Optimal Choice of Granularity in Commonsense Estimation: Why Half-Orders of Magnitude

Authors

Jerry R. Hobbs
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

11-2005

Comments

UTEP-CS-01-09b.

Short version published in the Proceedings of the Joint 9th World Congress of the International Fuzzy Systems Association and 20th International Conference of the North American Fuzzy Information Processing Society IFSA/NAFIPS 2001, Vancouver, Canada, July 25-28, 2001, pp. 1343-1348; full paper published in International Journal on Intelligent Systems, 2006, Vol. 21, No. 8, pp. 843-855.

Abstract

It has been observed that when people make crude estimates, they feel comfortable choosing between alternatives which differ by a half-order of magnitude (e.g., were there 100, 300, or 1,000 people in the crowd), and less comfortable making a choice on a more detailed scale, with finer granules, or on a coarser scale (like 100 or 1,000). In this paper, we describe two models of choosing granularity in commonsense estimates, and we show that for both models, in the optimal granularity, the next estimate is 3-4 times larger than the previous one. Thus, these two optimization results explain the commonsense granularity.