The problem of manipulation in voting in the case of multi-valued choice is studied.
We provide well-known and new schemes of preference extensions, allowing comparing
all possible social choices under an arbitrary number of alternatives.
We describe the known and introduce new indices of a degree and efficiency of manipulation.
These schemes of preference exten¬sions and indices are used to evaluate, via
computational experiments, the degree and efficiency of manipulation
of known voting procedures, taking into account multi-valued choices. The results
are given for five voting rules.