If some relatives died with no will, the order of their deaths could affect the inheritance result. When the order of death is unknown, to determine the inheritance result, there are two approaches: apply an inheritance method that is not affected by the order of death, or artificially assign the order of death. We prove that under some basic requirements, both approaches do not work. Therefore, if these requirements are satisfied, any inheritance law is ill-defined. Then 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.
Wang, Yue, Impossibility Results about Inheritance and Order of Death (May 14, 2021).