INDIFFERENCE AND SERIATION

Much mathematical work in the social sciences concerns itself with the organization of data, with the attempt to put complex interrelationships into a coherent pattern. In this paper, we shall discuss two problems of data organization in the social sciences which are solved using graph theoretical techniques. The first has to do with measurement, specifically measurement of indifference. The second has to do with seriation, the attempt to put data in a sequence or in serial order. We will use the results on indifference measurement to solve the problem of seriation. In what follows, we shall denote by (V, A) a directed graph, or digraph, where V is the set of vertices and A the set of arcs, and by (V, E) an (undirected) graph, where V is the set of vertices and E is the set of edges. We shall not allow multiple arcs or edges, but shall assume, unless mentioned otherwise, that in a graph (V, E) each vertex has a loop, an edge from the vertex to itself. Our diagrams of graphs will omit the loops. Finally, we shall assume that V is finite throughout.

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