Has anyone ever tried Negative Votes?

Proposal: In final popular elections, each voter has one vote as usual but can cast that vote either for a desired candidate/issue (a positive vote) or against the one they despise most (a negative vote).

This should:

1. yield near-100% voter turnouts;

2. put an end to claims of "popular mandates" by least-of-two-evils candidates;

3. discourage extremists.

Naturally, it will be necessary to retain the traditional "positive votes only" procedure for primaries or caucuses, since otherwise we would frequently be led by unknowns. (I generously assume that this would not be an improvement.)

Has this ever been tried, or even considered?

PS: I have set up a simple little poll at http://www.easypolls.net/poll.html?p=5192e250e4b0df6bcbc78948#.UZLg4ZE3hhk.facebook in case you'd like to register your personal opinion on this.