How the “Maximum Regret Principle” Guides Decision‑Making: A Mathematical Model Explained

In a recent live interview, Haier founder Zhang Ruimin shared his "maximum regret principle," a management approach that tackles pressure by first imagining the worst possible outcome of a crisis and then devising a response plan.

The principle can be expressed mathematically as a regret‑minimization model. First, define a set of decision alternatives \(D\) and a set of possible future states \(S\). For each pair \((d,s)\) there is a utility (or payoff) \(u(d,s)\). The regret for choosing \(d\) when state \(s\) occurs is the loss relative to the optimal decision for that state: \(r(d,s)=\max_{d'\in D} u(d',s) - u(d,s)\). The optimal decision under the maximum‑regret principle is the one that minimizes the maximum regret across all states: \(\min_{d\in D}\,\max_{s\in S} r(d,s)\).

Mathematical Model

Decision set \(D\): all possible choices.

State set \(S\): all possible future scenarios.

Utility function \(u(d,s)\): payoff of decision \(d\) in state \(s\).

From these elements, construct the utility matrix, compute the regret matrix, and select the decision that yields the smallest maximum regret.

Example Analysis

Consider a conglomerate deciding where to invest for the next year: new‑energy technology, smart‑home systems, or traditional home‑appliance upgrades. The future market may favor new energy, smart home, or remain stable for traditional appliances. A utility matrix (in millions of yuan) is assigned to each decision‑state pair.

For each state, the highest utility is identified, and the regret for each decision is calculated as the difference between that highest utility and the decision’s own utility. The resulting regret matrix shows the worst‑case loss for each option.

By comparing the maximum regret values, the smart‑home investment has the smallest maximum regret (20 million), making it the optimal choice under the maximum‑regret principle.

The case illustrates how anticipating the worst outcome and planning accordingly helps leaders stay calm, make decisive choices, and minimize potential losses, both in business strategy and personal life philosophy.