Monthly Archives: January 2022

Robustness is a form of efficiency

Efficiency means using the best way to achieve a goal. Mathematically, selecting the maximizer of an objective function. The goal may be anything. For example, the objective function may be a weighted average of performance across various situations.

Robustness means performing well in a wide variety of circumstances. Mathematically, performing well may mean maximizing the weighted average performance across situations, where the weights are the probabilities of the situations. Performing well may also mean maximizing the probability of meeting a minimum standard – this probability sums the probabilities of situations in which the (situation-specific) minimum standard is reached. In any case, some objective function is being maximized for robustness. The best way to achieve a goal is being found. The goal is either a weighted average performance, the probability of exceeding a minimum standard or some similar objective. Thus robustness is efficiency for a particular objective.

The robustness-efficiency tradeoff is just a tradeoff between different objective functions. One objective function in this case is a weighted average that puts positive weight on the other objective function.

Whatever the goal, working towards it efficiently is by definition the best thing to do. The goal usually changes over time, but most of this change is a slow drift. Reevaluating the probabilities of situations usually changes the goal, in particular if the goal is a weighted average or a sum of probabilities that includes some of these situations. A rare event occurring causes a reevaluation of the probability of this event, thus necessarily the probability of at least one other event. If the probabilities of rare events are revised up, then the goal tends to shift away from single-situation efficiency, or performance in a small number of situations, towards robustness (efficiency for a combination of a large number of situations).

To be better prepared for emergencies and crises, the society should prepare efficiently. The most efficient method may be difficult to determine in the short term. If the expected time until the next crisis is long, then the best way includes gathering resources and storing these in a large number of distributed depots. These resources include human capital – the skills of solving emergencies. Such skills are produced using training, stored in people’s brains, kept fresh with training. Both the physical and mental resources are part of the economic production in the country. Economic growth is helpful for creating emergency supplies, raising the medical capacity, freeing up time in which to train preparedness. Unfortunately, economic growth is often wasted on frivolous consumption of goods and services, often to impress others. Resources wasted in this way may reduce preparedness by causing people to go soft physically and mentally.

Solving a crisis requires cooperation. Consumption of social media may polarize a society, reducing collaboration and thus preparedness.