Juries are fairly rare things these days.
They were developed in 12th century English common law, and were originally investigators and act as witnesses (this was centuries before police forces or modern ideas about public law enforcement). At the time courts moved around, so were only in town for a short period any given year, and would hear all the cases at once. The jury, made up of local rich and influential people, was there to explain (under oath) what happened – stating the facts they were expected to know, being local – so the judge, from outside, could apply those facts to the law and give a ruling.
It was a way of balancing the power of the King (via the royal justices who answered to him) with the local establishment (who got to be on the juries).
The modern jury evolved from this over the centuries, emphasising the split between the jury who answer questions of fact (what happened) and the judge who answers questions of law (what does this mean). They work together to come to a verdict.
The US uses juries a lot (more than anywhere else) because when the US Constitution was being written juries were all the rage (particularly as a way to protect the upper-middle classes from the ruling classes). There is a whole load of awkward 18th century ideology wrapped up in juries (such as the idea that the best way to determine the truth of something is to ask a rich, white man his opinion), and so the US Constitution requires juries for criminal *and civil* trials, and even *grand juries*, which are now only used by the US and Liberia (modelled on the US).
Most other countries that used juries (mostly copied from the English common law system) have dropped them for most cases – even in England less than 5% of criminal cases go before a jury, and civil juries are only used in exceptional cases.
The idea behind a jury is that the average person is the best person to determine what is and isn’t true, particularly when it comes to testimony, and that a jury offers a level of protection against unjust laws. The former is demonstrably untrue (by the number of cases were juries reach crazy conclusions), the latter probably is (although also opens the door to lots of other problems – the US in particular had a big problem with racism in juries, and arguably still does).
The idea behind a bench trial is that judges are harder to sway and manipulate emotionally (lawyers going before a jury will have all sorts of research on how to have their clients and witnesses dress, speak, behave etc. to make the right impression on the jury), and also don’t have to waste the court’s time by explaining basic legal principles to the jury. Judge-only trials can get straight to the heart of the dispute, often briefing all the other issues on paper.
Trials (or appeals) with multiple judges are a sort of balance between this; reducing the problems of having a single point of failure (in the single judge), but still having experts or professionals making the decision.
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