Tie-Breaking or Not : A Choice Function Approach

This paper considers a new axiom of a choice function called equal treatment of individuals in an indifference class (ETI) in the context of matching problems. We show that when a choice function satisfies ETI and two commonly-used axioms, substitutability and size monotonicity, any individual for whom ETI applies must either be always accepted whenever the choice set includes them or be never selected. ETI is also generally incompatible with another axiom, q-acceptance. When ETI, substitutability, and size monotonicity are required, the degree of q-acceptance violation depends on the sum of the sizes of all indifference classes for which ETI applies, but when size monotonicity is replaced by consistency, it is characterized by the size of a particular indifference class. These results clarify the trade-off between ETI and other axioms, which would be helpful in designing a tie-breaking rule