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Q: How do I order a set of objects given a set of comparisons? ( No Answer,   1 Comment )
Question  
Subject: How do I order a set of objects given a set of comparisons?
Category: Science > Math
Asked by: mxnmatch-ga
List Price: $20.00
Posted: 16 Apr 2006 23:51 PDT
Expires: 20 Apr 2006 22:43 PDT
Question ID: 719680
Let's say I have 1000 objects and 10000 comparisons between individual
objects of the form
  (object1, object2, which is better, magnitude)
So, for example I might have:
  ("Bob","Jim","Jim","smarter")
  ("Bob","Jay","Jay","smarter")
  ("George","Jay","George","way smarter")

Given a large set of those (10,000 in this example), how do I take
that data and determine an overall ordering? In the above example it
would be something like
    Bob, Jim, Jay, George
or it could be
    Bob, Jim, Jay, George
Also, there are going to be plenty of contradictory comparisons where
some think Jay is smarter than Jim while others think Jim is smarter
than Jay.

I don't expect to be able to get any sort of perfect ordering because
I doubt there is one in most cases. But if most people think Jim is
smarter than Jay and Jay is smarter than Bob then I'd like to get a
final ordering that order Bob then Jay then Jim.

If it makes the problem simpler I could get rid of the magnitude in
each data point so that it's just a binary comparison where A > B or A
< B. But, if possible I'd like an way to include the magnitude.

Clarification of Question by mxnmatch-ga on 17 Apr 2006 00:04 PDT
And just to be clear, the real data will be of the form
  (objectId1, objectId2, comparison)
with data like:
  (92311,991101,1)
  (123572,917213,-2)
which would mean that 991101 is better than 92311 while 123572 is way
better than 917213.

Clarification of Question by mxnmatch-ga on 20 Apr 2006 22:43 PDT
That's good. I like the chess score idea. I'll see if I can make that work.
Answer  
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Comments  
Subject: Re: How do I order a set of objects given a set of comparisons?
From: frankcorrao-ga on 17 Apr 2006 08:35 PDT
 
I think if you think of this like sports results, there are any number
of ways you could come up with a fair, but subjective, results.  You
could use a simple tally with a bonus for the magnitude, somewhat like
(American) Football, though there magnitude is only used in
tie-breakers.  That works very well if you can guarantee that each
element in your set is compared with every other element and equal
number of times (a balanced schedule in sports parlance).  If that is
not the case, you could use a ladder system such as is often used for
games, like case's ladder(www.casesladder.com).  Or perhaps you could
use a rating system like is used is in chess (www.fide.com).  Just
interpert each comparison as the result of match and it should make
sense.

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