A method for obtaining an ordered metric scale

A method is presented for collecting data which will yield a scale on which the entities are ranked in preference (ordinality), the distances between the entities on the scale are ranked (ordered metric), and all combinations of the distances are ranked (higher-ordered metric). The sources drawn upon are von Neumann and Morgenstern (9), and lattice theory. An empirical example is given in which a higher-ordered metric scale is derived.I am grateful to Professor William L. Lepley (Department of Psychology) and Professor Jack R. Tessman (Department of Physics) for their critical reading of this paper. Paul Hurst and Robert Radlow participated in many discussions on the form of measurement discussed in this paper, and assisted in collecting data. I am also grateful to Professor T. C. Benton (Department of Mathematics) for certain source materials.