The case of Ohio River Contract Company v. Gordon, Judge of the Jefferson Circuit Court in 1916 revolved around a dispute between the Ohio River Contract Company and several laborers who claimed they were owed wages for work performed on a public improvement project in Louisville, Kentucky. The company sought to prevent enforcement of an order by Judge Gordon that it pay these claims from funds held by the city under its contract with the company. The Supreme Court ruled against Ohio River Contract Company, stating that while ordinarily such disputes would be resolved through legal proceedings rather than mandamus (a judicial remedy), this was not possible due to unique circumstances surrounding this case - specifically, that there was no other adequate means available for workers to obtain their unpaid wages given existing state laws at the time. Therefore, it upheld Judge Gordon's decision ordering payment from funds retained by Louisville City as security for completion of contracted works.

In the dissenting opinion for Ohio River Contract Company v. Gordon, Justice Holmes disagreed with the majority's decision to overturn a lower court ruling that had dismissed an injunction against a Kentucky state law. The law in question required all able-bodied men between 18 and 50 years old to work on public roads for six days each year or pay $3 instead. The company argued this was unconstitutional as it amounted to involuntary servitude, but Holmes contended that such laws were common practice at both state and federal levels throughout history without being deemed unconstitutional. He also pointed out that military service could be seen similarly yet is universally accepted as constitutional. Furthermore, he emphasized the importance of deferring to states' rights in matters like these unless there is clear violation of constitutionality which he did not see present here.