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Read August 12, 2008, 06:20:18 am #0
aditya

Apples and Oranges: Which is better?

For some reason I believe ordering things has fascinated humans and modelled human reasoning for a long time. Why do we order things? Why the inherent craving for IQs? Why find a sense of achievement in transforming an art like gymnastics into Gold, Silver, Bronze and others? I'll skip all these questions for now and agree that for some reason we are hard wired to see things as an order.

The question then is how do you ensure such an ordering is fair? Can we order the orderings based on some criteria like fairness?

I hope everybody is familiar with the rules of the game of tennis. I propose a mild variation to those. If in a set both the players end up at 6-6 (6 games each) then instead of playing a tie breaker call the set a tied set and break it only when after five sets none of the players is leading. Now both my rules and the rules of tennis ensure a fair ordering (ATP points can be computed the same way) but which is better?

The other slightly more relevant case is that of search engines. Yahoo! or Google which is better? And tomorrow there is a new search engine which claims its results are better than both. On what basis can you believe?

Let us try to find as objective an answer as possible to this question. The possible ways to rank is large set is innumerable, in such situations can we ensure optimality or can we at least move towards it?

I'll try to post all the literature I came across which is pertinent to this post.


Side note: This has been a question which is not new to OSL I'm just echoing back some ideas discussed in the past. It is important for us to consolidate our discussion so that we can look back upon those ideas.

Another side note: One of my friends was great at ordering the world around him, he could even order his colleagues! I hope he shares his secrets here.
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Read August 12, 2008, 10:10:59 am #1
sids

Re: Apples and Oranges: Which is better?

For some reason I believe ordering things has fascinated humans and modelled human reasoning for a long time. Why do we order things? Why the inherent craving for IQs? Why find a sense of achievement in transforming an art like gymnastics into Gold, Silver, Bronze and others? I'll skip all these questions for now and agree that for some reason we are hard wired to see things as an order.
I think we humans have an intrinsic need to know that we understand things, understand them enough to be able to judge them. This need often overshadows better judgment (sic) and we give in to judging anything and everything. You can still define certain objective parameters against which gymnasts can be judged; but how in this world do you judge art? It is one thing to have an opinion and even express it, but to say "X is better than Y, period" is totally not called for. Who is better: Michelangelo or Picasso or Husain? Mozart or Beethoven or Metallica? Yes, I'm sure you've an opinion about these, as do I. But please try not to impose your opinion on me -- I promise to reciprocate.

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The question then is how do you ensure such an ordering is fair? Can we order the orderings based on some criteria like fairness?
I do not have an answer, I do have a couple of questions though. Why should we be fair? What is fairness in this context?

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I hope everybody is familiar with the rules of the game of tennis. I propose a mild variation to those. If in a set both the players end up at 6-6 (6 games each) then instead of playing a tie breaker call the set a tied set and break it only when after five sets none of the players is leading. Now both my rules and the rules of tennis ensure a fair ordering (ATP points can be computed the same way) but which is better?
The variation you propose is quite interesting! But I think which is better is quite subjective -- depending to a large extent on the playing style of the players.

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The other slightly more relevant case is that of search engines. Yahoo! or Google which is better? And tomorrow there is a new search engine which claims its results are better than both. On what basis can you believe?
We need to start by defining what better means. If better means that the user's need is fulfilled by a higher ranked result, for example, there exists a simple statistical method to go about the ranking; this could probably be objective to the extent possible.

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Side note: This has been a question which is not new to OSL I'm just echoing back some ideas discussed in the past. It is important for us to consolidate our discussion so that we can look back upon those ideas.
For those not familiar with it, OSL stands for Open Systems Lab at IIIT Bangalore. It is run by sri and a lot of us on this forum have been there or still are. http://osl.iiitb.ac.in/

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Another side note: One of my friends was great at ordering the world around him, he could even order his colleagues! I hope he shares his secrets here.
Do I know this friend? Tongue


http://www.grok.in/
"Ignorance killed the cat, curiosity was framed."
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Read August 12, 2008, 03:59:39 pm #2
sanket

Re: Apples and Oranges: Which is better?

Ordering is a sophisticated level of classification. Classification is natural. Early human beings must have, among other things, classified things they find as edible or inedible. Then, as eating habits evolved to be more sophisticated further classes would have evolved. People then may also have found some things good and some not as good. Among the good, some that one likes to eat more often, and some less often. And so on. As the world became more complex, people grew comfortable with judging, classifying and ordering. It makes things easy.

Aditya said:
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If in a set both the players end up at 6-6 (6 games each) then instead of playing a tie breaker call the set a tied set and break it only when after five sets none of the players is leading.

Well, the way the game of tennis is structured is such that at every level, the winner has to be decided. Every match is a knock-out; every set has to have one winner; every game has to have one winner (why not tied games?). So, while your suggestion is fair, it is not in accordance with the structure of the game.

And regarding the search engines, as Sids said, the benchmarks have to be decided first.
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