Question

I have a couple systems which contain a users’ table along with some form of karma/weight/reputation. Sometimes it’s the number of posts a user has made, sometimes it’s the number of up/down votes a user has received across all their activity on the site.

USER {
    id int
    name string
    karma int
}

How do I use these numbers to calculate that user’s “weight” or “authority”? For example, the vote of one long-time member is often worth much more than 4 votes from brand new users.

I was thinking about adding up the total points/karma/reputation of all members and then trying to come up with a 1-100 scale.

SUM(user.points) / COUNT(user.*) = average user points

Then something like

CEIL(userA.points / average user points) = their weight on an issue

However, there also needs to be a curve on the points this way as I don’t want someone with 5,000 posts/karma to out weigh 20 new users votes.

Answer 1

Mathematically, your best bet is to weight by the log of the percentile ranking of user in question. However, that is painful in SQL.

Simpler would be to cheat and assume the mean is the same as the median (a very bad assumption statistically, but much simpler programmatically):

 SELECT 1 - log10(SELECT COUNT (*) FROM user 
 WHERE (SUM(user.points) / COUNT(user.*)) < user.points)  
 / SELECT (COUNT (*) from user))

In this way, your top 10% of karma would have one and a half the impact of your average user, almost twice the impact of a noob.
Changing the log base would scale this, obviously, where natural log (log() in mysql) would give the upper 10% 3 times as much impact as a noob, and twice the impact as average. Log2() is even more extreme. (Note: subtraction is required because the log will be negative.)

If you want a more severe effect you might try squaring the log. (Note: squaring makes the log squared positive, so addition is appropriate here.)

If you want a hyperprecise rule, you can go into standard deviations, but the sql gets cumbersome and slow. It all depends on how far down the rabbit hole you want to go….