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"The obligation to respect, ensure respect for and enforce international human rights and humanitarian law includes, inter alia, a State’s duty to: (b) Investigate violations and, where appropriate, take action against the violator in accordance with domestic and international law."

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UN (ECOSOC): The Right to Restitution, Compensation and Rehabilitation for Victims of Gross Violations of Human Rights and Fundamental Freedoms, para. II.3(b)

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The Right to Restitution, Compensation and Rehabilitation for Victims of Gross Violations of Human Rights and Fundamental Freedoms

Summaries

States have a duty to investigate alleged rights violations.
Where a violation is found to have occurred states have a duty to punish those guilty of the violation.