ok so the OP is not actually trying to describe or learn PoW
nor wanting to learn how bitcoin uses PoW
but wants to instead make a whole different system where PoW means something completely different.. as thats how i am reading his posts now
where he wants to create a new system without first understanding how the current system works
..
so here goes another attempt at explaining the current system
PoW is not about "selecting proposals" or selecting a president who controls the network..
PoW is just doing a complicated method of using electric and computational time to create a strong ID that fixes the contents of a block. whereby it would take someone else more electric to go back and change that block and afix a new block ID to the changed data.. and then try to do the same for the next newest block to overtake the leading blockheight to become the valid blocks usernodes read and follow.
which to even be capable of doing this and consistantly win every block requires alot more electric spent than the entire networks worth of mining hardware
PoW has nothing to do with changing rules. its about securing the DATA inside a block with a strong and expensive ID for the blocks contents of transactions
and that is it in a nutshell
if a malicious pool owner with such massive amount of hardware to achieve repeated winning blocks. all he can ultimately do is just select (be picky) about what transactions to include or not
separately from PoW
changing the rules(proposals) requires having a majority of user nodes, or more importantly the nodes used by businesses and serives using your changed rules code.. to THEN accept blocks that may contain a new format.
meaning you need to convince user nodes to adopt your code first.. BEFORE a new block format would be accepted
thus 2 separate activities
as for who wins the block creation. its not about nodes randomly accepting something(being picky).
its about nodes receiving something random
its the mining pool that manages to solve the puzzle with enough difficulty faster than its opponent, and if the block meets the rules. then that is accepted as the winner
because there is a bit of 'randomness' in the blockID creation. its not always the pool with the most hashpower that wins every time.
dumbing it down by (whatever the term is for several factors above Vigintillion)
one pools attempt at making a block might be searching for the number 987654(xVigintillion)
while another pool is searching for the number 1234(xVigintillion) where the end result needs to when converted to hex have a prefix of a certain amount of zeros
their next attempts would be a different number where a different pool has to find a lower number meaning it gets to win even though other pools might have more hashpower their number this time they need to find is higher thus needing more time to find it