First, a reading from Bizarro Matthew 14:15-21:
As evening approached, the disciples came to him and said, “This is a remote place, and it’s already getting late. Send the crowds away, so they can go to the villages and buy themselves some food.”
Bizarro Jesus replied, “They do not need to go away. You give them something to eat.”
“We have here only five loaves of bread and two fish,” they answered.
“Bring them here to me,” he said. And he directed the people to sit down on the grass. Taking the five loaves and the two fish and looking up to heaven, he gave thanks and broke the loaves into 5000 tiny crumbs and broke the fish into 5000 tiny slivers. He then directed his disciples to give each person one tiny crumb and one tiny sliver of fish muscle. The people each consumed 1.91 Calories* and remained very hungry.
In this Bizarro Matthew parody, Bizarro Jesus does not take hunger seriously. Sure, the people go from having no food to having some infinitesimal amount, but it would be silly to treat this as a morally or nutritionally significant change. The amount matters, and being > 0 is not enough. Bizarro Jesus cannot pat himself on the back and claim he's fed people. He hasn't fixed the problem anymore than doing a single jumping jack stops heart disease. It would be as if he'd distributed a penny (in current USD) to every poor person and then said that he'd reduce the problem of poverty.
Now consider a similar situation in democratic theory. Imagine we have a political system in which a small cadre of people--say the king and his advisors, the Central Committee, the aristocracy, or whatnot--make all political decisions, decisions which bind everyone else. The vast majority of people are powerless.
Suppose someone comes along and says, "I know how to fix the problem here. Let's keep the government bureaucracy which executes the rules, but instead of having a hereditary king or elite Central Committee, we'll let all 200 million members of our society vote as equals on who gets to be king or on the Central Committee." Here, we change things. The vast majority of people go from having no power to technically having some--a tiny, infinitesimal amount. But if you agree that Bizarro Jesus hasn't really fed people, then you should agree that distributing equals voting rights doesn't really empower people either, nor does it protect individuals from their government or give them any meaningful or worthwhile say.
Even if we got rid of the central government and bureaucracy, and instead had direct democracy all the time, the problem would remain. Everyone would have equal voting power, but that power would for almost all people almost all the time be tiny. To say individuals are empowered in this situation is like saying Bizarro Jesus fed everyone. Going from 0 to ε power is not empowerment or freedom. The amount of control matters. It is morally and intellectual unserious to claim otherwise.
One way of thinking about democracy--when it is working at its best, really--is that it empowers the People without thereby empowering any of the individual people who constitute the People. Of course, in practice, all democracies empower some people (e.g,. racial majorities) more than others (racial minorities), and empower some people (charismatic liars, the well-connected) quite a bit. But even in principle, the secret joke at the heart of large democracies is that equal basic power for all amounts to everyone having almost no power.
Sure, democracy might, in principle, equalize people in one particular respect, but that's not the same thing as empowering them.
*Yes, I looked this up, and this is a high estimate of the caloric content of 5 loaves of bread and two fish split among 5,000 people. I charitably assume Bizarro Jesus and his Bizarro Disciples don't take any for themselves.