[HN Gopher] Preston's Paradox
___________________________________________________________________
Preston's Paradox
Author : sebg
Score : 42 points
Date : 2022-05-16 17:50 UTC (5 hours ago)
(HTM) web link (www.allendowney.com)
(TXT) w3m dump (www.allendowney.com)
| bo1024 wrote:
| There is an extremely important difference between "every woman
| has fewer children than her mother" and "on average a woman has
| fewer children than her mother".
|
| You can see that in the first scenario the human race dies out in
| about 12 generations as the maximum possible number of children
| any woman can have decreases by 1 each generation.
|
| The second scenario is easily compatible with sustained long-term
| population growth. For example each woman initially has four
| kids, two of whom are childless and two of whom have four kids,
| etc. This doubles the population each generation but on average a
| woman has half as many children as her mother (two fewer).
| dmurray wrote:
| It doubled in the first generation (one woman and presumably
| one man produced four kids)
|
| In the following generation, the population didn't increase.
| Four people and their four partners collectively produced eight
| kids.
| RcouF1uZ4gsC wrote:
| > Preston concludes, "Those who exhibit the most traditional
| behavior with respect to marriage and women's roles will always
| be overrepresented as parents of the next generation, and a
| perpetual disaffiliation from their model by offspring is
| required in order to avert an increase in traditionalism for the
| population as a whole."
|
| This has huge political implications.
| pixl97 wrote:
| This is why most religions are actually fertility cults of one
| type or another. Disobey the fertility cult and you get the
| Onan treatment.
|
| Also this explains why many religions staying power. "Have lots
| of kids and teach them your religion".
| jimhefferon wrote:
| Interesting and new to me, at least.
|
| There is no place I can see to give feedback. Perhaps the author
| reads HN?
|
| > how many children they have ever born
|
| Surely "borne"?
| ars wrote:
| In American English "born" means given birth to, while "borne"
| means physically carry something (possibly a child, but not
| necessarily).
| ziddoap wrote:
| In regards to children, as in giving birth, "born" is correct.
|
| > _Both born and borne are forms of bear. Born is commonly used
| with the sense of bear meaning "to give birth." Borne is used
| in reference to carrying something (physically or figuratively)
| [...]_ [1]
|
| https://www.merriam-webster.com/words-at-play/borne-vs-born-...
| gweinberg wrote:
| 'and, occasionally, in the "give birth to" sense.' Odd choice
| of words to elide.
| ev7 wrote:
| "Birthed" might be the correct version.
| gweinberg wrote:
| I think it's actually pretty well known that with a stable
| population there are always a lot more people with fewer kids
| than their parents have than there are people with more kids.
| After all, a decent fraction of people never have any kids at
| all, but everyone's parents had to have at least one.
| readthenotes1 wrote:
| Paradox, or just pointing out human inability to multiply?
| SamBam wrote:
| Not really a paradox, but also not intuitive.
|
| If the average number of offspring were 3, and also _every
| woman_ had exactly 3 children, then mandating that every woman
| has one fewer children than her mother would stabilize the
| population in one generation, and wipe it out shortly after.
|
| The "paradox" happens because of the skewed distribution of
| family sizes.
| [deleted]
| ffhhj wrote:
| Maybe the king should have said "1 less _factorial number_ than
| the mother ".
| swframe2 wrote:
| I wonder if there is a more important paradox "wealthy people
| trying to increase their wealth will influence government laws so
| extremely selfishly that the world will suffer a catastrophic
| event that drastically lowers human population."
| daxfohl wrote:
| Side note is that if the rule is to have exactly the same number
| of kids as your mom, then the average asymptotically approaches
| the woman of the first generation who has the most kids.
|
| So the king did better than nothing.
| ReactiveJelly wrote:
| I missed the part where the paradox was explained.
|
| If every woman goes from having 3 children to 2, why did the rate
| go up?
| Strilanc wrote:
| Suppose there's 1 woman who had 10 kids, and everyone else had
| 3. Everyone then has max kids according to the "1 fewer than
| mother" rule. After 5 generations that 1 woman has 10 * 9 * 8 *
| 7 * 6 * 5 = 151200 descendants that will each have 4 kids.
| Everyone else went extinct several decades ago. So the average
| number of children per woman increased from 3 to 4.
| B1FF_PSUVM wrote:
| Because of the shape of the distribution.
|
| Those who had >= 4 were sufficiently numerous for the second
| generation going to 3.3.
|
| P.S. also, further iteration is not discussed. Possibly the
| average for that particular curve would come down on the second
| or third generation.
