Tuesday, February 28, 2006

A matter of preference

From Incomplete Preferences to Ranking via Optimization
P. Chebotarev, E. Shamis

This fascinating problem deals with how to determine a full ranking of a finite list of candidates given only partial preference data. For instance, if I prefer cola to coffee and green tea to black tea, and you prefer coffee to black tea, the following are compatible rankings for these preference data:
  1. cola
  2. coffee
  3. green tea
  4. black tea
  1. cola
  2. coffee
  3. black tea
  4. green tea
In this simple example there are two possible rankings; but in real-world situations, there are often none. How can one use a ranking to best approximate sets of incomplete prefence data, given that there will probably be no single ranking consistent with all preferences? I (and many others) would really like to know.

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