IIA does not allow "removing" an alternative from the available set (a candidate from the ballot), and it says nothing about what would happen in such a case: all options are assumed to be "feasible." In a Borda count election, 5 voters rank 5 alternatives ["A", "B", "C", "D", "E"].  3 voters rank ["A">"B">"C">"D">"E"]. 1 voter ranks ["C">"D">"E">"B">"A"]. 1 voter ranks ["E">"C">"D">"B">"A"]. Borda count ("a"=0, "b"=1): "C"=13, "A"=12, "B"=11, "D"=8, "E"=6. "C" wins. Now, the voter who ranks ["C">"D">"E">"B">"A"] instead ranks ["C">"B">"E">"D">"A"]; and the voter who ranks ["E">"C">"D">"B">"A"] instead ranks ["E">"C">"B">"D">"A"]. They change their preferences only over the pairs ["B", "D"], ["B", "E"] and ["D", "E"]. The new Borda count: "B"=14, "C"=13, "A"=12, "E"=6, "D"=5. "B" wins. The social choice has changed the ranking of ["B", "A"] and ["B", "C"]. The changes in the social choice ranking are dependent on irrelevant changes in the preference profile. In particular, "B" now wins instead of "C", even though no voter changed their preference over ["B", "C"]. Consider an election in which there are three candidates, "A", "B", and "C", and only two voters. Each voter ranks the candidates in order of preference. The highest ranked candidate in a voter's preference is given 2 points, the second highest 1, and the lowest ranked 0; the overall ranking of a candidate is determined by the total score it gets; the highest ranked candidate wins. Considering two profiles:  Thus, if the second voter wishes "A" to be elected, he had better vote "ACB" regardless of his actual opinion of "C" and "B".