No one is in charge of Bitcoin. Every node simply keeps the chain with the most work. Two things follow: the network sometimes forks and heals itself, and an attacker with enough hashpower can secretly out-build the honest chain to reverse a payment that already looked confirmed.
When two miners find a block at once you get a fork. The moment one side is extended, it becomes the most-work chain and the other side's block is orphaned: a reorg. Watch the highlight jump.
Each block mined on top of a payment makes reversing it exponentially harder, for any attacker below 50%. That's the whole reason to "wait for 6 confirmations".
Even just under half the hashpower gives a real chance of a double-spend; just over half makes it a near-certainty given patience. Security degrades smoothly, then collapses.
For a small miner, honest mining on the longest chain is the profitable strategy, which is why the network stays converged. (Above roughly a third of the hashpower, cleverer withholding strategies ("selfish mining") can beat it; another reason concentration is the thing to watch.)