THE PROBABILITY OF A GIVEN 1-CHOICE STRUCTURE.
UNIVERSITY OF THE WEST INDIES KINGSTON (JAMAICA)
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A 1-choice structure arises whenever each person in a group chooses exactly one other person according to some criterion. The purpose of the report is to study the situation in which these choices are made at random. Such a structure can be represented by a directed graph in which the points represent people and the directed lines their choices. The authors first describe the shape of such a 1-choice structure, and define its symmetry number. With the help of these properties they are then able to develop and prove a formula which gives a probability of obtaining a given structure in the random choice situation. In order to supply data for these results, they include in the Appendix the diagrams of all 1-choice structures with at most 6 points and the probability of each. Diagrams for 1-choice structures with 7 points were computed but are not included in the paper. Author