ABCore is a wrapper for Bitcoin Core for Android.
Bitcoin Core (formerly Bitcoin-Qt) is the bitcoin daemon software based on the original reference code by Satoshi Nakamoto. It is programmed to decide which block chain contains valid transactions. The users of Bitcoin Core only accept transactions for that block chain, making it the Bitcoin block chain that everyone else wants to use.
It is these users who keep Bitcoin decentralized. They individually run their own Bitcoin Core full nodes, and each of those full nodes separately follows the exact same rules to decide which block chain is valid.
There's no voting or other corruptible process involved: there's just individual software following identical rules—"math"—to evaluate identical blocks and coming to identical conclusions about which block chain is valid.