Reputation statistics and chaos theory

After a few hours here on Stack Overflow, I began to ask myself some theoretical questions related to reputation scores and total number of reputation points distributed by the system. It seems that the basic rules are:

• You'll get +10 reputation points each time your answer is clicked up
• A clicked down answer is -2 points for the answerer, -1 for the clicker
• There might be other scoring rules that I did not fully identified (selected answer, favorite question, etc) but which are less important.

Can we anticipate/foresee the total number of reputation points in relation with activity/number of users (being for example an increasing function)?

Or, is this function (being of total number of reputation points) erratic and leading to non-predictable and chaotic results? In this case we would be facing a good example of deterministic chaos, where fully deterministic initial conditions (here the scoring rules) can lead to unpredictable results.

Tiebreaker:

• Which conditions would yield negative values?
• What would be the consequences of generalised individual negative scores when you know that:
1. You need to have at least 15 reputation for up-votes and

Can we imagine a situation where all users are below 15, meaning that newbies cannot distribute or collect reputations?

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Down-click is -2. – MusiGenesis Oct 24 '08 at 14:38
Isn't it what I said? -2 for the clicked and -1 for the clicker – Philippe Grondier Oct 24 '08 at 14:42
yep - that's what he said :P – warren Oct 24 '08 at 14:48
The only one I can think of that you missed is +15 for an answer, and also the limit of 200 rep gain per day based on up votes (you still get your rep for answers being accepted no matter what), and +2 for accepting an answer. – Chris Marasti-Georg Oct 24 '08 at 14:51
And don't forget the limit of 30 votes per day. – CesarB Oct 24 '08 at 15:07
this site is definitely a strange attractor – Steven A. Lowe Oct 24 '08 at 15:49
A strange attractor as you said! I hope we'll get some answers by the stackoverflow team. – Philippe Grondier Oct 24 '08 at 17:41
There is +5 points for a +1 on your question – xanatos Aug 19 '13 at 14:32

Another partial answer is I do spend some finite amount of time moderating questions, and usually I upvote more than downvote, so I 'magically' create points. At the same time, one downvote means -3 points in the system, while one upvote means +10 points in the system. So the overall trend is towards some 'Ponzi point scheme' 8^)

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I am not sure about the Ponzi point ... what about if everybody gives points to everybody? Will the bigint values used for sum calculation be overflowed? – Philippe Grondier Oct 24 '08 at 17:50
The total number of tokens in the system is decoupled of the actual value in the system, because many wrong answers can be voted up, and points created... but without the good answers bubbling to the top. – florin Oct 27 '08 at 17:11

This questions me as well. Since we are dealing with a dynamic system wich depends on user input it might be usefull to model it with system thinking software such as Ithink.

With this software you can reconstruct the scoring model, set variables based on a year of stock overflow information (amount of questions, answers, ratios, etc) and run simulations predicting the score distribution.

Apart from this I think the stack overflow staff has a nice system that encourages answering questions, posting interesting questions and usefull commenting.

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I agree with the encourageing notation system. And it seems to work pretty well, as people are sticked to their scores! My next question will be about time/energy lost here and corresponding entropy creation! – Philippe Grondier Oct 24 '08 at 17:39

"Can we imagine a situation where all users are below 15, meaning that newbies cannot distribute or collect reputations?"

No, that's impossible. Much like Bill Gates couldn't possibly spend all the money he's made, you couldn't possibly imagine the amount of sabotage necessary to get Jon Skeet below 15 points. Even Tom Clancy couldn't dream that one up.

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I beg to differ. Once hacker got control over the database server, one single query will do the impossible: `UPDATE Users SET Reputation=1`. GO. Done, even Jon Skeet will have 1. ;-) – Shadow Wizard Aug 19 '13 at 14:25
Not for long... – StephenTG Aug 19 '13 at 14:26
@ShaWizDowArd That assumes SE doesn't back up their DBs at all... – Servy Aug 19 '13 at 14:32
@Servy smart hacker will nuke all backups as well. :-S – Shadow Wizard Aug 19 '13 at 14:33
Well, my answer was meant "within the guidelines of normal SO useage". In other words, even if a huge conspiracy developed to downvote all his posts, he still wouldn't run out of rep. Yes, someone could hack Bill Gates' bank account too, but that's not the same thing as spending it. – Johnny Bones Aug 19 '13 at 14:37

As a partial answer to "tiebreaker bullet the first", you can't have less than 1 rep. It's bounded so that no matter how often you're voted down, you can't go negative.

And you can't vote down if you're below a threshold, either (I think it's 100).

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Are you sure you can't go negative? But anyway if everybody is below the 15 reps level, nobody can vote for no one! How did this whole thing begin? – Philippe Grondier Oct 24 '08 at 20:50

I'll add in that you can't really plan it, as there is also a 200 point per day increase cap for upvotes....

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