If we take the following preferences
and assume voters in a cardinal method are following the polls and strategically exaggerate their preferences, then you’ll have an iterated Condorcet cycle in the polling (A is leading the polls, then suddenly C, then suddenly B, then repeat) where it isn’t clear who will win on Election Day. But now if one of the candidates drops out, you have a clear majority preference for one of the two remaining candidates, and under strategic voting, that majority-preferred candidate gets a boost in probability of winning. So while you can’t have a failure of IIA with cardinal methods when nobody changes their ballot to adjust to someone dropping out or entering the race, you can have them when voters do that, which it seems clear enough voters will do to make cardinal methods fail IIA at least once in practice.
Another obvious one:
26 A10 B9
25 A9 B10
C wins here, but if one of A or B drops out, then under strategic voting, the remaining one of them may have a higher chance of winning (if the majority faction maximally supports the remaining candidate).
Or if the example is modified to have C-top voters originally give some marginal support to B (because they prefer B>A) then B would win, but if B drops out that might make C win.
Also, by this definition of Pareto
if every individual prefers a certain option to another, then so must the resulting societal preference order.
isn’t it at least theoretically possible for cardinal methods to fail Pareto if, say, between two terrible candidates, everyone just rates both of them a 0, since they’ll be perceived as equal in the final result, rather than one being better than the other?