a lot of people intuitively believe that ranked choice voting (RCV) is better than approval voting because it seems to be more expressive to indicate a ranked ordering than to simply indicate which candidate you approve of.
this intuition is false. here’s why.
imagine a simple example of preferences like this.
# of voters - their ranking
335 hot warm
333 cold warm
ranked choice voting eliminates warm.
but wait! a huge 67% majority of the voters prefers warm to hot (2nd and 3rd row of voters), and a a huge 67% majority prefers warm to cold too! warm is preferred by a landslide to each rival, yet is eliminated.
this happens because the RCV tabulation process simply ignores those second choice votes for warm. it doesn’t look at your second choice votes until your first has been eliminated. you have the feeling that you recorded your nuanced preferences, but the algorithm can just ignore them.
why approval voting is better — statistics
imagine someone who approves X and Y, but not Z. that voter has indicated 2 rankings: X>Z, and X>Y. they might feel dissatisfied that they haven’t expressed a ranking between X and Y, but a lot of other voters will do that, by approving X or Y or XZ or YZ. and, statistically speaking, those voters who differentiate between X and Y will tend to have similar X-vs-Y preferences to the rest of the electorate, thus the results tend to be about the same as they would have been had everyone ranked every candidate.
indeed, a harvard stats PhD and expert on voting methods ran computer simulations to test this, and he found that approval voting generally got much more accurate results, i.e. results which better satisfied the average voter.
this graph includes colors which represent different strategic profiles. for instance, brown represents a situation where half the voters were honest, and half were strategic. whereas red is with everyone being strategic. the really fascinating thing is that approval voting does better with those two highly strategic cases than RCV (“IRV”) does with every single voter being honest (blue dot).
if you want to understand this esoteric science of voting methods better, i recommend the book gaming the vote by william poundstone.