From: "Tim Rhodes" <proftim@speakeasy.org>
To: <memetics@mmu.ac.uk>
Subject: Re: Defection Rates and Classes (was Parody of Science)
Date: Mon, 16 Aug 1999 03:37:10 -0700
[Comments inline.]
Derek wrote:
>The terms Tim used:
>
>P = number of people in the professional class
>W = number of people in the working class
>Rp = the reproduction rate for individuals in P
>Rw = the reproduction rate for individuals in W
>D = defection rate across classes (as a decimal)
>
>The equations:
>
>P' = ( ( P * (1-D) ) * Rp ) + ( ( W * D ) * Rw )
>W' =( ( W * (1-D) ) * Rw ) + ( ( P * D ) * Rp )
>
>Some of the values used:
>
>Starting P = 100
>Starting W = 900
>Rp = 1
>Rw = 2
>D = 0.05
>
>As I said, run at least 30 or more cycles and tell me what results you get.
>I think you will be quite surprised.
>
>Derek:
>
>It does, as you say, stabilise, and often very close to the starting
>proportions. For instance for the values you suggest above, the population
>grows at a rate of 90% per generation (!!), but the proportion of
>professional classes is maintained at an equilibrium of close to 9.4% which
>is largely achieved (to 2 decimal places) within 6 generations.
>
>But what does D mean above? and what justifies using 1-D?
The (1-D) term above is simply derived from the math -- if D=0.05 (in other
words 5% of the workers children move up), obviously 100% minus 5% (or (1-
D) in decimal terms) of the workers children don't.
To break the equations I used down further for you:
D = the potion of a class whose children change class
(1-D) = the portion of a class whose children stay in the same class
therefore,
(( P * (1-D) ) * Rp) = the number of children from professional class
parents that will themselves enter the professional class in the next
generation (old money)
(( P * (1-D) ) * Rp) = the number of children from working class parents
that will also enter the working class in the next generation
(( W * D ) * Rw ) = the number of children from working class parents who
will enter the professional class in the next generation (new money, if you
will)
(( P * D ) * Rp ) = the number of children from professional class parents
who will enter the working class in the next generation.
Hence, my equations:
>P' = ( ( P * (1-D) ) * Rp ) + ( ( W * D ) * Rw )
>W' =( ( W * (1-D) ) * Rw ) + ( ( P * D ) * Rp )
> Surely you need
>to have several Ds, D-up which would be the drift of workers upwards, but
>this would have to be a variable rather than a constant, since it would
>depend on how many spaces are available in the professional classes.
D-down
>could be more of a constant, as there is always room for more poor people
>(in fact for simplicity we could set it to zero and ignore it).
As I said, this was just a little model I threw together to test an idea I
had about what you'd been saying. (And not some grand thesis project,
Derek! I've spent more time on this post already than I did on the original
model!!!) But yes, D could -- and of course should -- be broken down into
D-up and D-down terms as you suggest.
And if you get me a grant, I'd be more than happy to expand the equations
even further! :-)
>So how about?
>
>P'old_money = P * Rp ie. the self-replenishment of the existing
professional
>classes
>
>P'new_money = W * D-up ie. the number of workers moving up to fill the
>vacancies
Unless I'm mistaken, both these terms are already represented in the
equations above. (Without the "D-up" distinction, of course.)
>where of course P'total = P'old_money + P'new_money
Right.
>and D-up = P'new_money/W
???! Although this is true, what have you gained by this term and how would
you use it in the equations? Seems like you're at risk of getting circular
here -- or I'm not following you.
>and hold P'/(P'+W) constant at say 0.1
Interesting...
What would the term P'/(P'+W) represent exactly? Again, I don't understand
how you're using this term or what you gain by using it.
Have you tried this out yet Derek? What results did you get and what
equations were you using? It sounds interesting.
-Tim R.
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