INSTITUTE OF MATHEMATICAL ECONOMICS

Wulf Albers, Andreas Guentzel

Working-Paper No. 286

January 1998

Abstract

A central idea of the theory of prominence in the decimal system is that every number is presented as a sum of full step numbers (i.e. the numbers a*10^i with a=1, 2, or 5, and i integer), where every full step number appears at most once in the presentation with sign +1 or -1. For example 42=50-10+2. The question is whether subjects really perceive numbers this way, and if they create numerical responses in a way that creates presentations of numbers as sums of full step numbers of decreasing amounts. The answer is not only interesting for further analysis of boundedly rational numerical decision processing, but also for the theory of prominence.
To approach the problem, we asked 30 subjects first to answer a set of questions by numerical responses, and thereafter to describe how they came to their responses, and - if possible - to give numbers they considered during the process of finding the numerical response. We did not consider reports where the subjects could not remember any number but their final response, and we restricted the analysis to questions which asked for probabilities.
The observed processes have a clear structure. They consist of three phases. In phase 1 an anchor point A=0, 50, or 100 is selected. In phase 2 the anchor point is refined by adding or subtracting a full step number F. This phase can be repeatedly applied until the obtained result A+F or A-F cannot be improved. In this phase new values of F replace the old ones. In phase 3 the result is stepwise refined by adding or subtracting full step numbers of decreasing order, until the decision maker reaches the limit of her ability of judgement.
Moreover there are several rules and properties which are fulfilled by the process, and which suggest that numerical decision processing has quite strict rules as the grammar of a language. Finally a detailed process model is given which describes 127 of the 134 considered reports in a reasonable way.
I thank Andras Guentzel who made the interviews of this investigation as part of his diploma thesis. He analysed the data under different aspects (see Guentzel 1993).