### Re: Tipping the Balance

by beth (Scribe)
 on May 13, 2004 at 07:10 UTC Need Help??

in reply to Tipping the Balance

Your model is too simple. Consider these facts:
• a good post will get a lot of upvotes (so far so good)
• a good post will be prominently placed (say it makes the front page) and so its peak vote-gathering time lasts longer than that of a mediocre post
• a post's rate of accumulating votes changes over its lifetime: it gets some votes at the beginning as people notice it; a lot of votes in sort of a "peak" stage; and then the number of votes per day begins to die off in what must be an exponential function (the same kind of function that governs, for example, a hot potato cooling off after it's removed from the oven). The votes/day asymptotically approaches zero.
• Posts are made at different times, so their curves overlap.
Consider this graph:
```

|      .
|    . 	   .
|   .  	      .
|  .  	       .
|    	         .
|      	       	   .
| .    	       	      .
|  		          .
|. 		       	       .
|__________________________________.___.____._____

Fig 1. Popularity curve of a single post

(b)
|  		   .  .
|      	         .     	 .
v|    (a)      .	       	    .
o|      .    .  	              .
t|    . 	   .   	     	       .
e|   .  	  .   .	       	(c)   	 .
s|  .  	 .     .       	  .    	    .
|    	         .      .    . 	        .
|      	       	   .           .       	     .
| .    	.      	      .        	   .	           .
|   		          .            .       	       .
|.     .	     . 	       .           .
|__________________________________.___________._______
t   i   m   e   -->

Fig 2. Overlapping curves for a moderately popular post
(a), a very popular post (b), and a minorly popular post
(c).

```
OK, so the ascii art kinda lost something in translation. Hopefully this gives you some idea of the mathematics of what you're up against. Note also that we were talking about "rates" and "accumulation", which suggest derivatives and integrals, respectively (but mostly integrals). You seem to be considering only the range at the end of all these curves, where the votes/day is close to zero, and it may be possible to do a linear approximation here. However, unless you are truly lazy (which maybe you are!) you will probably continue to make new posts at some frequency which should also be considered, so you would have to have at least a rough model of these exponential curves.

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Re: Re: Tipping the Balance
by Fletch (Bishop) on May 13, 2004 at 14:34 UTC
OK, so the ascii art kinda lost something in translation.

Oh yeah, I see it. It's a sailboat.</Mallrats>

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