[!NOTE] This only works with online players / loaded entities. If you want to accomodate offline players / unloaded entities, you’ll need a much more complicated system!
Thanks to scoreboard player operations this is a fairly easy question to answer, as the > operator will ensure the left score is at least as high as the right score.
Thus the way to do this is as follows (assuming you’re trying to find the highest score in an objective named score).
First you set up a fake player with the smallest possible score you can reasonably have, or alternatively you can use the smallest possible number (-2147483648).
scoreboard players set #max score -2147483648
then you execute as all the entities you want to compare, running the scoreboard operation as all of them. Here we’ll use all players in the example.
execute as @a run scoreboard players operation #max score > @s score
And now you can find whoever has the same score as the fake player (using Method #2 from here) to name your winner.
execute as @a if score @s score = #max score run I have the highest score!
This can be used to detect the player with the lowest score, just instead of > use < and instead of -2147483648 use positive 2147483648, E.G:
scoreboard players set #min score 2147483648
execute as @a run scoreboard players operation #min score < @s score
execute as @a if score @s score = #min score run I have the lowest score!