Question

What two kinds of government would be considered farthest apart in terms of placing importance on popular sovereignty

Answer 1

the answer is  democracy and dictatorship
In a democracy, we held popular sovereignty as the basis of our government, where the citizens have the power/influence to choose which type of Regulations that we prefer by choosing the right representative.
 In a dictatorship, only the head of the nation could determine the regulations in the country.

Answer 2

Democracy and Dictatorship are the two kinds of government would be considered farthest apart in terms of placing importance on popular sovereignty. Democracy is a system of government by the whole population or all the eligible members of a state, typically through elected representatives, while the government rule by absolute, imperious or overbearing power control is a dictatorship.