Appendix L: Zermelo Score System
The method of paired comparison has been applied to chess tournaments. The model used is that
proposed by Davison and Beaver [1] and has been implemented in Vega as a supplementary tool
able to provide a new, fairer standing at the end of a tournament. The proposed score system in
Vega is named Zermelo score system after the first scholar who proposed the method. In fact,
historically, the method was created with chess as the main application.
There are situations where a set of objects is to be evaluated on the basis of responses obtained
when the objects are presented in pairs. This method is known as method of paired comparison. It
has been used in contexts as marketing research, taste testing experiments, and other sensory
discrimination studies for which the responses to the objects are a function of a complex
physiological process. Moreover in several sports the competitors are ranked on the basis of their
performance when they meet in pairs. Chess is one of them.
Using the paired comparison method of experimentation, each pair formed from a set of m objects
is presented to a respondent who is asked to indicate a preference for one member of the pair. It is
assumed that the responses to the objects can be described in terms of an underlying continuum on
which the "worths" of the objects can be relatively located.
Translating the previous words into chess language is rather easy. The tournaments, both Round
Robin and Swiss systems, produce natural paired comparisons at each round and the response is just
the game result. We assume the game result depends on the player strength denoted by γ.
The task to calculate the unknowns is performed via an iterative procedure described in [1] and
implemented in Vega. Moreover the user has some possibility to tune the parameters.
Option: Zermelo Score System
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