What's an effective way of comparing orderings?

Asked Nov 28 '13 at 06:55

Active Dec 04 '13 at 03:20

Viewed 79 times

Given two orderings of some set of things, what's an effective way to quantify how similar the orderings are?

For instance, say I have the orderings

1 2 3 4 5
2 3 4 5 1

If I just use the number of elements in the right positions, I get that the two orderings are not similar at all, which I don't think is true. There must be a better way to quantify their similarity.

My intuition is that this ordering should take into account how many elements are displaced as well as how far the displacements are.

edited Dec 04 '13 at 03:20

asked Nov 28 '13 at 06:55

David Faux

3,425

How about the [1][Mann-Whitney $U$-test]?: [1][http://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U] – user99680 Nov 28 '13 at 07:00
1

how about you count the number of times you have to switch two Elements in order to get same ordering? – Robert.Sie Nov 28 '13 at 07:25
@user99680 About syntax for links in comments, see How do you cite a reference in a comment? or editing help. – Martin Sleziak Nov 28 '13 at 08:33
@David When you write orderings, do you mean permutations? If it is thecase, the tag ([tag:order-theory]) does not seem suitable for your question. Maybe you can use ([tag:permutations]). – Martin Sleziak Nov 28 '13 at 08:34
Good point. Thanks for that! Indeed, I mean permutations. – David Faux Dec 04 '13 at 03:20

What's an effective way of comparing orderings?

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