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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.''