In June of 1990, a conference was held on Probablity Models and Statisti­ cal Analyses for Ranking Data, under the joint auspices of the American Mathematical Society, the Institute for Mathematical Statistics, and the Society of Industrial and Applied Mathematicians. The conference took place at the University of Massachusetts, Amherst, and was attended by 36 participants, including statisticians, mathematicians, psychologists and sociologists from the United States, Canada, Israel, Italy, and The Nether­ lands. There were 18 presentations on a wide variety of topics involving ranking data. This volume is a collection of 14 of these presentations, as well as 5 miscellaneous papers that were contributed by conference participants. We would like to thank Carole Kohanski, summer program coordinator for the American Mathematical Society, for her assistance in arranging the conference; M. Steigerwald for preparing the manuscripts for publication; Martin Gilchrist at Springer-Verlag for editorial advice; and Persi Diaconis for contributing the Foreword. Special thanks go to the anonymous referees for their careful readings and constructive comments. Finally, we thank the National Science Foundation for their sponsorship of the AMS-IMS-SIAM Joint Summer Programs. Contents Preface vii Conference Participants xiii Foreword xvii 1 Ranking Models with Item Covariates 1 D. E. Critchlow and M. A. Fligner 1. 1 Introduction. . . . . . . . . . . . . . . 1 1. 2 Basic Ranking Models and Their Parameters 2 1. 3 Ranking Models with Covariates 8 1. 4 Estimation 9 1. 5 Example. 11 1. 6 Discussion. 14 1. 7 Appendix . 15 1. 8 References.