On fair compensation

This paper analyses the problems arising in the pure exchange fair division model, when some dimensions of the resources are personal, fixed, and cannot be redistributed. The remaining resources must then be allocated in a compensatory way. A set of desirable normative properties is defined. No-envy satisfies these properties, but is not generally non-empty in this setting and other criteria are examined, for which existence results are given. General impossibility results obtain. In particular, it is generally impossible to compensate fully and only for differential personal resources, when preferences differ.