It says that if the voters make the same decisions once the alternative is added, then the voting algorithm does. See Arrow’s definition of IIA on page 27 of the 2nd edition of Social Choice and Individual Values (you can find this part for free on Amazon).
Which seems to me obviously a bad criterion. You can add a compromise option that none of the voters would choose by way of maximizing their individual utilities, but which would maximize the sum of their expected utilities, for example.
It says that if the voters make the same decisions once the alternative is added, then the voting algorithm does. See Arrow’s definition of IIA on page 27 of the 2nd edition of Social Choice and Individual Values (you can find this part for free on Amazon).
Which seems to me obviously a bad criterion. You can add a compromise option that none of the voters would choose by way of maximizing their individual utilities, but which would maximize the sum of their expected utilities, for example.