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There is a much better explanation in this video: https://www.youtube.com/watch?v=7Q7rzqJ0YS8 As the third party becomes more and more popular, eventually they steal enough first votes away from the main party to cost both of them the election.

It's true that IRV limits the cost of vote stealing. But first votes still matter a huge amount in IRV, and you can only give one first vote. So there can always be some vote stealing. This is not a problem when third parties are really small and inconsequential. But if this actually worked to create viable third parties that had significant percent of the vote (the main goal of people that want such systems, otherwise there is no point), it would become a huge issue.

The link I posted shows that approval and range voting do vastly better in computer simulations of elections. Which is nice because approval voting is much simpler. And there is never a scenario where you shouldn't vote for your favorite candidate, under approval voting.

The last issue has been experimentally observed in Australia:

http://rangevoting.org/AusAboveTheLine07.html

People insincerely rank the competing party in last place, even though they don't really think they are the worst party. The major parties encourage this, and explain to their voters how to vote strategically.

More issues here: http://rangevoting.org/IrvExec.html




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