is the system where each voter has some fixed number (say five for concreteness) of "points" which she may divvy out (as her vote) to the candidates in any fashion she wishes. For example she could give 2 to Eisenhower and 3 to Lincoln.
The trouble with cumulative voting is that, strategically speaking, it is the same thing as plurality voting. A voter is strategically foolish – "wastes" part of her vote – if she gives anything less than her full point-count to just one candidate.
For example, suppose a plurality voter reasons: "I really favor Nader, but if I vote 'Nader,' then, I fear my vote will be stupidly 'wasted' because the real battle is between Gore and Bush. Therefore, I will actually vote 'Gore'."
If that reasoning was valid (and, in the USA 2000 presidential election, it was valid) then a cumulative voter can use this same reasoning for each of her 5 votes. The same reasoning is equally valid all 5 times. If you, say, vote 4 for Gore and 1 for Nader, then you've stupidly wasted 1 of your 5 votes. Obviously if all the Gore voters wasted 1 vote out of their 5, but all the Bush voters didn't waste any votes, then (if these two kinds of voters were approximately equinumerous) Bush would beat Gore by a 5:4 ratio. The Gore voters figure (again correctly) that they can't afford to be that stupid.
In view of this, cumulative voting does not fix plurality voting's problems at all. In contrast, with Range and Approval, you are always completely free to vote max for your true favorite; there is never a strategic reason not to do so and this never "wastes" even the tiniest smidgen of your vote.
In practice, probably Cumulative Voting would not be quite as bad as Plurality, because some people would be willing to spread their votes around, instead of putting all their votes on the lesser evil – but it is hardly worth dancing in the streets about.
Cumulative voting also has been suggested for use in multiwinner elections – the top W vote-getters win, if we want a W-winner election. It is not a very good method for that purpose either, but that would be a different discussion.
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