  In a context where a decision has to be taken collectively by several agents,
the social choice problem consists in deciding whether there exists a socially
acceptable rule that aggregates the individual preferences of the agents into a
social one. We analyze this problem for sets of alternatives defined by
equality constraints and obtain a solution that, in sharp contrast to the
classical ones, is expressed in an elementary language and ultimately reduces
the social choice problem to a standard constrained optimization problem.
  By considering a toy example we shall be able to interpret this general
result in terms of the rationality (in the sense of Economics) of the design of
the set of alternatives rather than, surprisingly, that of the agents involved
in the actual social choice problem.
