Allocating Resources with Imperfect Information

The distribution of resources is a critical issue that impacts all aspects of the Internet and society, with fairness playing a key role. Current standard algorithms for distribution typically measure fairness through methods based on envy or proportionality, requiring precise numerical values. However, there is a clear discrepancy between how these algorithms are intended to work in theory and their application in real-world situations. This is because users often do not have exact information about the resources and struggle to assign a numerical value to them. Our goal is to explore settings where agents do not take exact numeric values as input. In this framework, we do not assume that individuals can specify exact numerical values for resources. Instead, we assume that each agent has an ordinal preference for the items. That is, given two items, an agent can identify which is better, without assigning cardinal values to them. We consider new criteria for fairness in this setting, and discuss about their achievability in this article. Besides, we investigate the Probabilistic Serial mechanism where agents also only provides ordinal ranking over items, and particularly research on the incentive ratio of the mechanism.