I don't know what Estonia does, but there are ways to publish the votes in a secure way
that prevents anyone from decrypting a single vote, but lets anyone verify their vote was correctly counted using their own secret key.
httpp://news.mit.edu/2009/rivest-voting
Of course you need monitors
from all interested parties to prevent ballot stuffing, but that's true in every election. It's up to monitors to read the voter list and verify that (probabilistically) there are no/few fake voters on it.
According to this report [1], they published the source code and provided a video recording of installing the software (sounds like a joke):
> Despite positive gestures towards transparency — such as releasing portions of the software as open source and posting many hours of videos documenting the configuration and tabulation steps — Estonia’s system fails to provide compelling proof that election outcomes are correct. Critical steps occur off camera, and potentially vulnerable portions of the software are not available for public inspection.
httpp://news.mit.edu/2009/rivest-voting
Of course you need monitors from all interested parties to prevent ballot stuffing, but that's true in every election. It's up to monitors to read the voter list and verify that (probabilistically) there are no/few fake voters on it.