In this system, a voter facing multiple choices is given X number of points. The voter can then assign his points to one or more of the choices, thus enabling one to weight one's vote if desired.
Unlike preference voting where the numbers represent ranks of choices or candidates in some order (i.e. they are ordinal numbers), in cumulative votes the numbers represent quantities (i.e. they are cardinal numbers).
This form of voting is advocated by those who argue that minorities deserve better representation, and thus could (by concentrating their votes on a small number of minority candidates) ensure some representation from the minority.
There is nothing in this system that requires each voter to be given the same of points each, apart from general policies of electoral equality. So if certain voters are seen as being more deserving, perhaps because they are in an oppressed group, are cleverer, or make a bigger financial contribution, they could be assigned more points per voter.
If each voter has the same number of points then typically the number of votes would be equal to the number of winners, though there is no reason why this should be required. If each voter is given just one point then the system becomes identical to a single non-transferable vote. While giving voters more points may appear to give them a greater ability to graduate their support for individual candidates, it is not obvious that it changes the democratic structure of the method.
Tactical voting is the rational response to this system. The strategy of voters should be to balance how strong their preferences for individual candidates are against how close those candidates will be to the critical number of votes needed for election.
This describes how cumulative voting works in a single case. Where there is a General Election, several cases occur simultaneously in different constituencies. There is no automatic requirement that all of these should return the same numbers of winners under all implementations; indeed certain demographic rules for boundary changes might alter the number of winners as well as, or instead of, the boundaries. So the special case of one single winner is possible; if voters in this case also only have one vote then this is identical to First-past-the-post_election_system voting.