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Ok, I'm working on an creating a fantasy island.

It plays in a similar time like the 17th to 18th century.

Everyone on the island has one job, so he/she can focus on it.

I estimated ~35 Jobs so far which I think are necessary.

Now, every citizen should have a partner, so my minimal population would be ~70, because some jobs require more than one. It's just a rough estimate.

But that doesn't account for deaths of those partners, or a sudden disliking of a couple.

So my question is:

What is the "minimal" population to ensure free(1) partnerchoice of the citizens?

This should factor in:

possible homosexualities

possible no partnership at all (for example the Seaman that does it in a brothel on mainland)

(1) Free means every citizen can in the longrun choose from 3 potential partners.(if this statement even makes sense)

I don't know if this is calculatable :(

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  • $\begingroup$ Alucard, you will need to define "free". "More than one eligible partner" - is this sufficient? $\endgroup$
    – Alexander
    Commented Oct 17, 2018 at 17:07
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    $\begingroup$ On this planet, 7.7 billion isn't enough for everyone to have free partner choice. We're still struggling with this problem. $\endgroup$
    – Mathaddict
    Commented Oct 17, 2018 at 17:09
  • $\begingroup$ @Alexander ah ok, i edit this to the question! $\endgroup$
    – SAJW
    Commented Oct 17, 2018 at 17:11
  • $\begingroup$ Remember that death can happen at any time. You need an active body to replace any single on of them. Those people will need employment and partners, and then there's the issue of children and the amount needed during this time to ensure you have enough of them when you reach adulthood. Hope this is helpful. Good news is children during that era can help out with certain tasks. $\endgroup$
    – BlindingLight
    Commented Oct 18, 2018 at 2:26

2 Answers 2

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There is no possible population which can possibly meet this criteria.

Proof:

  1. The population is finite. Call the size of the population (excluding the unpaired individuals) "P"
  2. P should be even in order for everyone to become paired. P=2n (where n is the number of couples)
  3. As couples pair off they are no longer available choices for pairing reducing the number of available individuals able to pair off by 2 per couple. Call "s" the number of paired couples.
  4. After a number of couples have formed, there will be P' = 2n-2s individuals left to be paired with each other.
  5. When s reaches n-2, then the number of individuals left is four: P'= 2n-2(n-2) = 4. If a couple is formed from this group (assuming they can agree) then they are the last ones to be paired with each individual having 3 options to chose from. The last two people who wish to be paired must be paired with each other as they will have no other options to chose from.

QED

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  • $\begingroup$ actually that points out a flaw in my thinking! $\endgroup$
    – SAJW
    Commented Oct 17, 2018 at 21:31
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    $\begingroup$ Sweet! Reductionism for the win! $\endgroup$
    – Mathaddict
    Commented Oct 17, 2018 at 21:44
  • $\begingroup$ Suppose that the four people who are the must disgustingly unattractive all have high standards and are not willing to accept each other, and also no one else will accept any of them. Then there will always be a pool of at least 4 potential partners that any single person has available. They aren't really available since none of them are acceptable, but the official criteria are satisfied. $\endgroup$
    – J Thomas
    Commented Oct 17, 2018 at 21:47
  • $\begingroup$ This assumes a strictly sequential process of mate choice, and is not necessarily true. Consider the last step, with four people left unchosen. If two pairs form simultaneously (as in, for instance, they form during a party and then proceed to consumate seperately), your demonstration fails. Assumptions need to be stated. $\endgroup$
    – WhatRoughBeast
    Commented Oct 18, 2018 at 1:49
  • $\begingroup$ Thank you for this answer, this not only helps me with worldbuilding the creation and visualization of colonies, but gives me hope about my prospects in this world :D $\endgroup$
    – BlindingLight
    Commented Oct 18, 2018 at 2:22
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Let's assume that finding a mate would be the most difficult for homosexual individuals (among the listed in question.)

According to Demographics data, homosexual comprise about 4% of general population. To meet the "3 potential partners" requirement, the bare minimum size of demographic basket is 4. 4 men and 4 women means 8 people total. 8 is 4% of the population, so the total number is 200. This is assuming that everyone on the island is a fresh off the boat, with no children, no families and no commitments.

If we want to limit eligible population to childbearing age, the total number would go to 400. If we want to go further and limit the population to unmarried young people, the number will go over 1000.

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  • $\begingroup$ Er, I don't think what you're discussing would be a "mate". Nor would they ever be "childbearing". $\endgroup$
    – workerjoe
    Commented Oct 18, 2018 at 0:50
  • $\begingroup$ @Joe - Your vision of how homosexuals behave is entirely ignorant. At a minimum, have you never heard of a "turkey-baster baby"? Some years ago I read an estimate by the head of a gay organization who estimated that half of all gays are married with children. $\endgroup$
    – WhatRoughBeast
    Commented Oct 18, 2018 at 1:52
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    $\begingroup$ If they are all australians then everybody is a mate. $\endgroup$
    – The Square-Cube Law
    Commented Oct 19, 2018 at 12:05

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