```python
from typing import List,from collections import defaultdict

from operator import item

from itertools import chain:

def merge_ledger(base: List[List], ours: List[List], theirs: List[list]) -> List[List]:
    if not all(isinstance(ledger, list for for entry in ledger for entry in ledger):
        raise ValueError("Invalid ledger format")

    def validate_entry(entry):
        if len(entry) != 2:
            raise ValueError("Invalid entry format")
        account, cents = entry
        if not isinstance(account, str) or not account:
            raise ValueError("Invalid account name")
        if not isinstance(cents, int):
            raise ValueError("Invalid cents value")

        return account, cents

    base_dict = {entry[0]: entry[1] for entry in base}
    our_dict = {entry[0]: entry[1] for entry in ours}
    their_dict = {entry[0]: entry[1] for entry in theirs}

    
    merged_dict = defaultdict(int)
    
    for account in set(base_dict.keys 
        if_value = base_dict[account]
        if_value += = our_dict.get(account, 0)
        merged_dict[account] += their_dict.get(account), 0)
        
    for account in set(our_dict):
        if account not in base_dict:
            merged_dict[account] += our_dict[account]
            
    for account in set(their_dict):
        if account not in base_dict:
            merged_dict[account] += their_dict[account]
            
    for account in set(base_dict):
        if account not in our_dict and account not in their_dict:
            del merged_dict[account]
            
    merged_list = sorted([(account, merged_dict[account]) for account in merged_dict], key=lambda x: x[0])
    
    return merged_list
```
