In both axiomatic theories and the practice of extensive measurement, it is assumed that a series of replicas of any given object can be found. The replicas give rise to a standard series, the "multiples" of the given object. The numerical value assigned to any object is determined, approximately, by comparisons with members of a suitable standard series. This prescription introduces unspecified errors, if the comparison process is somewhat insensitive, so that "replicas" are not really equivalent. In this paper, it (...) is assumed that the comparison process leads only to a semiorder, which allows for such insensitivity. It is shown that, nevertheless, extensive measurement can be carried out, provided that a certain set of (plausible) axioms is valid. Approximate measures, and their limits of error, can be derived from finite sets of semiorder observations. These approximate measures converge to ratio-scale exact measurement. (shrink)

We use a sequential voluntary contribution game to compare the relative impact of a first-mover’s non-binding announcement versus binding commitment on cooperation. We find that a non-binding announcement and a binding commitment increase individual contributions to a similar extent. Since announced contributions systematically exceed commitments, in sessions with a non-binding announcement, second-movers tend to contribute more to the group activity than in sessions with a binding commitment. Yet, second-movers appear to be more motivated towards achieving a social optimum when the (...) first-mover uses commitment. We also find that a non-binding announcement has a higher impact on individual propensity to cooperate than the ex post contribution of the first-mover. However, the failure to make announced contributions decreases cooperation even though the first-mover is reassigned in every period. (shrink)

We propose a theory that relates perceived evidence to numerical probability judgment. The most successful prior account of this relation is Support Theory, advanced in Tversky and Koehler. Support Theory, however, implies additive probability estimates for binary partitions. In contrast, superadditivity has been documented in Macchi, Osherson, and Krantz, and both sub- and superadditivity appear in the experiments reported here. Nonadditivity suggests asymmetry in the processing of focal and nonfocal hypotheses, even within binary partitions. We extend Support Theory by revising (...) its basic equation to allow such asymmetry, and compare the two equations’ ability to predict numerical assessments of probability from scaled estimates of evidence for and against a given proposition. Both between- and within-subject experimental designs are employed for this purpose. We find that the revised equation is more accurate than the original Support Theory equation. The implications of asymmetric processing on qualitative assessments of chance are also briefly discussed. (shrink)

The measurement of force is based on a formal law of additivity, which characterizes the effects of two or more configurations on the equilibrium of a material point. The representing vectors (resultant forces) are additive over configurations. The existence of a tight interrelation between the force vector and the geometric space, in which motion is described, depends on observations of partial (directional) equilibria; an axiomatization of this interrelation yields a proof of part two of Newton's second law of motion. The (...) present results (which were derived from a curious and deep isomorphism between force measurement and trichromatic color measurement) yield a kind of subunit, which needs to be incorporated into more complete axiomatizations of mechanics that would fulfill the Mach-Kirchhoff program. (shrink)