Question

For a social choice function F, prove or find a counterexample that F satisfies no veto power is equivalent to F is non-dictatorial. First state the definition of “no veto power” and “non-dictatorship” and then prove or disprove.

Answer 1

Veto Power - Power to overrule a mutual decision

No Veto Power - No such power to overrule a mutual decision

Dictatorship - Governed by a dictator

Non-dictatorship - Not governed by a dictator

If veto power exists with one individual, then that individual can overturn the decision of others.

In this case if that individual is exercising his veto power, concentration of power is with him.

In other words, it can be said that the individual holding veto power is equivalent to a dictator.

Thus, no veto power is equivalent to non-dictatorship.