[HPforGrownups] Wizarding numbers: 24 000

[Robert Shaw]

No: HPFGUIDX 83197

Mikael Raaterova wrote:
> To summarize my findings below:
>
> - About 30 percent of Hogwarts students are muggle-borns
> - No more than half of the 11-17 years old wizard-borns in the British
> isles attend Hogwarts
> - The wizarding population is about 24 000 (bounded at 20-30 000)
>
[Reasoning snipped]
>
> Feel free to poke holes in my reasoning. I'm not entirely convinced
> that my attempt holds up to scrutiny, but i don't think i made any
> glaring errors.
>

I'm a mathematician, not a sociologist, but your reasoning looks
sound, given your assumptions.

Having only 50% of wizard-borns at hogwarts is unexpected
(which shows you haven't been fudging your numbers) but is
not incompatible with canon.

Mikael also wrote (in reply to me)
>
>> As an aside, much of that increase is actually due to immigration.
>> How do wizards deal with that?
>>
>> The Hogwarts' quill records the names of wizards born within range,
>> but Indian muggle-borns whose parents have just immigrated will not
>> be listed.
>
> And will thus not get a magical education nor become wizards. Hence
> they won't affect the wizarding population.
>
It means that the muggle population from which muggle-borns can
be drawn is smaller than the raw census data indicates, though
only by a few percent,  reducing the number of muggle born wizards
by the same percent.

It's also possible that the percentage of muggle-borns in the
immigrant population is different, just as the percentage of
red-heads is, and for much the same reasons. While there's
no evidence for this, it wouldn't be surprising.

This is one of many possible small corrections to your model.
Since they are unlikely to all be in the same direction they don't
alter the mean prediction, but they do widen the error range
somewhat.


I asked:
>> Does the Ministry hunt down immigrant muggle-borns, and notify
>> other countries of emigrants, or do the muggle-borns in such families
>> slip through the cracks?
>

Mikael replied:
> Why would the MoM care about non-listed magical muggle-born children?
> If the Hogwarts quill don't register them, they don't exist.
>

Presumably for the same mix of reasons as any muggle-borns are admitted
to
Hogwarts.

Untaught wizards would keep having magical accidents, which are a public
nuisance. Dark wizards might find it easy to recruit the untaught as
cannon-fodder.
Some wizards might be offended by the notion of potential wizards
(members
of a superior breed) being forced to live as mere muggles.

>
>> If the ministry lost track of many muggle borns during the
>> mass muggle migrations of the last centuries this could have
>> a significant impact on wizarding demographics.
>
> Possibly. Migration don't affect the muggle population in any
> dramatic way,

Most of the time.
>From memory, in the 1800's over a third of the muggle Irish
population emigrated.

In some of the British ex-colonies there have been times when
more than half the population were first generation immigrants.

 Mikael claimed:
> Changes in muggle numbers have to be *huge* to affect the number of
> muggle-born wizards.
>
> Robert Shaw replied
>> The change may be huge, but since the muggle population is also
>> huge this cancels out.
>>
>> A 5% change in muggle numbers will produce a 5% change in
>> muggle-born numbers, to a first approximation.
>
> To take Robert's last point first, a 5% change in muggle numbers will
> produce a comparably *smaller* change in the numbers of muggle-borns,
> given the longevity of wizards, muggle-born or otherwise.
>
To clarify, I meant the number of wizards born to muggles in the
year in question, not the total number of muggle-borns.

> As to the first point, I need to clarify myself. I *should have* said
> "Changes in muggle numbers have to be really, really huge to affect
> the number of *wizards*" (i.e. not only muggle-born wizards. This
> makes a difference, see below.
>
Hugeness is relative. (A mountain looks huge next to me, but
small next to the earth.) Talking percentages is more objective.

I agree the percentage change in muggle-born numbers is
smaller than that in muggle numbers, but it is of the same
order of magnitude.


Mikael also wrote:
>
> If we look at muggle birth numbers (actually, UK birth numbers) over
> the last hundred years, the *maximum* fluctuation for *any*
> consecutive seven-year period deviates from the mean by only 20 %
> (this including effects of migration, to boot). Assuming that wizard
> birth numbers vary as much, my estimate of wizarding numbers of about
> 24 000 is bounded at 20 or 30 000 (assuming my die-off model is
> reasonably accurate).
>
Which is to say 24,000 +25%/-16%

Those are decent error bounds,  but there is still quite a lot of leeway
within them.

>
> Whew. If you managed to wade through this delusional demographic
> debate to the bitter end, you have my deepest respect.
>
The bitter end? We've barely scratched the surface of this topic.
For a full discussion we'd need to pull out the partial differential
equations, and brush up on our statistics.

Still, intelligent debate is always fun, even with the gloves on.

Despite the unsoundness of some of your assumptions, I think at
least half your conclusions are at least half right. You can assume I
mostly agree with everything I cut.

--
Robert