> But also it gives voters the option to actually vote for whom they want to vote for instead of who they think will win.You already have the option to vote for who you want to vote for in "first past the post", you just might get an outcome you don't like very much...
IRV and every other voting system is the same way: you can vote your heart, but you'll get an outcome you prefer more often if you vote tactically. There's even a theorem: https://en.wikipedia.org/wiki/Gibbard–Satterthwaite_theorem
For the specific case of IRV, consider an election like:
* 32% of people: Clinton, Sanders, Trump
* 33% of people: Sanders, Trump, Clinton
* 35% of people: Trump, Clinton, Sanders
Now, this is a terrible election and there's no clear winner because people's preferences point around in a circle. Under traditional voting Trump wins, while under IRV Clinton is eliminated and Sanders wins. But if a few people preferring Trump > Clinton > Sanders had instead voted just Clinton > Trump > Sanders we could have had:
* 32% of people: Clinton, Sanders, Trump
* 33% of people: Sanders, Trump, Clinton
* 32% of people: Trump, Clinton, Sanders
* 3% of people: Clinton, Trump, Sanders
Then Trump would have been eliminated first, with only 32% of the first place votes, and his second place votes would have gone to Clinton, making her win. So by voting for a candidate they liked less, these voters got an outcome they liked more.