In Burch et al. v. Louisiana, the U.S Supreme Court ruled that a conviction by a non-unanimous six-person jury in a criminal trial was unconstitutional. The case involved Gary Burch who had been convicted of simple battery in New Orleans by a five-to-one verdict from a six-member jury, which was permissible under Louisiana law at the time. However, on appeal to the Supreme Court it was argued this violated his Sixth and Fourteenth Amendment rights to an impartial jury trial and equal protection of laws respectively. In its decision, the court held that while states have discretion over their own judicial systems including juries' size or unanimity requirements for convictions; they must not infringe upon defendants' constitutional rights when doing so - particularly where serious offenses are concerned such as those carrying potential jail sentences like Mr.Burch's case did.

In the dissenting opinion for Burch et al. v. Louisiana, Justice William Rehnquist disagreed with the majority's ruling that a non-unanimous six-person jury verdict in a criminal case was unconstitutional. He argued that there is no constitutional requirement for unanimity in jury decisions and pointed out that historically, English common law did not always require unanimous juries either. He also noted that several states had allowed non-unanimous verdicts at various points without any apparent detriment to justice or public confidence in the legal system. Furthermore, he contended that it was inappropriate for the Supreme Court to impose its own preferences on state courts regarding how they should conduct their proceedings when there is no clear constitutional mandate requiring them to do so.