Instead of each person voting for a single candidate, they order
their votes by preference; their first choice gets the vote. Should the
voting tally not give a single candidate a majority, the votes for the
candidate with the fewest votes are tossed; those votes are then recast
for the candidates who got second choice on those particular ballots.
Repeat as needed, moving down individual voter's lists as needed until
a candidate gets a majority.
Advantage: It's much harder to game.
No "this state will get me more votes than that state"; votes are
votes, period. I won't say it's impossible to game, but you'd likely
need to be a statistician to do so.
It's a BIT harder to be a
demagogue. Right now, if the person you vote for doesn't win, tough;
this encourages us to vote for the least worse candidate with a chance
of winning instead of the best candidate. But if you know that you can
have a say in the major candidate race AND express a preference for a
principled outsider, you're more likely to take a chance on the
outsider. To win as a demagogue, one would have to be thought the BEST
candidate by a majority of the population, not just the least worst. If
you can't be everyone's favorite, you're better off trying to be high
on everyone's list so that some of those principled outsider votes can
come your way; this means, focusing on your base only isn't a good idea.
There
is a better option still, though. The SF author Kim Stanley Robinson
suggested a variant on this idea. Instead of making each person vote
only for the highest candidate on their list who isn't eliminated, the
vote is cast for EVERYONE on their list. The value of the vote for each
candidate is weighted according to his/her position on the list; the
winner is the candidate with the highest weighted vote count. Imagine
you're a candidate in such a system; how do you figure out what
campaign strategy will get you your magic point total? Unless
you've somehow managed to rig the weighting system or the tabulation
process, or you have some statistical wizards working magic on
demographics, your only viable strategy is to manage your finances the
best you can, deal with as much of the populace as you can, and hope
your policies and attributes give the numbers you need.