The HFFD algorithm requires that all agents agree on the relative ordering of items by cost. This means:
Valid Example (IDO):
Agent 1: [5, 3, 1] (5 > 3 > 1)
Agent 2: [10, 6, 2] (10 > 6 > 2)
Agent 3: [2.5, 1.5, 0.5] (2.5 > 1.5 > 0.5)
Invalid Example (Not IDO):
Agent 1: [5, 3, 1] (5 > 3 > 1)
Agent 2: [1, 6, 2] (1 < 6 > 2) - Different ordering!