The problem is not that they would do worse. The problem is that they would be entirely dependent on the information they were provided. Anybody who gives them that information has their own opinion, and whether they want to or not, that opinion informs the way they dispense information. This means the random members of the population aren't deciding based on objective evidence. They can't really form their own opinions if every bit of information is biased one way or another.

That is why I said it was similar to a trial-by-jury. The jury isn't versed in law or in the details of the case, so they get all the information they need to make a decision from the lawyers presenting the case. That leads to situations like one we had in my home country: A woman was sentenced to life in prison for a murder without any evidence. None at all. She had motive and was 'an asshole', and that was enough for the jury to be sure she did it.

If there was a way to objectively give them the facts of the case and the knowledge they need, the system would be perfect, but unfortunately that's not possible. And until it is, i would rather have people making decisions based on their own badly informed opinions than people making decisions based on others' opinions with a veneer of legitimacy.