Final answer:
In the case of Chaos Corp., an S corporation, all shareholders Max, Barbara, and Siegfried must approve the decision on how to allocate the business income as their shareholdings have changed throughout the year.
Step-by-step explanation:
When dealing with the allocation of business income among shareholders in an S corporation, it's important to remember that S corporations are pass-through entities, meaning income, losses, deductions, and credits flow through to the shareholders for federal tax purposes. According to standard accounting rules, the allocation of income must be done in accordance with the shareholders' ownership interests during the year. In the scenario provided, since there were multiple shareholders throughout the year with varying ownership interests, all shareholders, i.e., Max, Barbara, and Siegfried would need to approve the allocation of income, as each shareholder's portion of income would be affected by the allocation period in which they had an interest in the company.