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# The Mathematics of Irrationality: Reconciling Emotion and Reason

Decision-making connects cognition and behavior, and is thus essential to everyday life and necessary for survival. It drives our personalities and allows us to discern and adapt to changing situations in our environments. People generally make logical decisions, ones that will maximize the reward of the consequential outcome and minimize the likelihood of an undesirable result. However, internal biases—such as emotions and preferences—influence and sometimes impair this sense of rationality. For this reason, psychiatric patients with dysfunctional cognitive and emotional circuitry often make irrational decisions.

During a minisymposium at the 2017 SIAM Conference on Applications of Dynamical Systems, currently taking place in Snowbird, Utah, Sridevi Sarma of Johns Hopkins University spoke about an experimental trial and consequential model to facilitate understanding of the interactions between logic and emotion in irrational decision-making. She introduced the two key factors of decision-making: reason (the desire to rationally maximize reward) and the internal state (comprising emotions, preferences, past experiences, etc.). Sarma sought to investigate the combination of these factors in the brain.

Sarma designed a gambling-based cognitive trial where participants played a modified version of the card game "War," with an infinite deck of only five possible cards. Image courtesy of Sridevi Sarma.
To do so, she introduced a human decision-making “wish list” that evaluates cognitive rationality studies. The list included the following: human data, behavioral data, electrophysiological data (electric activity in relevant brain regions), the capture of electrophysiological data at millisecond resolution, and coverage of all brain areas. The ideal study achieves everything on the list. For example, while researchers have conducted successful cognitive studies in primates, these studies are devoid of human data and the use of all brain areas. In lesion studies, lesions occurring in relevant decision-making regions of the brain could alter the decision-making process. Unfortunately, these tests only satisfy human and behavior data. Functional magnetic resonance imaging (fMRI) is perhaps the most popular cognitive approach, but the data neither yields millisecond resolution nor is particularly electrical.

Sarma then presented her setup, which checks off all items on the wish list. She worked with patients suffering from medically-intractable epilepsy, which doesn’t respond to medication. The resulting seizures are so debilitating that they prevent victims from partaking in everyday activities and result in death without proper treatment. Sarma’s participants had undergone an invasive procedure called stereoelectroencephalography (SEEG), which involves the implantation of 10-12 depth electrodes directly into patients’ brains via small holes in the skull. Each depth electrode has several contacts that allow doctors to monitor seizure activity. 11 SEEG patients participated in Sarma’s experiment; given the rarity of the condition and resulting surgery, this is extremely valuable data.

Sarma chose to focus her cognitive trial on gambling. “We know that when people gamble in the casinos, they are bringing their emotions and prior experiences into play,” she said. “There is a window of opportunity where they have to base the decision on something other than reason.” The 11 participants played a version of the card came “War,” but with an infinite deck of only five possible cards: 2, 4, 6, 8, and 10. After seeing their card, they had to bet either $5 or$20 on whether their card was greater than the computer’s card. If their card was higher, they would win the amount that they bet. If it was lower, they would lose that amount. Thus, someone who drew a 2 or 4 would likely bet only \$5 and minimize their probable loss. Someone who drew an 8 or 10 should bet high to maximize their anticipated win. However, the 6 card was a little trickier. “The expected reward condition on a 6 card is 0,” Sarma said. Thus, 6 brings risk into play, as one would expect risk-takers to bet high and the risk-averse to play it safe.

Results of cognitive trials demonstrated that the internal bias pathway was dependent on previous occurrences. Image courtesy of Sridevi Sarma.
Sarma shared data from the participants’ 150 trials. “As a population, they are risk averse,” she said. “That happens to follow the trend of the expected outcome.” The reaction times for all five cards formed a bell-shaped curve, as participants made the quickest decisions on the two extremes (2 and 10), but had to think more carefully for 6. However, there were quite a few perplexing bets. “Some people bet low on a 10 or high on a 2,” Sarma said. “They’re doing it based on something internal that we can’t measure, but can estimate based on what we can measure. The variability here is really driven by this internal state.”

Having formulated her hypothesis, Sarma built a model for each patient. She used a closed-loop decision-making system with two pathways: a logical pathway, where rationality is based entirely on the card, and an internal bias pathway, which is dependent on previous occurrences. “How you feel about the current trial depends on what’s been happening in past trials,” Sarma said. “Feedback is coming through on this pathway.” This is the unobservable, internal state she mentioned in her hypothesis.

She presented a state-space model and estimated both the model’s parameters and the internal state. All 11 patients ranged from internally-biased to logically-dominant (i.e., some had a fixed strategy and bet on each card the same way). In short, human brain coverage in the experiment was enormous. Sarma conducted spectral analysis with time series, and looked for spectral activity in each brain region that modulated with the model’s variables. She realized that key cognitive structures of each code reflect different parts of the overall decision-making system. The angular gyrus, for example, seemed to encode the card value, as power in the region increased when the participant or computer’s card was shown. “That area is used to process numbers, so it was probably calculating risk,” Sarma said. Gamma power in the cuneus region revealed information about participants’ card types. Low power accompanied a low-risk trial. But when gamma activity was high, participants likely had a 6 card. “Pathological gamblers have higher activity than normal in the cuneus,” Sarma said. Lastly, the amygdala processes emotional reactions and decisions.

Neural substrates of the model components. Image courtesy of Sridevi Sarma.
Sarma closed her presentation by displaying a map of logic, internal pathways, and their neural correlates. Different colors represented a logical state, an internal state, or overlap between the two. The internal state—characterized primarily by emotion—was steadily present throughout the entirely of the trials. However, logic was present most heavily when participants saw their card or the computer’s card, because their minds were actively rationalizing.

Sarma concluded by referencing the following control question: can you actually change a gambler’s decision in a task? The answer is yes, simply with electrical stimulation in the brain (SEEG is meant to do just that). “Just by stimulating one of those contacts, you can alter the behavior of an individual,” she said. This type of manipulation is valuable for clinical purposes. Ultimately, Sarma’s models offer novel insight into the process by which individuals cognitively combine logic and internal, emotionally-driven biases to make decisions.

 Lina Sorg is the associate editor ofSIAM News.