The only way to realize the absolute secrecy required for voting is to use anonymous votes. Thus votes can be:

1. anonymous records
   The following is an example of anonymous record: an unknown lady likes black roses.
   Since only the lady herself could confirm she likes black roses, we should ask her to know if the above sentence is true. But we don't know who she is, so we can't confirm, nor deny, she likes black roses.
   Having no references to external entities to check with, we can decide to trust or distrust anonymous records but for sure we are not able to verify their truthfulness.

   By the way, anonymous records are unusual in the real world; to be honest it's even difficult to imagine human activities in which files of anonymous records are useful.

   Files of cast votes must be made of anonymous records, to ensure that nobody will ever be able to identify what each voter voted for. Thus for each cast vote, electoral files can have the following information:
   • the name or the code of the chosen candidate or party
   • the name or the code of the polling station where the vote has been casted
   • the serial number of the voting machine which casted the vote
   • ... other info BUT anything which could ever link to the identity of the voter.....

   Thus electoral files will contains info of the following kind: an unknown elector casted his vote for candidate "A"
   It's easy to see that in the above situation no votes verification is possible since each vote could be verified only by the one who casted it, but nobody knows who he is! The above statement is true whichever techniques are use to collect and store votes: we can use criptography, secret passwords, special networks, Mathematical Voting Systems and any other techniques, but at the end of the story all we have is always an anonymous file as the one described above!
   All we can verify is that the final result of each candidate is actually the sum of his/her recorded votes, but this is not a real verification since it doesn't ensure that recorded votes store the actual electors' choices.
   We can't verify the truthfulness of electoral results based on anonymous records.

2. anonymous physical objects
   Obviously we can verify the number of anonymous physical objects thus we can verify the truthfulness of electoral results based on them.

Democracy also requires electoral results to be verifiable, thus we can't use anonymous records as votes since can't be verified.

In Democracy the term "verifiable" means "verifiable by the common people", thus we can't honestly think a string of bytes recorded on some electronic media as a physical object because it can't be directly verified by any human being.

votes must be anonymous human-readable tangible objects
collected, transmitted and tallied up publicly.

It is not by chance that democracies have always used ballot papers and public electoral procedures!