In Beazell v. Ohio, the U.S. Supreme Court ruled on a case involving ex post facto laws - laws that retroactively change the legal consequences of actions committed before the enactment of the law. The defendants were convicted for forging and uttering certain instruments under an Ohio statute which allowed them to be tried jointly instead of separately as per previous legislation at their time of offense. They argued this joint trial violated their rights because it was more disadvantageous than separate trials would have been, thus constituting an ex post facto application of law. The court disagreed with this argument, stating that changes in procedure do not necessarily violate the prohibition against ex post facto laws unless they affect matters of substance by increasing punishment or changing elements necessary for conviction from innocence to guilt. In essence, procedural modifications are not considered unconstitutional if they don't alter substantial personal rights or defenses available according to existing law when alleged crimes occurred. Therefore, since joint indictment didn’t materially disadvantage defendants nor increase their potential penalties compared to separate indictments under old procedures; hence it wasn’t deemed as violating constitutional prohibitions against ex post facto legislation.

In the dissenting opinion for Beazell v. Ohio, it was argued that the application of a new law to an act committed before its enactment violates the ex post facto clause in Article I, Section 10 of the U.S. Constitution. The justice believed that changing sentencing guidelines after a crime has been committed is fundamentally unfair and unconstitutional because it retroactively alters legal consequences. It was also emphasized that laws should provide predictable outcomes and not be subject to change based on legislative whims or shifts in public sentiment. Therefore, applying this new law would undermine principles of fairness and due process by punishing individuals more severely than they could have anticipated at the time their actions were taken.