IRV, which stands for "Instant-Runoff Voting", is a type of voting for single-winner elections in which voters NUMBER their ballots according to their preferences (IE "1" for top candidate, "2" for their second-favorite candidate, etc.), rather than mark one with an "X" by his/her name.

Candidates must get a 50%+1 majority in order to be declared elected. If nobody achieves said majority, then the candidate with the least amount of votes is dropped off and his/her votes transferred to other candidates until one candidate wins.

The intention is that a candidate has an absolute majority without any of the following:

1. tactical voting (voting for a major candidate so that a reviled candidate doesn't win)
2. spoiler effect (a third-party candidate "taking votes" from a major candidate)
3. negative campaigning (where candidates campaign so that it's like "Vote for me and nobody else." -- INSTEAD, candidates would say, "In case I'm eliminated, make sure to send your votes to him/her.")

IRV was invented in 1870 by William Robert Ware (a U.S. American architect), who based it on the single-winner version of the multi-winner Single Transferable Vote, which itself was invented by Carl Andrae (a Danish politician and mathematician) and shaped by Thomas Hare (an English lawyer).

In national politics, IRV is used in the following countries (There may be more, but here's what I found so far.):

~ Australia (Australian House of Representatives; by the way, Australia's notorious for demanding that voters rank ALL of the candidates in order for a vote to be considered valid)
~ Ireland (Irish Presidency; Ireland's small and doesn't have to resort to an electoral college like the U.S.)
~ Fiji (Fijian House of Representatives)

Other names that IRV goes by are Alternative Voting, Preferential Voting, Ranked-Choice Voting, the Hare System (after Thomas Hare), and Ware's Method (after William Robert Ware).

((I'm not 100% sure if Urban Dictionary would approve of me listing websites here for informational and education purposes, but...))

For more information on IRV, you can visit http://www.instantrunoff.com/.

SOURCES USED:
~ Instant-Runoff Voting @ Wikipedia (http://en.wikipedia.org/wiki/IRV/)
~ Instant Runoff Voting (http://www.instantrunoffvoting.com/)
Here's a sample of what a voter's ballot would look like when using IRV:

Alex = 5
Jane = 1
Chris = 3
Sue = 4
Rudy = 2

If Jane (ranked #1) has the least amount of votes, then she gets eliminated and this voter's ballot would go to Rudy (ranked #2) until one of the four remaining candidates (Alex, Chris, Sue, and Rudy) wins or gets eliminated and so on.
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