Question

Alan wins a local election, with Mary taking second place and Jay in last place. After the election, the election board determines that Jay's paperwork was not in order. As a result, Jay is ejected from the ballot, and Alan wins the election. Is there evidence that the voting system used in this election violates IIA?

Answer 1

The independence of irrelevant alternatives (IIA), also known as binary independence or the independence axiom the social preferences between alternatives x and y depend only on the individual preferences between x and y and introducing a third option, thereby expanding the choice set, must not change the original preference between x and y change.

In the given question, Alan was had the maximum votes, followed by Mary and Jay. We do not know the percentage vote break-up. So, it is possible that without Jay in the race, the votes for Jay would have gone to Mary, making her the winner.

Hence we can conclude that the voting system  used in this election violates IIA.