All users prefer the longest chain. In the case of two solutions being broadcast at about the same time, then each miner will probably prefer the solution they

All users prefer the longest chain. In the case of two solutions being broadcast at about the same time, then each miner will probably prefer the solution they received first, and will base their solution attempts off of that chain. It is very unlikely that both chains will each have a new block broadcast at the same time. Whichever chain gets a new block first will be the winner and everyone will switch to that chain, abandoning the now-orphan chain.