From: kmw@bigfoot.com   
      
   As the author of the paper with the Olympics example, maybe I can help   
   resolving some misunderstandings here.   
      
   On Feb 6, 7:20 pm, Ted Dunning wrote:   
   >   
   > "it looks like you are roughly doing the following:   
   >   
   > a) defining an edit distance tuple in a standard way,   
   >     but not reducing it to a single scalar distance measure   
   >     as would be typically done   
   > b) defining a partial order on edit distance tuples   
   >     based on total domination of all elements of the tuple.   
   > c) looking at the distribution of the number of points   
   >    in this partial ordering."   
      
   Ted is right re (a) and (b), but I'm not sure about what he means by   
   (c). Points are assigned u-scores (using his phrase "total domination")   
   as   
      
   	the number of points dominated   MINUS   
   	the number of points dominating   
      
   Marina is right to challenge Teds statement that computing u-scores   
   means   
      
   > presuming that all edits are equally important.   
      
   "Total dominance" is independent of any sets of weights chosen, because   
   pairwise comparisons that would depend on the choice of weights are   
   disregarded as "ambiguous". (This is what makes the ordering   
   "partial".)   
      
   On Feb 8, 6:24 pm, Ted continued   
      
   > Essentially what you are saying is that if you can't justify an assumption   
   > of unequal weighting, you have to assume equal weighting. [...]   
   > Wittkowski implicitly agrees that there is an assumption of equal weighting.   
   > He does this by saying that the fact that golds are more important   
   > should be considered.   
      
   There is a difference between   
      
   	no assumption and   
   	the assumption of equal weights   
      
   Ignoring that gold medals are more important than silver medals does   
   does *NOT* imply assuming equal weighting. With equal weighting, among   
   the tuples   
      
   	a) 1 gold, 2 silver   
   	b) 2 gold, 1 silver   
      
   would be considered "identical". For the computation of "standard"   
   u-scores, however, (a) and (b) would be considered "ambiguous".   
      
   The distinction between "identical" and "ambiguous" is crucial. A tuple   
   (2 gold, 0 silver) would be considered "dominated" by both (a) and (b)   
   under the assumption of equal weights, but by (b) only withing the   
   partial ordering used to define u-scores.   
      
   If the additional knowledge is added by forming tuples   
      
   	a') 1 gold, 3 gold or silver   
   	b') 2 gold, 3 gold or silver   
      
   the tuples can be ordered.   
      
   Thus, as Marina had suggested, if deletions are more informative than   
   transposition, one could define categories   
      
   	deletions (gold)   
   	deletions or transpositions (gold or silver)   
      
   Of course, which knowledge to add depends on the context. Thus, genetic   
   and typing errors may require different approaches.   
      
   Knut   
      
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