Understanding Decision-Making Without Probabilities: Maxi-Max, Maxi-Mean, Mini-Max Regret (Full Transcript)

Speaker 1: Welcome. In this brief video, we will be discussing decision-making without probabilities. In this first part, we will consider the Maxi-Max or the optimistic approach, the Maxi-Mean, also known as conservative or pessimistic approach, and the Mini-Max, regret approach to decision-making. The table seen here is referred to as a payoff table or decision table. The alternatives on the left here in the rows are referred to as decision alternatives. They are the options available for the decision-maker to choose from. We will assume that the decision-maker can only choose one of these alternatives, invest in bonds, stocks, or mutual funds. In the columns, we have the economic conditions. Since the decision-maker does not have control over these, we refer to them as states of nature or outcomes. The values in the table are called payoffs. They could be profit, cost, distance, time, and so on. In this example, we treat them as profits. The Maxi-Max or optimistic approach. Using this optimistic approach, we choose the alternative with the best possible payoff. Looking at bonds, the best payoff is 45, the best is 70 for stocks, and the best is 53 for mutual funds. The overall best is 70. Therefore, the decision is to invest in stocks. The Maxi-Mean or conservative approach. Using this pessimistic approach, we choose the alternative with the best of the worst payoffs. We first choose the worst payoff in each alternative and then choose the best of the worst. Looking at bonds, the worst payoff is 5, the worst is minus 13 for stocks, and the worst is minus 5 for mutual funds. The best of these is 5. Therefore, the pessimistic or conservative approach is to invest in bonds. The Mini-Max Regret approach. Using this approach, we choose the alternative with the minimum of all maximum regrets across all alternatives. Regret, also known as opportunity loss, is the difference between the best payoff in a particular state of nature and the actual payoff received. For example, if the economy is growing, the best payoff is 70. If we happen to have invested in bonds, then the regret will be 70 minus 40, which is 30. If we invested in stocks, then there is no regret. If we invested in mutual funds, then the regret is 70 minus 53, which is 17. Again, if the economy is stable, the best payoff is 45. So if we invested in bonds, there is no regret. The regret is 45 minus 30 if we invested in stocks. If we invested in mutual funds, there is also no regret. For declining economy, the best payoff is 5. If we invested in bonds, there is no regret. If we invested in stocks, the regret is 5 minus negative 13, which is 18. If we invested in mutual funds, the regret is 5 minus negative 5, which is 10. Here is the regrets table. Since the decision is to be made based on Mini-Max Regret, we first determine the maximum regret for each alternative and then choose the minimum. For bonds, the maximum regret is 30. For stocks, it is 18. And for mutual funds, it is 17. The minimum of these maximum regrets is 17. The decision is to invest in mutual funds. See you in part 2. Thanks for watching.