Apparently we live in a pretty special Galaxy.
How odd that one of the closest other galaxies is our near twin.
There is a correlation here - being close together means that they form in similar conditions and exist in similar environments. They are also of similar age. If you look at a galaxy far away, it has properties that are very different from the Milky Way.
Regardless, the vast majority of galaxies are much smaller than either Andromeda or the Milky Way. The local group exemplifies this fact: it includes tiny dwarf galaxies (some orbit the Milky Way at distances much closer than Andromeda). In this way both Andromeda and the Milky Way are quite special.
Andromeda, 2.5 million light years away, has 14 dwarf galaxies around it that we can see. Imagine that there must be many more that we can never see because of distance and because the dim galaxies are hidden by Andromeda’s light.
I am not an astrophysicist, but it does not seem there is a good anthropic principle to explain this. Perhaps it’s just the larger galaxies have more rolls of the dice?
What percentage of stars are galaxies our size or larger?
Do galaxies sizes follow a power law distribution?
Correct; the mass and luminosity distributions of galaxies are well described by a power law or a broken power law, at least, based on current understanding.
So how does that translate into probabilities? What percentage of population I stars would be in big galaxies as opposed to small ones?
This is an interesting question - I don’t know the answer. I wonder if someone did any calculations on this. The main competition is between: bigger galaxies = more stars, but bigger galaxies = rarer. There are also complications based on the different types of galaxies, e.g. two galaxies can have the same mass but different number of stars due to one of them having more dark matter.
I remember reading that there is a lot of radiation in the area around the galactic core, so the distance between a solar system and the galactic core may play a part. It is also worth noting that we are currently on the outer part of the Milky Way.
As to straight probabilities, if smaller galaxies are much more numerous the rolls of the dice may even out between large and small galaxies.