How do you even come up with these weird convoluted non-arguments, we have many choices on a single ballot here too. It's called a list. You can put lists on paper.
In Canadian federal elections, the vote counting process is:
1. Open the box.
2. Dump the ballots onto the table.
3. Make sure the box is empty.
4. Pick up ballots one by one, say "this looks like a vote for "Mr. X", and place into the appropriate pile.
5. Count how many ballots are in each pile.
This particular process doesn't work if you have multiple choices on one ballot. I'm not saying that you can't use paper ballots for more complex elections -- you absolutely should, for the well-known verifiability reasons -- just that the counting process is never going to be as simple as the Canadian (or UK) process.
Where I live, the ballots we use are cut into one piece per question. Then the pieces are counted separately.
There was a court argument over the use of scales by some municipalities. The scales are used to weigh piles of votes to determine vote count. So ballots with multiple question are cut, sorted, then weighed. I'm looking into lead pens to give my vote more weight :-)
1. Open the box. 2. Dump the ballots onto the table. 3. Make sure the box is empty. 4. Pick up ballots one by one, say "this looks like a vote for "Mr. X", and place into the appropriate pile. 5. Count how many ballots are in each pile.
This particular process doesn't work if you have multiple choices on one ballot. I'm not saying that you can't use paper ballots for more complex elections -- you absolutely should, for the well-known verifiability reasons -- just that the counting process is never going to be as simple as the Canadian (or UK) process.