# The patrilineal inheritance system

### Why the oldest child inherit most of the parents' property in many cultures

I live in a Chinese family that is fairly stereotypical by all measures. When my grandfather died, it was said that all of his properties was inherited by my father. My aunt, who is younger than my father, inherited nothing. This feels…wrong… Or to put it more precisely, it is contrarian to human moral intuitions. Why is there such a custom that seems so bizarre and immoral yet lived on for thousands of years in Chinese culture? Even more bizarre than that is the fact that the same custom (the oldest child inherit all properties) is present in India, medieval Europe, the Roman empire, e.t.c.

Why is that the case? Why do so many civilizations adopt the same custom of inheritance that only bequeath properties to the eldest heir? A simple explanation would be to sweep it under the rug of patriarchy.

Look, all the cultures you have mentioned are patrilineal. It’s just one of those weird patriarchal customs that ancient people were too un-enlightened to overthrow.

Imagine yourself a patriarch living in the ancient ages. You’ve made a good fortune for yourself and became a member of the rich educated elites. Your partner has died but you have two wonderful children.

Bad news, you got an unidentified disease and you know you will die soon. You’ve got a couple of days left to get your affairs in order. You plan your funeral. You have your grave dug. Now, you have to decide how to split the money you’ve got left between your two children. Do you give all your money to the elder son? Do you split your money equally between the two? Being a smart patriarch, you want to strategically maximize the chances of your offsprings succeeding. By “succeeding” I mean becoming a member among the rank of rich educated elites.

You understand that the more money your offspring has, the more likely they are to succeed. You are very mathematically inclined. So you write down a function P(X) = probability of someone with X amount of money succeeding.

If you have X money left and decide to give all that money to your elder child, then your elder child has P(X) chance of succeeding and your younger child has P(0) chance of succeeding. So the total probability of at least one of your offspring succeeding is P(X) + P(0) (you can also think of this as the expected number of successful children if you so incline).

If you decide to split your money equally between your two beloved children, then each of them has P(X/2) chance of succeeding. And the total probability of at least one of your child succeeding is P(X/2) + P(X/2).

So your question now is:

Is P(X) + P(0) > P(X/2) + P(X/2) ?

Or is P(X/2) + P(X/2) > P(X) + P(0) ?

Well, if a person’s chances of success is linear to the amount of money/resources they have, then the two ways of splitting your money should be equally good. If a person’s chances of success grows slower than linearly with respect to the amount of money/resources they have, then you should split your money equally between your heirs. If a person’s chances of success grows faster than linearly with respect to the amount of money/resources they have, then you should give all your money to only one heir.

I think it is fairly clear that in an ancient society as well as today’s society, a person’s chances of success grows faster than linearly with respect to the amount of money they have. I mean, there are tons of second order effects: With more money to start with, you can afford a better education and get a good job with higher probability. With more money, you are more likely to know people who can pull strings for you in the future. With more money, you can eat healthier and save potential medical costs…

So, in almost any society, you, as a wise patriarch, will be “better off” giving all your properties to one heir instead of splitting them between your heirs.

Of course, these customs were not necessarily invented by some wise patriarch who did the right math and went through arguments about society. The customs are created through the process of evolution:

Patriarch A decided to have his eldest heir inherit all his properties.

Patriarch B decided to split his properties amongst his heirs equally.

Then, when the next generation rolls around, there is a good probability that an heir of Patriarch A will still be as successful as their father. The probability that an heir of Patriarch B is as successful will be lower. So the total number of Patriarch Bs in the elite class will decrease overtime as they are outcompeted by Patriarch As.

Eventually, all you have left is a mysterious custom carved on a piece of saintly boulder that reads:

“Leave all your properties to your eldest heir. Leave your blessings and well-wishes to the rest of your children :)”

Why the eldest instead of the youngest? My take is that the eldest is generally the dominant (farm) labor as their parents become old. So a custom that bequeath wealth to the youngest heir could cause too much instability.