There are many ways to give '3rd parties' a chance. A simpler one is, let folks vote for ALL acceptable candidates, not just choose one. E.g. vote for your party AND for the compromise candidate. This could drive candidates toward the middle.
Its very different from IRV, which is a forced-ranking method which elects the candidate with the majority of first place rankings if one exists, and if not throws out all votes for the candidate with the lowest number of first place rankings (leaving the next-ranked candidate first on those ballots) and then tries again, repeating until some candidate has a majority of first place rankings.
Neither is, IMO, a particularly good single winner election for candidates for political office (though there are some other uses of voting for which I think Approval is a good method -- for instance, in social situations where opting out of an activity is permissible and an approval vote has a crystalized meaning of "I opt out unless one of the alternatives I've marked is selected, and I commit not to opt out if one of those alternatives is selected"), but they are the most commonly recommended alternatives to the US's more common methods of plurality and majority-runoff vote-for-one elections, probably because they are the alternative mechanisms that are structurally most similar (AV can be viewed as a generalization of plurality -- he who gets the most # of votes wins -- without a vote-for-one restriction, and IRV is simply using a ranked ballot to allow a simple generalization of majority-runoff to be done off a single balloting.)
http://ScoreVoting.net/BayRegsFig.html http://ScoreVoting.net/AppCW.html