It's possible to make verifiable secret systems. Some have even been tested in real elections in the US as part o projects by NIST (for arcane reasons, NIST controls voting technology in the US :P). For example, Takoma park in maryland has used scantegrity a few times (2009, 2011).

The paper is behind a window, it is not a receipt and you don't take it with you. It is secret.