Proximity-sensitive individual deprivation measures

•We propose and characterize a generalization of the linear index of individual deprivation.•The class allows for increases in income of a higher-income individual to have a stronger impact the closer they occur.•The subclass of our measures with this property is axiomatized in our second result.

We characterize a generalization of the linear index of individual deprivation. Our class allows for an income increase of a higher-income individual to have a stronger impact the closer they occur to the income of the person under consideration.