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Is the distribution of net votes to questions or answers on Stack Overflow modeled by a power law?

In other words, if you ranked all questions by score, are there (roughly) x times as many at rank i than there are at rank i-1?

Say that questions with 237 upvotes are at rank 5 on Stack Overflow, and there are seven questions with 237 votes. Then, at rank 6 (with, say, 235 votes) there would be 7x questions (for example, 12 questions).

Does anyone know the values of x, or whether a power law models the distribution of upvotes to questions / answers on Stack Overflow?

This is relevant beyond being statistically interesting. It's possible that we could use this information to enact policies that will deal with "gaps" in the long term. When power laws (as opposed to other kinds of laws) apply, posts with high scores attract disproportionately high numbers of votes over time than posts with lower scores. Is this what we really want? What policy could affect this? Maybe a vote cap, or a "tiered upvoting" system wherein posts with high scores could only be upvoted further by users with high rep?

Personally, I would like to see the effect of amplifying the power law... i.e. giving more preferential position to higher-ranking posts. But maybe that's because I like experiments.

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Migrate to Cross Validated or Mathematics? =) –  casperOne Feb 15 '12 at 19:32
    
thnks :P now I found another place to become a member –  Cris Stringfellow Feb 15 '12 at 19:33
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Possibly a question that can be answered through the Data Explorer? –  Charles Feb 15 '12 at 19:34
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This blog post entitled Power Laws may interest you. :) It's a shame there was never a follow-up with more data. –  Jeremy Banks Feb 15 '12 at 20:14
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When I saw this question's title, I expected an angry, semi-coherent rant about some moderator decision you didn't like. The actual question was a pleasant surprise. –  Pops Feb 15 '12 at 20:44
    
@PopularDemand I was afraid, admittedly... –  casperOne Feb 15 '12 at 20:45
    
Context for my earlier comment: this question's original title was "Power law in operation on stackoverflow." –  Pops Feb 15 '12 at 21:36
    
Clarification on rank. Assume the top three questions score are (237,237,236) what is their rank. (1,1,3);(1,1,2); or (1,2,3)? –  Some Helpful Commenter Feb 15 '12 at 21:52
    
ooh data explorer.i'll look into that –  Cris Stringfellow Feb 16 '12 at 8:07
    
@PopularDemand that's really funny. –  Cris Stringfellow Feb 16 '12 at 8:07
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@CrisStringfellow yeah, but it gets less funny by the time you're reading your 20th such post. –  Pops Feb 16 '12 at 13:40
    
@ConradFrix it's either of the first two you gave. –  Cris Stringfellow Feb 16 '12 at 16:54
    
@PopularDemand yeah, "Power Law in operation" would be a pretty crazy rant. but i also meant it is funny to me that my title suggested that interpretation...i didn't expect that. The new title is a better title. I just read your edits. They are good. –  Cris Stringfellow Feb 16 '12 at 16:59
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1 Answer

up vote 16 down vote accepted

Well, someone is probably going to kill me (The query took ~20 seconds), but I did a query to sum this up on the Data Explorer. For the reference, this includes both questions and answers, I'll try it again some other time with just questions. Here's the plot:

enter image description here

And the same plot as a log scale:

enter image description here

So, it looks to me that this isn't quite a power function, but something a bit different. Just for reference, the highest peak is at 0, with 3,227,172 questions/answers that haven't been upvoted even once.

For reference, here's the log plots of a few other sites, which do seem to better follow the power distribution.

Science Fiction and Fantasy

Gaming

Super User

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that's great. certainly has a very looong tail. the effect is even more pronounced at lower ranks, like a power law with scaling. –  Cris Stringfellow Feb 16 '12 at 8:11
    
between the region of say 128 down to 64 votes it does seem to follow a 10x power law. then there's a threshold at novotes like a sink or attractor they will never escape. Above 300 they seem to be on a trickle-flow converybelt to ever high ranks. between 128 and 300 it seems like the mountains of moderation (by votes). if you get to there you can keep getting shunted up, but there's definite preferences. and below 64 it's like the market is optimally efficient at deciding the value of a post. nice graphs plus comparisons. –  Cris Stringfellow Feb 16 '12 at 8:20
    
just a side note there's only 2.6 Million questions so 3,227,172 questions that haven't been upvoted even once. isn't right. Perhaps you should add where posttypeid = 1 if you want to limit your results to just questions. Alternatively you could just edit your answer. –  Some Helpful Commenter Feb 16 '12 at 15:31
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Hmmm, good point, mixing questions/ answer. I'll edit my answer for now, and try to do it right later... This was my first attempt at a data query, so... –  PearsonArtPhoto Feb 16 '12 at 15:40
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In case you're interested here's a fairly up-to-date description of data.se schema. –  Some Helpful Commenter Feb 16 '12 at 15:51
    
If you want you can try this query. It uses rank instead of raw score and limits it to questions but it still produces similar output to your original query. I think that the curve follows f(x) = k^x. I'm not a stats guy so I have know idea if that is meaningful or not. –  Some Helpful Commenter Feb 16 '12 at 17:18
    
@ConradFrix: I just fixed my scripts instead to do the right thing. It runs a bit quicker now:-) I'll update the charts later, right now I'm a bit in the middle of stuff, so... –  PearsonArtPhoto Feb 16 '12 at 17:40
    
@ConradFrix nice work on the additional query. –  Cris Stringfellow Feb 17 '12 at 5:00
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