[EM] Part 2, Meet Warren Smith

MIKE OSSIPOFF nkklrp at hotmail.com
Tue Jan 16 00:59:36 PST 2007

From: "MIKE OSSIPOFF" <nkklrp at hotmail.com>
To: nkklrp at hotmail.com
Subject: Warren EM 2
Date: Tue, 16 Jan 2007 07:57:31 +0000

Warren said:

well, you never showed us your math, but it is obvious
to me that you messed up
for several reasons

I reply:

I repeately gave instructions for the derivation of the formula for 
Bias-Free. But let me repeat it here again:

The idea is to make s/q  (combined seats/combined quotas) equal to 1 in each 
cycle. A rounding point is to be chosen to accomplish that.

Assuming a uniform state-size frequency distribution, integrate s/q - 1 over 
the cycle.Set the result equal to zero. Solve for R, the roiunding point.

If it's necessary to spell it out in more detail, in the cycle that goes 
from integer a to integer b, with rounding point R: In the part below the 
rounding point, s = a. So s/q - 1 is a/q - 1. Integrate that from a to R. In 
the part above R, s = b. So s/q - 1 = a/q - 1. Integrate that from R to b.

Set the sum of those integrals equal to zero. Solve for R.

Now, hopefully Warren will stop referring to the "myterious b^b/a^a 
formula", and claiming that it's incorrect due to ilgnorance of its 
derivation. But, Warren, I'm not going to hold your hand and walk you 
through the actual work. I've described it well enough.

Mike Ossipoff

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