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Another unmeasurable distance is ★★★ movie ratings.

Movie ratings are drawn from the set {★,★★,★★★,★★★★,★★★★★} and related by the total ordering >:

  • ★★★★★ > ★★★★
  • ★★★★ > ★★★
  • ★★★ > ★★
  • ★★ > ★

and the transitivity of > gives the rest of the relations.

TWO PLUS TWO ≠ FOUR

However ★★★★ is not the same thing as 4, because 4 comes with all the baggage of being an integer. Baggage like the usual metric whereunder

  • |42| = 2,

whereas |★★★★−★★| ≠ ★★.

If one naïvely assumed {★,★★,★★★,★★★★,★★★★★} ≅ {1,2,3,4,5}, that would mean

  • |★★★−★|  =  |3−1|  =  |★★★★★−★★★|  =  |2|.

Which would be wrong.

HOW I THINK PEOPLE USE ★★★ RATINGS

There’s no reason to believe that the distance between ★★★★★ and ★★★ is 2 or that it’s the same distance as between ★★★ and ★. I believe there is a wider gulf between ★★★ and ★ for most people.

It depends on the person but creo q’ a lot of people basically only use three, four, and five stars. Mostly they just use four and five stars because they only watch movies they like.

Then when faced with two choices (★★★★ versus ★★★★★) they may think back to other movies they’ve rated, and wish they had a finer scale of gradation, or just something else to say about them — like in an orthogonal direction.

People use ★★ and ★ but not no creo very judiciously. It’s kind of like the hotness scale … but that’s another topic.



WHAT’S NEXT

I actually have a long, in-depth critique of the ★★★★ system—which also suggests better ways to do surveys in general. But I’ve gone on too long already so let me just preview that critique by saying:

Bad data in, bad recommendations out. Don’t blame yourself, Netflix Prize contestants.

PS: Really wanted a subjunctive mood while writing this. Thanks a lot, English Language. Not.

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