Two possible answers: republic or democracy. They are not exclusive. You can't have a democracy without self-rule, but you can choose other forms of representation. Here's what I mean.
Liberalism is the idea that people are capable of self rule. It's the rejection of divine right to rule. We can see this in the influence of Locke on British law and on the American colonies.Locke is the go-to guy for this. Liberalism just means the opening up of something. Before the industrial revolution, kings relied on divine right to rule. Liberalism was in part a justification for the common man to take control since a new working class was riding, one that was regimented into groups of people who had a new shared identity that they didn't have before. Naturally, they were going to want to be able to determine their own conditions in life and have political freedom. This paves the way for liberal economics, capitalism, as a merchant class rises in the context of a new nationalism. So:
Liberalism opens up avenues of power. It takes sovereign power from a closed system of estates, and argues that men are capable of ruling themselves. This is because men have their own intrinsic moral values and can be their own moral agents of virtue. This means they are free and equal, free from any claims of divine rule. This logically implies that men have the right to life, liberty, health in which to enjoy that liberty, and political freedom, or as Locke puts it, property. Property is the source of political power, meaning freedom since it enables you to participate meaningfully in self-determination. Jefferson renamed it "pursuit of happiness." Life, liberty, and happiness imply the need for health, which also is in the original list.
Sovereignty is final authority. In political terms, it means the monopoly on violence within a nation's borders. By the above, you have self rule, where the people own the sovereign power. This is representative government when the public delegate their power to delegates in order to ensure their own defense and economic stability, so they can go off and fulfill their mandate of liberty and wealth and work and whatever, and pursue economic activity and go be awesome without having to worry about every single thing.
This self rule and representation is described by the Latin for "public matters" or "the public has decided," which is Res Publica. This is a REPUBLIC.
But that does not mean it has to be democratic. It can have limited political opposition even though it has suffrage. Since the people are free to decide, because it's liberalism, they can choose an elective form. Some forms are better than others, and I'm measuring that by "how likely is it the people will lose their freedom?" So in England, for instance, you have a constitutional monarchy in a pluralistic system that ensures that the monarch cannot simply usurp power. You could have a constitutional timocracy, but how long before an oligarchical timocracy threatens the freedom of the state and repeals any redress for replacing the leadership? So you have these other forms of republic that could work but without meaningful political opposition--parties--you are not guaranteed to keep your freedom.
Pluralism means the amount to which the state allows popular choice and voice to have an impact on political decisions. The EU, for example, has a big plurality of opposition parties. We have parties, but the question is how meaningful the opposition is. But when you have at least one loyal opposition party, you have a democracy.
So the answer to the question is, it's a republic. If they are not really speaking on behalf of the people, it's not legitimate. If the people can replace them through peaceful, regular, fair elections, it would be a democracy. But as long as it's been delegated by the people, whether constitutional monarchy or democracy or some other representative form, it's a republic.
No such thing. There will always be friction. All we can do is try our best.
