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 04:28:38 -0700
Sorry, this line:
>(( P * (1-D) ) * Rp) = the number of children from working class parents
>that will also enter the working class in the next generation
Should read:
>(( W * (1-D) ) * Rw) = the number of children from working class parents
>that will also enter the working class in the next generation
-----Original Message-----
From: Tim Rhodes <proftim@speakeasy.org>
To: memetics@mmu.ac.uk <memetics@mmu.ac.uk>
Date: Monday, August 16, 1999 3:22 AM
Subject: Re: Defection Rates and Classes (was Parody of Science)
>[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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===============================================================
This was distributed via the memetics list associated with the
Journal of Memetics - Evolutionary Models of Information Transmission
For information about the journal and the list (e.g. unsubscribing)
see: http://www.cpm.mmu.ac.uk/jom-emit