They'd have to publish the ledger in real time and/or instantly show how those 10 to 20 voters voted, to the voter, for this to be effective. Otherwise whoever is paying or blackmailing that voter can ask the voter to mark their id and hand or transmit it to them immediately. They can later verify that the vote was given to the right choice once the ledger is published and take appropriate action for or against the voter. Voter cannot easily fake their choice, and in the case of blackmail, consequences for bad luck can be bad.

Edit: If you do show all 20 votes, you'd have to have votes for all candidates on them.

Also if someone is trying to manipulate a bunch of votes, they'd run into dupes and know one is lying.