Simplified version of double-entry bookkeeping for personal and business finance?

Asset = Equity + (Income - Expense) + Liability

Everything could be cancelled out in double entry accounting.

By your logic, if the owner contributes capital as asset, Equity is "very similar" to Asset.

You will end up cancelling everything, i.e. 0 = 0.

You do not understate liability by cancelling them with asset.

Say you have $10000 debtors and $10000 creditors. You do not say Net Debtors = $0 on the balance sheet.

You are challenging the fundamental concepts of accounting.

Certain accounts are contra accounts. For example, Accumulated Depreciation is Contra-Asset. Retained Loss and Unrealized Revaluation Loss is Contra-Equity.

Ditto Nate Eldredge in many ways, but let me add some other thoughts.

BTW there are not four types of account, but five. You're forgetting equity, also called capital.

Would it be possible to design an accounting system that does not have 5 types of accounts, maybe is simpler in other ways, and is internally consistent and logical? I'm sure it is. But what's the advantage?

As Nate points out, the existing system has been in use for hundreds of years. Lots of people know how it works and understand it.

I'd add: People have long since worked out how to deal with all the common situations and 99% of the odd cases you're likely to hit. If you invent your own system, you're starting from scratch. You'd have to come up with conventions to handle all sorts of situations. How do I record buying a consumable with cash? How do I record buying a capital asset with credit? How do I record paying off debts? How do I record depreciation? Etc etc. If you worked at it long and hard enough and you're a reasonably bright guy, maybe you could come up with solutions to all the problems. But why?

If you were approaching this saying, "I see these flaws in the way accounting is done today. I have an idea for a new, better way to do accounting", I'd say good luck, you have a lot of work ahead of you working out all the details to make a fully functioning system, and then persuading others to use it, but if you really do have a better idea, maybe you can revolutionize the world of accounting.

But, "The present system is too much trouble and I don't want to bother to learn it" ... I think that's a mistake. The work involved in inventing your own system is going to end up being way more than what it would take to learn the existing system.

As to, Aren't liabilities a lot like assets? Well, in a sense I suppose. A credit card is like a checking account in that you can use it to pay for things. But they're very different, too. From an accounting point of view, with a checking account you buy something and then the money is gone, so there's one transaction: reduce cash and increase office supplies or whatever. But with a credit card there has to be a second transaction, when you pay off the charge: So, step 1, increase debt and increase office supplies; step 2, decrease debt and decrease cash. Credit cards charge interest, well you don't pay interest to use your own cash. Etc.

One of the beauties of double-entry book-keeping is that every transaction involves a debit and a credit of equal amounts (or a set of debits and credits where the total of the debits equals the total of the credits). If you combine assets and liabilities into, whatever you call it, "balance accounts" say, then some transactions would involve a matching debit and credit while others would involve a positive debit and a matching negative debit and no credit. I'm sure you could make such a system work, but one of the neat built-in protections against error is lost.

There's a very logical distinction between things that you have or that others owe you, and things that you owe to others. It makes a lot of sense to want to list them separately and manage them separately. I think you'd pretty quickly find yourself saying, "well, we have two types of balance accounts, those that represent things we have and which normally have positive balances, which we list on chart A, and those that represent things we owe and which normally have negative balances, which we list on chart B". And before you know it you've just reinvented assets and liabilities.

It's possible, but wrong. Each component of the accounting equation serve its fundamental purpose. In accounting, there are no plus/minus signs in the account entries (although permitted) because the accounting equation and debits/credits define the mathematical structure.

Accounting is not math - it is build on top of the math with specific definitions and structure. Changing any premisses will deconstruct it, so it is no longer accounting - it is something else.

Assets are what you own. Liabilities are what you owe. There is simply no reason to mix them up in a bucket, since they would simply net to zero (ignoring equities, expenses, income). It is like saying you have nothing, but you do have a house just purchased for $100k (asset) AND a mortgage of $100k (liability). So here it comes the philosophical question: do you have a house and a mortgage, or do you have nothing? You do have a title of ownership for the house, and the bank has a title of ownership of the loan. So combining the two accounts, what would you call it? "The net result of things I owe and own"?

The reason why this is wrong is because it is not accounting. You are basically challenging the principles and notation of a science. It is the same as saying that you would like to use the plus sign + for fractions in math. It is wrong.

Why does nobody do this? Because it would make things more complicated. Merging assets and liabilities would require some other method to decoupling them. Minus and plus signs won't work because it would cancel them out, so you would need a third notation (say asterisk *) to indicate what is an asset and what is a liability.