McMASTER UNIVERSITY STATISTICS SEMINAR

Week of October 26 - 30, 1998

SPEAKER:	Dr Duncan Luce Distinguished Professor in (and founder of) the Institute for Mathematical Behavioral Sciences, University of California-Irvine.
TITLE:	"A Non-Linear Surprise in the Utility of Gains and Losses"
DAY:	Wednesday, October 28, 1998
TIME:	3:30 p.m. [Coffee in BSB-202 at 3:00 p.m.]
PLACE:	BSB-108

SUMMARY

For 50 years utility theory has studied models that have a bi-linear numerical representation in the sense that the impact of both consequences and events appear in linear form. Experience with practical decision problems suggests trouble, and R. Chechile and A. Cooke (1997) showed empirically that bi-linearity fails badly for binary gambles with a gain and a loss. Independently, in 1997 Luce, using the added primitive of joint receipt of alternatives, developed a class of models that are bilinear for gains and losses separately but are inherently non-linear for mixed gains and losses. One version involves only rational assumptions; a second is based on a single non-rational, but empirically sustained assumption. Reanalysis of data from 144 subjects favors these non-linear models over bilinear ones almost 6 to 1 and of the non-linear ones the non-rational to the rational also nearly 6 to 1. The model is applied to data on buying and selling prices showing, among other things, that the non-rational version predicts observed non-monotonicities first reported by M.H. Burnbaum.

ABOUT THE SPEAKER

Dr R. Duncan Luce received his PhD in Mathematics from MIT in 1950. His research interests span a number of topics in the application of mathematical models to psychological, economic and social phenomena. In recent years, he focussed on individual choices, extensions of the theory of measurement with applications to psychology and social sciences, and the study of judgement and decision making with an emphasis on the measurement of utility. He received the Distinguished Scientific Contribution Award from the American Psychological Association, is a member of the National Academy of Sciences and the American Philosophical Society. He served as President of the Federation of Behavioral, Psychological and Cognitive Sciences and is author or co-author of 7 books; editor or co-editor of 14 books; and author or co-author of about 200 scientific articles.

REFERENCES

A bibliography of recent work is available at Dr Luce's web site at the Institute for Mathematical Behavioral Sciences, University of California-Irvine.