@Martijn Bakker
The system of Jury trials is that the jury must be convinced, beyond all reasonable doubt, on the basis of the evidence that is presented before them, that the person is guilty. There are a number of things here that guard against arbitrary justice (mob rule, kangaroo courts or the decision of a single person).
Firstly the person must be proven guilty. Not proven innocent but proven guilty. Note that mob justice is often the other way round.
Secondly it is 'beyond reasonable doubt'. If a jury thinks 'he might have done it' then its not good enough to find the person guilty.
Thirdly it is 'on the basis of the evidence'. It is the job of the police and prosecution to gather and present evidence, the job of the defence to test that the evidence is properly gathered and not just made up. It is the job of the jury to listen to what is said and weigh up and make a decision based on what is said.
The system is imperfect. A lot of people who have committed a crime may go free. The lawyer may be rubbish and fail to extract proper witness evidence or highlight significant evidence. The police may fail to gather sufficient evidence. The jury may have a concious or unconcious bias (the accused was ugly/black/gay/a woman/looks like a criminal/done it before). But it's the system we have and it's a damn sight better than the knee jerk justice of mob rule.