Whoever is generating the hash has access to the plaintext map of accounts can alter it at will before hashing it.  You have to take the word of the person who is doing the hashing, and I don't see a way around that.

If your account map is { (A, 5), (B, 2) } you could add all the accounts, then take the total amount, 7, and append a nonce, so you have 7_snei238nbd, and then just sign that with the private key of whoever is doing the hashing.  Third parties can verify the signature but they cannot forge messages.

You could go further and take the SHA-256 hash of the account data, and append it to the total and the nonce before signing.  Then if the signer/hasher is challenged or "audited" they can't arbitrarily assign values to keys.  They are locked into revealing how the values were assigned to keys at the time of signing.