If we believe that the appropriate compromise is no one's first choice, the first thing IRV does is throw away any "appropriate compromise".
If we believe that the appropriate compromise is no one's first choice, the first thing IRV does is throw away any "appropriate compromise".
interestingly, IRV is not even monotonic! It's easy to construct a situation where converting people to have the same ranking as you causes you to get a candidate you like less. (The concave parts of the voronoi diagrams describe areas where this happens.) If you're curious about this, a few years back some friends and I tried to make a video describing this phenomenon: [0]. (Our editing and presentation skills are nothing to write home about but I think the video is interesting.)
Range can't satisfy Condorcet (that is, if there is a candidate that would win every head-to-head, that candidate should win the election).
Of course, the most common approaches to RCV also fail that criterion, but it's potentially a way some ranked methods are better than range methods.
That is not necessary a desirable feature. If that is desirable or not depends on your value system of what elections should achieve. What is 'fair' or 'correct' is not universal.
If a moderate of their party runs, it'd be easy for their own members to vote for the moderate as #1 ahead then #2 the more extreme person, and not for the awful evil other party person. The opposition can also vote for the moderate of the dominant party, #1, their candidate #2, and not for the aweful extremist.
The relationship with RCV for non-competitive races (e.g., those districts that are gerrymandered or naturally not competitive which is the majority in the USA) is the RCV can easily address the extremes versus moderates. Moderate candidates don't run because they won't get support from their party and are perceived to be stealing votes. E.g., If you're not voting for $EXTREMIST you're voting for the $THEM. RCV lets you vote for the moderate AND your party's extremist in order to thwart the other side.
The winner in RCV will always be someone's first choice.
In instant runoff it is certainly true that the winner is always someone's first choice, and that was my point - sometimes the winner the method selects should not be the winner.