We present simple and direct arguments to characterize strongly group strategy-proof social choice functions whose range is of cardinality two. The underlying society is of arbitrary cardinality, and agents can be indifferent among alternatives.

Extensive measurement is the standard measurement-theoretic approach for constructing a ratio scale. It involves the comparison of objects that can be concatenated in an additively representable way. This paper studies the implications of extensively measurable welfare for social choice theory....