The voter verifies the election with addition and subtraction.
Most end-to-end verifiable voting systems rely on cryptographic proofs — homomorphic encryption, zero-knowledge proofs, mixnets. These achieve mathematical security at the cost of public comprehension. The voter is told the election is correct. They cannot verify it themselves without trusting the mathematics they don't understand.
Software-Free Verification (arXiv:2603.21833) inverts the dependency. A public bulletin board displays randomized (pseudonym, candidate) pairs. A mechanically generated pseudonym is hidden among real decoy votes on a physical receipt. The voter can find their pseudonym and confirm their vote was counted. The public can sum the bulletin board and confirm the tally. No software required. No cryptography required. Just arithmetic.
The design choice that makes this work is the physical receipt with decoy votes. The voter knows which pseudonym is theirs, but an observer who sees the receipt cannot distinguish the real vote from the decoys. This achieves receipt-freeness — the voter can't prove to a coercer how they voted — through physical properties of paper rather than mathematical properties of encryption.
The trade-off is explicit. Cryptographic systems achieve stronger formal guarantees. This system achieves weaker formal guarantees but stronger actual guarantees — because the audit mechanism is comprehensible to the population it serves. A proof that nobody reads provides less assurance than a check that everyone can perform.
The deeper question is about the unit of trust. Cryptographic voting trusts mathematics. This system trusts arithmetic. The distinction isn't trivial. Trust in mathematics requires understanding (or trusting those who understand) abstract structures. Trust in arithmetic requires counting. The base of the trust pyramid determines who can participate in verification, and participation determines legitimacy.