The vote should go to any adult resident within a nation who can (with help for some) exercise that right. This is because any person who is subject to the law should be able to have a say in its formulation. This would mean -
(1) VOTES FOR THE IMPRISONED
This is currently a live issue, see contrasting takes here and here. I go beyond either approach in arguing for the full enfranchisement of all prisoners.
Prisoners are subject to one of the most powerful aspects of law, imprisonment. They thus all have a powerful case for enfranchisement. "No imprisonment without representation".
If instead we insist on taking the vote away from people because they are nasty and anti-social, where will that end?
Sometimes prisoners are discovered to have been subject to a miscarriage of justice. Under the current arrangements they have also been subject to the further miscarriage of justice of being denied their voting rights whilst in prison. Full enfranchisement would overcome that aspect also.
There are many people who have never been captured nor convicted for the crimes they committed. They are able to keep their right to vote, whilst those imprisoned are not. The present position makes no sense at all.
(2) VOTES FOR ALL RESIDENTS FROM OVERSEAS
Nor is it right that we have residents in this country who come from nations outside of the Commonwealth and the Republic of Ireland and who are not entitled to vote. They are also subject to our laws.
(3) VOTES FOR THOSE MISSED OFF CURRENT ELECTORAL REGISTERS
Then electoral registers are in a mess, with up to 2 million people missing even though they do qualify to vote under the current arrangements. They are also subject to the laws of the land. We need an electoral registration system which is proactive and recognises that all adults have the same rights as they are subject to the same laws.
WHICH OF THE ABOVE SHOULD INITIALLY BE ENFRANCHISED?
The most serious problem in terms of numbers disenfranchised probably means that (3) above is the priority, then (2) and finally (1). Yet they are all democratic requirements which arise due to the same principle. Ideally, therefore, all these shortcomings could be overcome at the same time. If a person can’t see this, then I doubt whether they understand what democracy is about.
WHY SHOULD WE HAVE A FULL FRANCHISE?
The answer to the question "Why should people have the vote?" provides the answer to the question "Who should have the vote?". People should have the vote because they are subject to the laws, regulations and policies of those they elect. So everyone so effected (but not outsiders such as UK citizen's resident overseas who need to be granted franchise rights in their country of residence) should have equal rights to the UK franchise. The only people who should be excluded are the young and those who have a serious lack of the relevant mental capacity. In deciding who these excluded groups are, we should err on the side of caution so that we don't exclude groups of people unreasonably. The dividing line is a matter for judgement and can not be derived from the democratic principle itself. In connection with the young, I would take 16 as the starting age. We could also then use registration through the school system to ensure that all receive their initial franchise rights.
Here is a brief history of the franchise, but we still have some way to go before we reach a full franchise.