A large non-voting would-be constituency means that there is little mandate for politicians to drive policy.
If say 90% of the population didn't vote, plus there were public demonstrations of discontent, officials would be so afraid of a revolution (or other radical action) it would in theory temper their ambitions.
Tocqueville touches on this in Democracy in America.
Politics is how complex societies make decisions at the largest scale. Despite the wet dreams of the tea party contingent, politics and government-by-mandate aren't optional in the 21st century and haven't been for a long time. Tocqueville died in 1859, back when things were simpler.
If 90% of the population refuse to vote then you would end-up with one of two outcomes:
1. A minority government governing with a mandate from <= 10% of the population. Cue politician saying 'look, I got 80% of the votes cast'. Expect: extreme social unrest, dictatorship by minority, authoritarianism.
2. No government. Not as great as some might think. Expect: nothing-gets-done, social collapse, power vacuum, enemy nations sharpen their knives.
First-world politicians in this century won't have their ambitions "tempered" by large scale withdrawal from voting - all this would do is remove the main mechanism that restrains them. Even in a society that has backed itself into this kind of local minima, politics and politicians would still exist.
If say 90% of the population didn't vote, plus there were public demonstrations of discontent, officials would be so afraid of a revolution (or other radical action) it would in theory temper their ambitions.
Tocqueville touches on this in Democracy in America.