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In lugnet.admin.general, Shiri Dori writes:
> Great! I like this and agree to the reasoning, 'specially the sqrt part of
> more people voting influencing more.
Oh -- while I was out grocery shopping I just realized this:
What is sqrt(n)? It's nothing more than a fancy way of writing n^(1/2).
So: What if the exponent didn't have to be exactly 1/2, but instead was
allowed to vary? Then what dynamics arise? Well, first some definitions.
Let n be the number of votes; let V[1], V[2], V[3], ..., V[n] be a set of
votes; and let s be the sum from i=1 to n of V[i].
Now define a scoring function W(s,n,a) = s / n^a, where a is a non-negative
real number. Now here's the cool part: What happens with different values
of a?
If a = 0, then we have W = s / n^0 = s / 1 = s, or in other words a simple
pure summation. This produces arbitrarily large scores (positive or negative).
If a = 1/2, then we have the sqrt(n) function described earlier. This also
produces arbitrarily large scores, but this time they're dampened by the
sqrt(n).
If a = 1, then we have W = s / n^1 = s / n, or in other words a simple classic
average. This produces scores always within the unit interval [-1,+1].
And if we set a to be a number between 0 and 1/2, what we get is something
between a pure summation and a sqrt(n) dampener -- less dampening, in other
words.
And if set a to be a number between 1/2 and 1, what we get is something
between a sqrt(n) dampener and a classic average -- much more dampening, in
other words.
Still other interesting things happen with a < 0 and a > 1. With a > 1, the
dampening becomes so strong that increased voting actually decreases the
resulting score -- bringing relatively less-voted-upon items into the
limelight. And with a < 0, the dampening becomes so weak that it becomes
an "un-dampener," resulting in inflated summations. (Recall that dividing
by n^-a is the same as multiplying by n^a.) So for -1/2 < a < 0, the inflation
is mild, and for -1 < a < -1/2, the inflation is strong, and for a < -1, the
inflation is ultra-strong.
Anyway...the point is that just by adding a single member-configurable
preference (the exponentiation variable, with a default of a = 0.5),
a whole bunch of different curve behaviors could be had, almost for free,
and the coolest and most useful of these being a = 0, a = 1/2, and a = 1.
> Channels? Huh?
http://www.lugnet.com/admin/general/?q=channels+rss
--Todd
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Message has 1 Reply:
 | | Re: Article scoring
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| Upon more reflection, I'm thinking that the "square-rooted-average" sum(V,1,n) w = ---...--- sqrt(n) isn't so great afterall. Its biggest plus is that it distinguishes nicely between sets of votes which have the same average and a different number (...) (25 years ago, 6-Mar-00, to lugnet.admin.general)
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Message is in Reply To:
| | Re: Article scoring
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| In lugnet.admin.general, Todd Lehman writes: <interesting (to me) yet long techie details snipped> Great! I like this and agree to the reasoning, 'specially the sqrt part of more people voting influencing more. (...) ;-) (...) I agree, cool! (...) (...) (25 years ago, 4-Mar-00, to lugnet.admin.general)
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