Well, it could happen like this:

- Walk in, present some form of ID

- You sign the slip or give a thumbprint so they record that you've voted

- Random token is generated and given to you

- You enter the token in order to vote

- You keep the token as one way to verify your vote was cast

It'd be hard to match the voter to the token if they don't write down the token and associate it with your name.

That might work, as long as no one (including the voting machine) was recording the time you arrived or the time you voted.

Storing the timestamps is a design decision which can be intentionally omitted.

There is also no law of computing which states that the ordinal of the voting record is determined by the chronology of the votes. That is to say that you don't have to keep things ordered by time - or at all; it's not like an 8AM vote should be treated different than a 5PM one.

Well, couldn't _only_ the voting machine record the time the token was used as long as the token is random? (They could just generate N tokens -- one for each registered voter -- and pull one from the pool each time.)

If they recorded the time you took your token and the time the token was used then they'd have a small enough pool of people to work with. I know in my state if a precinct has a small enough pool of registered voters it doesn't show the vote totals from the precinct because of privacy issues.

you don't have to couple the two.

You don't have to, but unless it's illegal, they'll tend to be coupled just for the sake of convenience.