Non-personal identification is nothing to do with having something to hide. It's about preserving the unbiased nature of the vote. Some people have no problem loudly proclaiming which way they swing but others like to keep their own counsel. It's to allow the full, unfettered participation of all that the 'secret' ballot has evolved. 'Secret' is, as others have pointed out, a misnomer. Non-attributed would be a more accurate term.