There is generally little disagreement about the common law provisions of the Seventh Amendment.
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Without the Declaration of Independence and the Constitution of the United States of America, the United States of America would not exist. As such, the values laid out in these two documents are, by definition, American values. And any values held in opposition to the values in these documents are, again by definition, unAmerican.
The Seventh Amendment
In Suits at common law, where the value in controversy shall exceed twenty dollars, the right of trial by jury shall be preserved, and no fact tried by a jury, shall be otherwise re-examined in any Court of the United States, than according to the rules of the common law.
The Seventh Amendment guarantees a trial by jury for civil trials in federal courts. This guarantee may be waived in favor of a “bench trial” where a judge decides the issue instead of a jury, and in some cases Congress has specifically said that bench trials are an acceptable way to decide a case. Former sheriff Joe Arpaio was convicted of criminal contempt of court for refusing to obey a court order in a bench trial before Donald pardoned him (an act which may or may not raise Constitutional questions about the a President’s authority to pardon criminals). As a result, while trials by jury are the norm in the United States, bench trials exclusively before a judge are in alignment with American values.
Per common law, facts are decided at lower courts, while appeals courts only decide matters of law and procedure. The one exception to this common law precedent is when new information forces a re-examination of the facts, and even then matters of fact are usually retried in a local, lower court rather than in an appeals court. The most common example of this is in cases where exculpatory evidence (evidence that demonstrates innocence, or at least raises a reasonable doubt of guilt) is discovered after someone has been found guilty of a crime. Refusing to re-try a case in this situation is unAmerican.
Common law also says that jury decisions must be unanimous. This can result in hung juries (and subsequent mistrials) when one or more individuals cannot be convinced of a verdict. It can also be manipulated in ways that result in jury nullification, an unAmerican concept per the Sixth Amendment.
Common law permits judges to nullify a jury verdict by declaring a mistrial in cases when something happens that is obviously and clearly wrong according to the facts or according to the law. It is per this aspect of the Seventh Amendment that misconduct by police or a prosecuting attorney can result in the dismissal of a case. This also results in judges being able to throw out a verdict and demand that a retrial be performed if a jury clearly gets the verdict wrong.
Finally, retrials are before a new jury per common law. Even a bench trial must be retried before a jury rather than as another bench trial.
Common law may be overruled by Congress in certain cases, and doing so is in accordance with American values.