Introductory note to 1928

Zermelo’s 1928 paper on measuring participants’ playing strengths in chess tournaments is a remarkable work in the history of paired comparison modeling. Apart from several contemporary papers by Thurstone (1927a, 1927b, 1927c), Zermelo’s paper was an isolated excursion into paired comparison methods that was far ahead of its time. After this paper, the field remained mostly dormant for about 25 years until seminal publications by Bradley and Terry (1952) and Mosteller (1951a, 1951b, 1951c) led to increased interest in paired comparison methodology. Subsequently, work in paired comparison methods has remained an active area of research since the 1950’s, and with paired comparison applications to large data sets including marketing research problems involving choice preference among consumers, the field continues to be active. Scholarly work in this area arguably led to popularizing paired comparison methods in the form of competitor rating systems. For example, in the United States, a rating system due to Elo (1978) for chess players was implemented in the early 1960s (supplanting a fairly crude system developed in the 1950s) which had as a basis the model appearing in Zermelo’s paper. The system was adapted to ensure computational simplicity for the analysis of large collections of players whose abilities were changing over time. Elo’s system eventually was adopted by the World Chess Federation ∗Address for correspondence: Center for Health Quality, Outcomes & Economics Research , Edith Nourse Rogers Memorial Hospital (152), Bldg 70, 200 Springs Road, Bedford, MA 01730, USA. E-mail address: [email protected]. Phone: (781) 687-2875. Fax: (781) 687-3106.