LedgerBadger is similar to the venerable BillMonk, which served us well for several years. However, it has a few key differences, which I describe here.
Perhaps the most significant difference is that each LedgerBadger user maintains his/her own personal ledger. Your ledger is simply the list of transactions that you have an approved stake in. Your ledger can only be modified by you -- nobody else can add, delete, or modify transactions in your ledger. This means that your balances when you log out are exactly the same as when you log back in. This also means that transactions are immutable -- once created, they cannot be modified, even by the creator.
By themselves, these contraints sound overly restrictive. If everyone maintains their own ledger, how can you share debts with others? The answer is that users attach themselves and others to transactions with stakes While transactions are immutable, each name in a transaction can be staked by a user, thereby including that transaction in their ledger. The transaction creator can attach preliminary users to their transactions, and each user must then approve their stake in that transaction. You'll find such pending transactions at the top of the transactions page. If you don't think the transaction is correct, you can simply remove yourself from it (and potentially create a new correct transaction). In this way, different versions of the same event can compete with each other -- hopefully, in the end, everyone agrees to stake themselves in the same transaction, and the unused ones simply aren't attached to anyone.