In both Approval and Score, the best strategy will always involve giving maximal support to your 1st choice(s) and no support to your least favorite(s) (how you score the other candidates will depend more on the situation). This is because this maximizes the chances the candidates you prefer most win and minimizes the chances the candidates you want least win. Because of this, Score and Approval always pass the [[Majority criterion|majority criterion]] in the two-candidate case, and the [[Mutual majority criterion|mutual majority criterion]] (indeed, even the [[Smith criterion]] and [[Condorcet criterion]]) when voters' preferences are dichotomous (i.e. they view all candidates as either good or bad, implying they are all either one of the voter's 1st choices or one of their last choices) for any number of candidates, if all voters are strategic.
If half of the voters give every candidate in a set of candidates the maximal score and all other candidates the minimal score, they can guarantee that one of the candidates in that set will tie or win (because every candidate in that set will have at least 50% approval, while all other candidates, receiving support from at most half of the voters, will have at most 50% approval). When a majority of voters do this, they can guarantee one of the candidates in the set will win, rather than only tie or win, therefore Score voting passes a weak form of the [[Mutual majority criterion|mutual majority criterion]].
Range voting has an advantage over approval voting if