Permitting blanks is absolutely necessary to avoid mistreating spoiled ballots. Namely, suppose you enter an illegible score in some candidate's slot. (Which probably would happen a few percent of the time.) Would you prefer that
Once we agree blanks are needed, we see they also have advantages. You can use them to express "no opinion." If you were to write "0" (or any other number) that would be expressing an opinion – in the csse of 0 that that candidate is very bad. X gives the ability genuinely to express no opinion – if you vote X for Candidate Joe, then, as far as Joe's final score is concerned, it is just as though you were not present in the voting booth.
A lot of voters want that capability. (And you still have the capability of giving Joe "0" if you want. This is not taken away from you.)
There also is considerable evidence that in many elections for many candidates, most voters know nothing (and many of them want to leave the decision about that candidate to others). E.g. consider elections of US Judges.
There is also this argument about "unbiased estimators."
Detailed discuission of "blanks"
Properties of "averaging"
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