How to Calculate the Maximax

When you make business decisions, you may be guided by optimism, realism or pessimism. Decision theory is the study of how people make choices. If, say, you decide that expanding your product line is a good move, what leads you to that conclusion? Deciding based on the best possible outcome – the maximax – is one approach.

TL;DR (Too Long; Didn't Read)

When you use the maximax decision-making approach, the first step is to list your potential choices and the possible outcomes of each. Look at the maximum possible gain from each choice and select the option that offers the biggest gain. That's maximax thinking – choosing the maximum of the maximums.

Maximax and Other Standards

Suppose you're contemplating raising prices for your services. If you knew exactly what effect a price hike of 10 percent, 15 percent or 25 percent would have on your revenue, the decision would be easy. In most cases, you don't have complete certainty, but you have to make a decision anyway.

Faced with uncertainty, different business owners judge the best choice based on different criteria. Decision theory identifies several approaches:

  • Expected value. You calculate the most likely outcome of each alternative and pick the one with the best payoff. It's considered a criterion of realism.

  • Maximax. You consider the best possible outcome of each option and pick the biggest potential payoff regardless of risk. This optimistic approach gets its name because you're hoping for the best of the best: the _maxi_mum of the _max_imum.

  • Maximin. This is the pessimist's approach: Figure out the worst possible outcome of each pathway and then pick the best of the worst outcomes or the _maxi_mum of the _mini_mums.

  • Minimax, sometimes called the minimax regret standard. This is for people who kick themselves and say, "If only I'd picked option B instead!" They look at the maximum losses likely under each alternative and go with the option that offers the _mini_mum of the _max_imums.

  • Laplace criterion. Given the current information, all outcomes look equally likely. You go for the biggest payoff.

Crunching the Numbers

Decision theory isn't just about the types of decisions you make. It's also about making them well. Whether it's your nature to use maximax or minimax regret for your judgment calls, decision theory helps you do it thoughtfully. If you're not sure which approach you want to use, you can try out all of them.

The formulas for the different criteria can involve a lot of number crunching. Maximax is one of the simpler methods. If you're considering raising prices, make projections for the possible outcomes at different price points. Look at the best possible outcome for each higher price and pick the best of the best.

With a maximin calculation, you look at the smallest possible gains and pick the best of these. It's a more conservative approach. A minimax regret calculation looks at how much you're likely to lose if you pick the wrong price and then goes with the smallest possible loss. The Laplace criterion and the criterion of realism require more math.

Why Use Maximax?

Maximax decision making is a strategy that appeals to risk takers and business owners who like an aggressive, shoot-the-moon approach. They're willing to take a long shot if there's a chance they'll win big. Minimax regret, by contrast, may work better for someone who can't stand losing money.

Making Maximax Better

Using the maximax approach doesn't mean making decisions based purely on hope. Before you pick the maximum of the maximum, do your research so you have a realistic idea of the maximum outcome for each possible choice.

You may be able to improve the results of your maximax strategy by gathering more information. Hiring an economist can give you a better prediction of economic and market trends. Simply taking a little extra time may give you more certainty about what's going to happen. The lower the uncertainty, the better decisions you can make no matter which method you use.