Impossibility results about inheritance and order of death

If several relatives died with no will, the order of their deaths could affect the inheritance result. When the order of death is unknown, there are three approaches to determine the inheritance result in this simultaneous death situation: apply an inheritance method that is not affected by the order of death; artificially assign the order of death; stipulate that persons with unknown orders do not inherit each other. The last approach is adopted by the current French Civil Code (denoted as the French Approach). We prove that under some basic requirements, the French Approach is the only valid solution to the order of death problem. Therefore, the inheritance law of a country that does not adopt the French Approach either has unsolvable inheritance problems or violates basic requirements. In the appendix, we study the existence and uniqueness of inheritance methods that are invariant for different orders of death and only violate one requirement, such as gender equality.