TRUE & FALSE

i) If the production of a good gives rise to negative externalities, then it is optimal to produce less of the good.

ii) The majority and dictatorship rules satisfy the IIA property.

iii) The q-quota rule states that a coalition is decisive if and only if there are q number of people in the coalition. This rule satisfies the transitivity property.

iv) The Gale and Shapley's men-proposing deferred acceptance algorithm is both stable and strategy proof (from the perceptive of men).

v) In apportionment problems, the outcome suggested by the Jefferson's method satisfy population monotonicity property.