Now, I do believe that my vote was actually counted, but I have no rational basis for this, as I don't have any kind of record or visibility into the process.
I don't think any voting process can actually really tell you that your vote was counted. At the end of the day you're just trusting that the people running it aren't corrupt, or at least that there are enough people involved that keeping shenanigans a secret would be incredibly difficult.
In a digital system, I'm not finding jack shit. It doesn't exist anywhere except as a counter, I can't check whether it's my vote or randomly created after the fact (after suspicion was announced), and I can't trust the system itself, because it's defined by, developed by, and operated by some random group of people who managed to slap the thing together and make a sale. I can't get in there and check out any of it myself (even as just a vague threat), and the conspiracy group is sufficiently small as to be viable (I only have to "convince", what, 40 people, to cheat the votes?).
What I don't understand is why not use something like the SAT exams -- trivially hardware-counted, but also physically transparent and available -- and solve like 90% of the problem that way?
We know many people want to tamper with elections. The CIA has done that much. The same is not true for cars. Steal cars, yes. But cause a random car to crash on purpose? Thats pretty rare. If were common, I personally would not trust my cars electronics either. And neither should you.
I can see how the argument still holds water if half the time the outcome of the election didn't go his way.
The Joe is for example driving a car full of electronics and somehow he doesn't have issue trusting his life to it. And, if anything, i'm pretty sure that deep understanding of that car's electronics and software would make the Joe to only trust his car less (one can google the software expert's opinions during the Prius self-acceleration story)