Republican democracy

A democratic republic is both a republic and a democracy.

A republic is:

A democracy is:

Absent qualification, not all citizens in a 'republic' are necessarily entitled to vote, and absent qualification, a 'democracy' is not necessarily sovereign.

As both, a "democratic republic" is ideally:

In practice, governments only approximate those ideals. Not all persons in all states are citizens and not all citizens are entitled to vote. Suffrage is commonly restricted to citizens of voting age; and may be restricted by several other criteria.

Ideally, elections ensure that governmental authority is wielded according to the will of the citizens. However, wielding power indirectly, through representatives, assures some disparity between the will of the people and the actions of government. In the best cases, citizens elect only their wisest peers as representatives – amplifying governmental wisdom beyond that of the average citizen. However, delegating authority to representatives often yields other, less desirable results.

Given the lofty ideals implied in the phrase, it is unsurprising there is disagreement on how a "democratic republic" is best implemented – and disagreement on whether a particular government, as implemented, is appropriately described as a "democratic republic". Several countries with the term "democratic republic" in their official names – colloquially known as Algeria, the Democratic Republic of the Congo, Ethiopia, North Korea, Laos, Nepal, Sri Lanka, and East Timor – most of which are identified as "not free" by the U.S.-based, U.S.-government-funded non-governmental organization, Freedom House. Other organizations use a variety of factors to characterize the quality and equity of governance, as reflected in their various indices of freedom. The differences between states labeled "democratic republic" can be quite dramatic, as with the 'Democratic People's Republic of Korea', rated the least democratic government in the world.

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Wikipedia