Slave are captives taken in a just war, and by right of Nature subjected to the absolute dominion and arbitrary power of their masters. ...Being not capable of any property, they cannot in that state be considered any part of civil society.
Gist of Idea
Slaves captured in a just war have no right to property, so are not part of civil society
John Locke (Second Treatise of Government , 085)
If the test of citizenship is being capable of holding property, presumably children and mentally damaged people (including the very old) will also fail to qualify. I see no principled reason why slaves should not be allowed to vote. Note 'just' war.
Locke,John: 'Two Treatises of Government' [Everyman 1988], p.158