Say Adam the accuser is taking Dave the Defendant to court. If Dave loses in his local district, I've heard that he can appeal the decision and be re-tried in a higher court (all the way to the Supreme Court, theoretically). But is the opposite also possible? I.e. if Dave is acquitted, is Adam allowed to re-try him in a higher court, hoping Dave will be found guilty this time?
In the US, the prohibition against double jeopardy provides a hard restriction against re-trial and appeal of an acquittal. The government cannot appeal an acquittal (U.S. v. Sanges, 144 U.S. 310, Ball v. U.S., 163 U.S. 662), and a verdict of acquittal without judgment is also a bar to re-prosecution. The exception is that if the defendant was never in jeopardy – the judge had been bribed – then there can be a new trial (Harry Aleman v. Judges of the Criminal Division, Circuit Court of Cook County, Illinois).
However, Adam does not take Dave to court. Adam may make an accusation that motivates the prosecutor to file criminal charges.
When Adam sues Dave (not a criminal matter), there is no acquittal or conviction, or guilt. There may be a finding of liability, or not. Either side can appeal to the top, as long as there is a legal basis for the appeal. If Adam is found not liable because the judge makes a legally erroneous ruling, if Dave objected properly to the ruling, Dave can appeal if successful, the court could then change its mind and find Adam liable.
In Canada, Attorneys General are limited in the grounds on which they may appeal an acquittal: the appeal must be based on a ground of law alone. See Criminal Code, s. 676(1)(a):
The Attorney General or counsel instructed by him for the purpose may appeal to the court of appeal... against a judgment or verdict of acquittal ... of a trial court in proceedings by indictment on any ground of appeal that involves a question of law alone
See also R. v. Chung, 2020 SCC 8 (citations removed):
 Under s. 676(1)(a), the Crown can only appeal an acquittal on a “question of law alone”. An appealable error must be traced to a question of law, rather than a question about how to weigh evidence and assess whether it meets the standard of proof. Therefore, the Crown cannot appeal merely because an acquittal is unreasonable.
 Errors of law arise, for example, where “the legal effect of findings of fact or of undisputed facts raises a question of law” and where there is “an assessment of the evidence based on a wrong legal principle”. These two types of errors are somewhat similar; they both address errors where the trial judge’s application of the legal principles to the evidence demonstrates an erroneous understanding of the law, either because the trial judge finds all the facts necessary to meet the test but errs in law in its application, or assesses the evidence in a way that otherwise indicates a misapprehension of the law.
On the appeal from an acquittal, the court of appeal may (Criminal Code, s. 686(4)):
dismiss the appeal,
order a new trial, or
when the trial was originally before a judge alone (rather than a judge and jury):
enter a verdict of guilty with respect to the offence of which, in its opinion, the accused should have been found guilty but for the error in law, and pass a sentence that is warranted in law, or remit the matter to the trial court and direct the trial court to impose a sentence that is warranted in law.
The U.S. has a near absolute prohibition on appeals from acquittal, as described in user6726's answer.
If Adam is suing Dave in a civil trial, the answer is yes. (Technically, they would be Pam the Plaintiff and Robert the Respondent.) Whoever lost could file an appeal claiming that there was some kind of error in the trial, such as allowing evidence that should not have been allowed, or giving the jury incorrect instructions. (Just saying that the jury’s verdict was wrong, is not enough for an appeal to be taken seriously.) An appeals court might or might not then agree to hear the appeal. If it does, it would allow both sides to submit briefs arguing their case, and possibly give oral arguments where they answer the judges’ questions. This is not a new trial, there is no jury, and no new evidence gets introduced. However, the court of appeals might order a do-over trial with a new jury.
If you are thinking of a criminal trial with a defendant, no. (With an asterisk.) The Fifth Amendment to the U.S. Constitution prohibits trying someone who has been acquitted again for the same offense, which is called “double jeopardy.” The defendant can appeal a conviction, but the prosecution cannot appeal an acquittal by a jury. (Also be aware: there are no private prosecutions in the United States. Criminal charges are always brought by the government.)
I got some good comments discussing exceptions. Certain types of misconduct, such as bribing the judge to acquit, can get a not-guilty verdict overturned. The reasoning is, since the defendant was never in real jeopardy, there is no double jeopardy.
While private prosecutions are not allowed in federal court (Linda R. S. v. Richard D., 410 U.S. 614 (1973)), there are a few state or local courts that allow them under some circumstances. North Carolina allows a private attorney to assist the public prosecutor, who remains in charge of the case; and Texas allows a local judge to appoint any competent attorney to prosecute when there is no district attorney available. But Adam the Accuser never gets to appeal.
No, you cannot be retried hoping for a conviction. Generally. There are a few funky exceptions:
- if jeopardy did not actually attach (you bribed the judge or jury)
- the trial never actually properly started (the jury was improperly empaneled or the oaths given to witnesses was incorrect, for example - extremely rare)
- you are going to be tried in a different jurisdiction (jeopardy only applies to the jurisdiction of the trial)
- if your acquittal was for a crime that has, post-trial, escalated.
This last one requires a bit of explanation. Let's say you shoot someone and they are severely injured, but live. You are put on trial for attempted murder, and are acquitted. The person shot later dies due to the damage done by the shooting. You can be tried for murder, even though you were previously acquitted of attempted murder for the exact same event.