In his 1951 publication Social Choice and Individual Values Kenneth Arrow proved that it is not possible to construct a voting system to select between 3 or more choices which satisfies the following "reasonable" criteria:

  1. citizen's sovereignty: if all members of society prefer one particular option over another, then society should prefer that one too.
  2. non-dictatorial: the social choice function should not simply follow the preference order of a single individual while ignoring all others.
  3. positive association of social and individual values: if an individual modifies his or her preference order by promoting a certain option, then the societal preference order should change only by (possibly) promoting that same option.
  4. independence of irrelevant alternatives: if we restrict attention to a subset of options, and apply the social choice function only to those, then the result should be compatible with the outcome for the whole set of options.

See: http://www.wikipedia.org/wiki/Arrow's_paradox for more.

See VotingAnomalies? for examples of how existing voting systems fail these criteria.

SocialChoice