The research, titled "Space Complexity in Choice" and published in the prestigious journal Econometrica, analyzes how the size of decision problems, the order of information processing, and its structure determine the memory required to solve them, and how these memory demands influence the probability of making the correct decision. The work has been published in one of the world's most relevant scientific journals in economic research, edited by the Econometric Society of the United States.
The study demonstrates that decisions on similar issues, even with the same information, can present different levels of difficulty depending on how the data is structured and processed. Through a mathematical formulation, Sanjurjo explains how the organization of information and the order of analysis can influence both the complexity of the process and the effectiveness of the final choice. In fact, the order of processing can make a difference of approximately 40 percentage points in the hit rate when decision problems include many alternatives and attributes, while differences are much smaller in smaller problems.
“"The results thus point to a more general idea about human rationality. When a decision overwhelms us, we can adapt by reorganizing how we process information. The ability to decide well depends not only on the objective characteristics of the problem or how much information we have, but also on how we structure that information to reduce what we need to keep simultaneously in memory."
Sanjurjo comments that a simple example to understand this is choosing between several products by comparing different characteristics: price, quality, duration, etc. One can examine all the information for one product before moving to the next. But one can also look first at the price of all, then the quality of all, and so on. The available information and the final decision are exactly the same, but the demands on our memory can be very different.
The experiments conducted confirmed one of the theory's main predictions: in smaller problems, with few alternatives and attributes, both processing orders require similar amounts of memory, and participants achieve similar results. However, as the problem size increases, the difference in memory needed for each order grows linearly, as does the difference in hit rates. In larger problems, the latter reaches approximately 40 percentage points. On average, considering all problem sizes, participants succeeded in 87.5% of decisions when following the order requiring less memory, compared to 66.1% when following the one requiring more. Thus, the results show how spatial complexity, a mathematical measure of memory demands, can predict the difficulties people experience when making decisions.
The UA researcher explains that the central idea of the work comes from theoretical computer science, where "space complexity" measures how much memory a machine needs to solve a problem. Sanjurjo applies this same measure to human decisions, quantifying the working memory needed to process information and reach a decision, thus explaining why different ways of solving the exact same problem can have very different difficulty levels.
In an experimental situation where no one instructed participants on how to process the information, 98.5% spontaneously constructed the type of order that theory identifies as having the lowest spatial complexity. Furthermore, their performance was very high, succeeding in approximately 90% of decisions.
