Wizarding numbers: 24 000

[Mikael Raaterova]

No: HPFGUIDX 83315

Robert Shaw, replying to me;

> > 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.

Well, that's a relief. Of course, my assumptions may still be invalid, but 
that remains to be discussed...


>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.

Getting unexpected results is in itself not proof of non-fudging, but I 
didn't consciously bias my analysis.


> >> 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.

If emigrants reduce the population, and immigrants are ignored by the 
quill, then basing the analysis on live births would *overestimate* the 
number of muggle-borns, since some of the predicted muggle-borns would 
leave the british isles before they have a chance to enter Hogwarts while 
immigrating potential wizards don't get the chance.

Anyway, it's not "a few percent" in any case, according to the data I 
managed to find. Net migration to the UK (including Irish Republic, which 
would be within Hogwarts area) varies in the range of 100-300 000 in recent 
years, so relevant migrants are at maximum still less than 0,5%. However, 
only immigrants with children aged 0-10 are relevant to the issue, and the 
net migration to UK of children aged 0-14 (still including Irish Republic) 
varies between -19 000 to +14 000 during the last 30 years (though in 
recent years you seem to have a stable inflow of a few thousand children 
per year) . The rate of magical births to Muggles should be about 0,0073%, 
or about one muggle-born per 15 000 muggle births. So immigration is likely 
to add 0 muggle-borns, +/- 1, per year. If we assume stable inflow of a few 
thousand, then immigration would add a muggle-born every few years.

It occurs to me that the quill might not actually be able to distinguish 
between births and immigration, since both types constitute magical 
children suddenly appearing within its detection range. In that case, 
effects of immigration are entirely negligible, especially when the margins 
of error in my model are considered.


>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.

Fair enough. I'll buy that. In the light of what I said above, I don't 
think these sporadic non-registered children matter one whit, given the 
approximate nature of my model.


> >> 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,

Sorry, i meant to say *wizard* population.

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

Assuming, as always, that the wizarding population is fairly stable, then 
before the muggle population explosion that began in the late 1800s, the 
wizard-to-muggle ratio would have been much larger than it is today, and 
the small population of muggles (relative to today's sizes) would have 
added fewer muggle-borns to the wizard pop. Thus, I maintain that a third 
of the Irish emigrating in the 1800s wouldn't necessarily affect the wizard 
population in any dramatic way.

A little thought experiment to illustrate my point: Assume that we *halve* 
the number muggle-borns born over *fifty* years (which would correspond to 
a change in Muggle demographics of society-shattering proportions), using 
recent figures, e.g. going from 43 muggle-borns per year to, say, 23 per 
year. This would make a grand difference of 1 000 muggle-borns, ceteris 
paribus, or slightly more than a 4% decrease in wizard 
population.   However, some of the these missing muggle-borns would 
reasonably have had children. If wizards have their children between the 
ages of 20 and 40, and they have enough children to replace their own 
numbers, we can expect about 600 children and 100 grand-children not born 
during these 50 years. It would still amount to a total decrease in wizard 
population of *7 percent* and would change the proportion of muggle-borns 
in the population from 25 % to about 19 %. Now, if the loss of muggle 
fertility is perpetuated, the muggle population, and thus the muggle-borns, 
would quickly plummet to extinction, leaving the wizards (all of them 
pure-blood by then) to inherit the world.

While the wizarding population decrease wouldn't be linear (due to the 
knock-on effect of non-births), and thus would be most noticeable in the 
latter years, a 7% loss over fifty years is hardly dramatic. UK's 
population has increased 20% in the last 50 years, and while British 
society has changed quite a lot in that time, most of those changes have 
been caused by the increased mobility of individuals and advances in 
welfare and technology. Changes in size matters little to social change (as 
was demonstrated by Durkheim in his classic book Division of Labour, 
already in the early 1900s, which has not been disproven) unless the 
changes are big enough to sabotage the workings of the societal system. 
Halving muggle fertility would over time inflate the number of retired 
people (a huge drain on a welfare state's expenses, in terms of pensions 
and medical infrastructure) while at the same time slashing the 
productivity of the working force because it would only be half its earlier 
size. British society as we know it would collapse or change beyond 
recognition.


> > 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%

Yeah, yeah. Had I wanted to be pedantic, I would have said 19 200 to 28 
800, but I wanted to convey a sense of the general magnitude of the wizard 
population to our non-demographics-oriented audience (assuming we actually 
have an audience...) so I resorted to the magic of big, round numbers instead.


> > 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.

Sorry, I meant the bitter end of my long and complicated post, not the 
discussion.


>For a full discussion we'd need to pull out the partial differential
>equations, and brush up on our statistics.

The weakest point in the analysis is the die-off function. The inflexion 
point and slopes of the mortality curve is pure guess-work, since we have 
no indication whatsoever of how wizarding age-group mortality is 
differentiated, except that at high ages it has to be lower than for 
Muggles, or the ages of Dumbledore and Marchbanks would be impossible. 
Lowering the life-expectancy (124 in the model) decreases the wizarding 
population, and raising it increases the population. Tampering with the 
fraction of muggle-borns among the Hogwarts students also affects the 
wizard population. Putting conceivable limits to these two variables, we 
also limit the spectrum of possible wizarding populations.

If wizarding life expectancy at its lowest is roughly that of the Muggle 
world, we should expect the muggle-borns at Hogwarts to constitute 9 % of 
muggle-born wizards, and the wizard-born students to constitute 13,5% of 
wizard-born wizards assuming that half of the wizard-born students are 
half-bloods). Since Dumbledore is seen as old, I'd say that the upper limit 
for wizarding life expectancy is below his age. If so, we should expect the 
muggle-borns at Hogwarts to constitute 4 % of muggle-born wizards, and the 
wizard-born students to constitute 6% of wizard-born wizards (assuming that 
half of the wizard-born students are half-bloods). The deviation in muggle 
birth numbers over any 7-year period is 20 %, so I'd let the fraction of 
Hogwarts students that are muggle-borns vary from 25% to 36%.

We know that there are 1000 students at Hogwarts and that muggle-borns are 
25% of the wizarding population. Given the assumptions, this should limit 
the *possible* wizarding populations to be above 11 000 (when 25 % of 
Hogwarts students are muggle-borns, and they are 9 % of all muggle-borns) 
and below 36 000 (when 36 % of Hogwarts students are muggle-borns, and they 
are 4 % of all muggle-borns).


>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.

Wouldn't that make my analysis 75% wrong? Quip aside, which of my 
assumptions do you find unsound?

/ Mikael