A fork choice rule is a general term.
For some history I've found, one of the early written descriptions of the term is from March 2017
A fork choice rule is a function, evaluated by the client, that takes
as input the set of blocks and other messages that have been produced,
EV means expected value. It is the average you will receive if you repeat the experiment a large number of times.
p=0.9 means if you choose that branch you have 90% probability of it being the correct one.
The locking happens when you "vote".
You can vote both alternatives. They analyze that case and propose possible solutions to prevent that behavior.
It's true that PoS could lead to centralization and in a way encourages centralization - being a technical improvement over PoW in the context of energy use - PoS nodes run the same software with the same energy requirements regardless of the number of coins staked.
I would like to point out firstly that blockchain attempted to take a centralized world and ...
Someone who's been keeping up with the Ethereum 1.0, 1.X, 2.0 differences can correct me and supply more detail, but I believe at least in the 1.0/1.X world, it was decided to roll Proof of Stake (Casper) and Sharding into a single feature release, rather than release them separately.
Clearly this is going to take a while to be feature-complete, so the ...