Here is a nice simple model of the trade-off between redundancy and correlated risk. Assume that each time period, each planet has an independent and constant chance of destroying civilisation on its own planet and an independent and constant chance of destroying civilisation on all planets. Furthermore, assume that unless all planets fail in the same time period, they can be restored from those that survive.
e.g. assume the planetary destruction rate is 10% per century and the galaxy destruction rate is 1 in 1 million per century. Then with one planet the existential risk for human civilisation is ~10% per century. With two planets it is about 1% per century, and reaches a minimum at about 6 planets, where there is only a 1 in a million chance you lose all planets simultaneously from planetary risk, but now ~6 in a million chance of one of them destroying everything. In this case, beyond 6 planets, the total risk starts rising as the amount of redundancy they add is smaller than the amount of new risk they create, and by the time you have 1 million planets, the existential risk rate for human civilisation per century is about 63%.
This is an overly simple model and I’ve used arbitrary parameters, but it shows it is quite easy for risk to first reduce and then increase as more planets are settled, with a risk-optimal level of settlement in between.
Here is a nice simple model of the trade-off between redundancy and correlated risk. Assume that each time period, each planet has an independent and constant chance of destroying civilisation on its own planet and an independent and constant chance of destroying civilisation on all planets. Furthermore, assume that unless all planets fail in the same time period, they can be restored from those that survive.
e.g. assume the planetary destruction rate is 10% per century and the galaxy destruction rate is 1 in 1 million per century. Then with one planet the existential risk for human civilisation is ~10% per century. With two planets it is about 1% per century, and reaches a minimum at about 6 planets, where there is only a 1 in a million chance you lose all planets simultaneously from planetary risk, but now ~6 in a million chance of one of them destroying everything. In this case, beyond 6 planets, the total risk starts rising as the amount of redundancy they add is smaller than the amount of new risk they create, and by the time you have 1 million planets, the existential risk rate for human civilisation per century is about 63%.
This is an overly simple model and I’ve used arbitrary parameters, but it shows it is quite easy for risk to first reduce and then increase as more planets are settled, with a risk-optimal level of settlement in between.