| daxfohl wrote:
| Imagine a population of 2 women, one who has 2 children and one
| who has 100. Average is 51. Next generation 2 women have 1
| child each and 100 women have 99 each, so the average is about
| 98. Eventually it will go down to zero, but initially it goes
| up.
| alcover wrote:
| You're supposing they bear females only ?
| daenz wrote:
| Because every woman didn't go from 3 to 2. The average was 3.
| Some families had 10 and went to 9.
| redavni wrote:
| To the young people here. Ignore the last line in the article.
|
| You should never ever allow statistics at this level impact your
| decision to start a family. If you are intelligent enough to be
| reading an article about statistics on the Internet, please
| reproduce.
| cryptonector wrote:
| This. We're already facing large reductions in population
| world-wide due to low fertility. Sure, the overall turning
| point is a few decades away, but it's certain, and in many
| countries it's in the past.
| sidpatil wrote:
| Aren't you just citing different statistics?
| ACow_Adonis wrote:
| when we say the overall turning point is a few decades away,
| under most assumptions that don't involve massive war or
| pestilence or ecological collapse, even with a substantial
| drop in fertility, my child(ren), by the time they are old,
| will still be living in a world with higher total population
| than the current one.
|
| we are basically in no risk of running down the population
| within any of our lifetime...
|
| ... on the proviso that everything doesn't go pear- shaped.
|
| And with a recognition that those risks of things that might
| go pear-shaped are probably highly correlated with the
| carrying capacity of the planet with regards to human
| population numbers.
| toolz wrote:
| I don't have any good answers here, but it would seem that a
| negative consequence of welfare for lower income classes would
| have them disproportionately incentivized to have children (as
| their welfare would represent a much higher % of their total
| income). With this being the case I have to imagine that's a
| large contributing factor to associating large families with
| lower income and thus it loses the former advantage of large
| families being a high status indicator and thus higher income
| (and presumably higher intelligence/ better adjusted) families
| were responsible for a larger percentage of the population.
|
| I have no idea what a humane incentive would look like, but I
| do wonder if we could find one if giving higher income families
| more incentive to reproduce relative to lower income families
| (or more directly I'd want to incentivize higher intelligence
| and better adjusted families, I just don't know how to measure
| that so I use income class to differentiate).
|
| Presuming in all of this, that it isn't controversial to want
| intelligent and adjusted people to be responsible for the lions
| share of genetic makeup of future generations.
| cryptonector wrote:
| Or, you know, reduce welfare and help people get off welfare.
| whatshisface wrote:
| Well, I guess eugenics is back... It was a nice 100 years.
|
| Scary "Idiocracy" figures aside, this discussion is
| incomplete without the incel statistics. The data is
| relatively conclusive that anyone below a certain threshold
| has no chance of getting a date - which should be included in
| your long-term model of population planning. I think you will
| find that all the eugenics you could possibly want is already
| happening, the "program" is being administered by everybody,
| and the social norms that permit it are unimpeachable.
| lr4444lr wrote:
| It has little to nothing to do with genes. You want a
| productive working class that produces more than it
| consumes to support the people who - for whatever reason -
| do not.
| cryptonector wrote:
| You could provide incentives to those who would rather
| not produce to straighten up and fly rite.
| JadeNB wrote:
| > You should never ever allow statistics at this level impact
| your decision to start a family. If you are intelligent enough
| to be reading an article about statistics on the Internet,
| please reproduce.
|
| I think that reading articles on advanced topics on the
| internet at best demonstrates one's self-assessed, not actual,
| intelligence. There are more than enough people in the world
| who are sure that they're the smart ones.
| umvi wrote:
| So the _average_ shifts slightly up in the short term because of
| whales, but the population still will trend to zero in the long
| term. Not really a paradox, just a slightly unexpected short term
| statistical anomaly.
| renewiltord wrote:
| Ah, if a^i_t is the number of children in the t'th generation in
| the i'th 'matrilineal line': a^i_t = 0.5 *
| k^i_t * a^i_{t-1} * (k^i_t - 1)
|
| Fertility rate has a quadratic relationship with number of kids
| per woman, since half the kids will be women capable of kids
| themselves. Whatever, my superscripts are fucked, but the idea is
| that the relationship being quadratic means high-birth women are
| going to be much more influential than low-birth women and so
| linear measures of central tendency don't capture that.
|
| Cool.
___________________________________________________________________
(page generated 2022-05-16 23:00 UTC)