It is possible to conduct a secret ballot even if the votes are sent in to a central polling station (Lipton and Widgerson, Honsberger 1985).
See also Arrow's Paradox, Ballot Problem, May's Theorem, Quota System, Social Choice Theory
References
Honsberger, R. Mathematical Gems III. Washington, DC: Math. Assoc. Amer., pp. 157-162,
1985.
Lipton, R. G.; and Widgerson, A. ``Multi-Party Cryptographic Protocols.''