Ask HN: Requirements for voting software

My housing community plans to buy an electronic voting system as a service from our administrator company. I consider this a very dangerous arrangement since we would pass all control over the basis of our self-government to a contractor.

All of this is exacerbated by the terms of use that make the voting secret, waive all warranties of the system and forbids us from disclosing any information about the system (i.e. consulting external experts) - in this way the people will have no way to check if the voting system is working correctly.

Is that even possible to have an honest secret voting in such an arrangement? In the current way it not only limits our means of control of the voting process honesty - but it is secret only to the members of the community and not to the administrator. I guess this might be possible with some cryptographic systems - but it would probably not be practical when most of the users are not computer experts.

What would be the other requirements for such a system that you'd recommend?