Did you read the whole article? His most significant proposal is that modern democracies adjust their procedures to use something called "sortition" that dates back to ancient Greece.
In sortition, rather than polling the entire populace about complicated issues on which they are likely not well informed, we select a balanced random sample of people from the populace , provide them information, and then allow them to engage each other on the issue. Then we have those people vote.
This has several advantages:
1. It actually places "faith in a large number of people selected from all social backgrounds" depending on how large your sample, as opposed to letting elected politicians decide, which is the definition of "a small number of people selected from a potentially narrow social background".
2. It solves the problem where a huge number of people end up voting because of gut instinct or misinformation. Consider the passage of Proposition 13 in California which prohibits the raising of property taxes. If you poll the entire population, that referendum is going to win 100 times out of 100, because for most people the gut check decision is "no I don't want my taxes to go up". However, the correct way to consider that proposition is to get an understanding of how property taxes are used, how they are collected, what the procedures are for changing them in the legislature, etc. and then come to a determination. That determination might be "Yes", it might be "No", or it might be "we should not limit increases in property tax rates but instead limit increases to the real value of collected taxes, by accounting for changes in property values". [1]
[1] I'm not proposing that is the right answer, I'm just suggesting that you might arrive at that conclusion if you actually had time to study the issue. Almost by definition, the vast majority of people do not have that time.