This is the familiar "Points System". The voter may give to each candidate any number of points, within some specified range, such as 0-10 or 0-100. Approval voting is the 0-1 Range method.
Range is now more often referred to as Score.
A few criterion-compliances:
FBC, Participation, Mono-Add-Top, Consistency, IIAC, Pareto, Plurality Criterion, Monotonicity