It's not centralized. It's democratic.
But it isn't democratic. How do you vote? How do you guarantee the vote is fair, accurate, and timely? How do you ensure the people voting are informed? How do you make sure the person who has the ACTUAL POWER to make the changes follows the will of "the people".
You vote by rejecting the chain you think is wrong. You do this either by checkpointing the one you think is right, or allowing someone to do it on your behalf (e.g. by connecting to them). You're motivated to checkpoint the one you think the rest of the world is likely to agree with, because if you're wrong, you've just made yourself a potential victim of double spending by anybody (who can spend their funds both in the majority chain, and the one you swallowed.)
Bottom line is, you always want to be with the majority opinion for your own security, and that alone will motivate people to come to a consensus on the basis of popularity alone. A real attack chain that appears out of obscurity and rolls back a large number of blocks is going to have approximately 0% popularity and which is the right chain isn't going to be the subject of much debate.
Rejecting an attack chain isn't a battle of philosophical opinion. It's not like right versus left, or Christians versus Muslims. It's more like, what did we all observe. If an attack happens, we'll know we observed an attack. End of story. It would be about as uncontroversial as asking the world whether the World Trade Center towers fell on 9/11/2001.
They fell. No serious percentage of the population disputes it. No one is attempting to write a history book that says the original towers are still standing.
Unless some massive bandsaw slices the earth in half and splits the network and all the mining power in half for an extended period of time, a naturally occurring chain reorg 5+ blocks deep is statistically unlikely. We should plan on that event being an attack, and have Bitcoin go into a safety mode, favoring an intact system that is temporarily unavailable over an available one that is useless because none of the information in it is accurate due to being under control of an attacker.
