Now, continue that train of thought. Imagine that the person not voting is one of the politically ignorant mentioned in the quote.
What are they going to do at the polls? Are they going to add signal or noise? What is accomplished by them choosing a candidate at random?
Letting people who are informed make decisions for you happens all the time. Engineers and safety officers determine speed limits. Architects determine how the buildings you enter are constructed. Panels of electricians, firemen, and manufacturers determine the electrical codes that keep your house from randomly catching fire or electrocuting you. Interested people organize community events you attend. What makes politics any different?
My personal ideal would be that only the informed vote. Anyone has the right to become involved, as well as the right to abstain and accept the choice of their peers. Unfortunately, many people form their political opinions in echo chambers and are less informed than they think.