Would a group of people selected at random do a better job addressing the nation’s problems than the current Congress?

One of the principles discussed by the founding fathers was that politicians have enough personal wealth and educational wherewithal to avoid

1. being bribed easily
   
2. being economically threatened / intimidated, after political service
   
3. being manipulated with assaults of advocacy, or just generally not knowing how the big[ger] system works.

it would change the game, but unlikely for the better — and worse it may cultivate a 'diva' behavioral pattern common to sudden wealth / power (lottery winnings, new rich, etc). This diva pattern has been well-shown by And Warhol's "15 minutes of fame" and in parables like The Hunger Games, Lord of the Flies, etc.