Reply #7: Permutation: you get multiple paper ballots, each marked

[sean in iowa]

with the same randomly generated serial number, but you don't keep it. The county election officials get the official copy, the Democratic Party gets one, as do the Republicans, and then a consortium of small parties.

Each of the three non-official bodies can audit the election, and a certain level of discrepancy generates an official recount.

There are some kinks to be worked out, such as how this system would avoid mischievous assertions of discrepancy, but this is worth pursuing. At any rate, the ballot remains truly secret.