Define a collective choice procedure as satisfying the ‘‘top condition'' if an alternative is never among the social choices unless it is on top of at least one individual preference list. Prove or disprove each of the following:

a. Plurality voting satisfies the top condition.

b. The Condorcet method satisfies the top condition.

c. Sequential pairwise voting satisfies the top condition.

d. A dictatorship satisfies the top condition.

e. Approval voting satisfies the top condition.

f. Runoff voting satisfies the top condition.

g. If a procedure satisfies the top condition, then it satisfies the Pareto condition.

h. If a procedure satisfies the top condition, then it selects the Condorcet winner (if any).