments is described which should produce a great deal of additional information about the small world experiment.