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The trouble with Score is that optimal voter strategy there is to min-max your ratings -- score(max) everyone you'd accept and score(min) everyone else -- which would make it functionally equivalent to Approval if everyone did so; however, since not everyone will, voters who use the full score range are just voluntarily, albeit unwittingly, diluting their ballot power to determine the actual winner vs. voters who use min-max strategy.
E.g., suppose your favorite is a minor-party longshot, and your second choice is a major-party frontrunner; you might naively rate your favorite 5/5 and your second 4/5, but that doesn't much help your favorite actually win since they're a longshot, and it nerfs the support you give to your second who stands a fair shot at winning, so why pull that proverbial punch? It's more effective, and more likely to maximize your chances of a satisfactory outcome, to just rate them both 5/5. Moreover, suppose you rate your worst-evil candidate 0/5 and your lesser-evil 1/5; sure, at least lesser-evil isn't That Guy, but you really don't want either to win, so why give them any support at all that might help them edge out someone you like better? It's more effective to just rate them both 0/5.
STAR addresses that problem by giving voters a compelling reason to use the full score range, as the summed/average scores don't determine the final winner, only the top-two runoff finalists, and then the finalist rated higher on more ballots wins, thereby making relative scoring relevant. Attempting insincere strategy here is about as likely to backfire as succeed, so voters might as well just rate each candidate sincerely using the full score range available.