Sat, Jun 27 · 2:00 PM CDT
On May 30, 2026, our group of four continued exploring Steven Pinker’s Rationality and delved deeply into the utility curve and its profound economic and psychological implications. First, we examined a famous wager made by the philosopher and mathematician Blaise Pascal, who reframed the existence of God as a probability problem. His sure bet is that God exists: If He exists, you gain everything; if He does not, you lose nothing. Taking this expected-value framework to a casino, how do different games of chance compare? Shooting craps is a dice game where players bet on the outcome of a roll using two six-sided dice. The casino may require $1 to play the game, and will give $4 for a roll of 7. What’s the utility of playing this game? There is a ⅙ chance to win $4 and ⅚ chance of losing $1, the utility is (⅙)($4) + (⅚)(-$1), giving you a -$0.17 loss over the course of many throws of the dice. In a game of roulette, it takes $1 to play, and the winning choice will give $35. There is a 1/37 chance of spinning a 7 and a 36/37 chance of losing, giving the utility of (1/37)($35) + (36/37)(-$1), giving you -$0.027 loss over many spins. The odds favor the casino with either game, but for the gambler, roulette can be less aggravating. Utility is not reserved solely for games of chance; it serves as a framework to align our actions with our values outside the casino. We often discover our true values simply by observing how we act—measuring how much we care about everything from providing for our children to returning a lost wallet. But is this truly rational decision-making? Assumptions are made in the study of making rational choices and used in the same manner Euclid used axioms to construct geometric theorems. Commensurability is the ability to compare disparate things using a common standard to determine if their values are "in the same ballpark". Transitivity is if $A > $B and $B > $C, then $A > $C. Closure is the property where an operation applied to members of a group always yields another member of that same group. Consolidation unifies disparate data into a cohesive, single entity. Independence is the principle that separate events do not influence one another (e.g., a coin flip has no memory of the previous flip). Consistency is the absence of internal contradictions; truth cannot contradict other truths. To build a smooth, traditional utility curve—where utility sits on the y-axis and wealth/money sits on the x-axis—a person's behavior must strictly adhere to these pillars. The resulting concave graph rises steeply at first but flattens out at higher wealth levels, demonstrating diminishing marginal utility or diminishing returns. However, psychologists Daniel Kahneman and Amos Tversky did not just use the traditional economic utility curve—they changed it to include losses in the financial deliberations. They found that different income levels do not share the same utility curve; while these curves all possess the general mathematical property of flattening as wealth increases, the steepness and the exact point of flattening shift dramatically depends on whether a person is low-, middle-, or high-income, with the implications that $100 inherently means much more to a low-income individual than to a high-income one. To model actual human behavior, they replaced the smooth concave curve with an asymmetrical, S-shaped curve re-centered around a subjective reference point. While a traditional symmetric curve implies the joy of gaining $100 matches the sadness of losing it, Kahneman and Tversky proved that the pain of a loss is roughly twice as intense as the pleasure of an equivalent gain on the steepest part of the curve for low-income individuals, but becomes less pronounced for those with high incomes, implying low-income individuals are more risk-adverse and those with higher incomes are more risk-seeking. The utility curve successfully sells commercial insurance, enticing us to pay a small premium today to avoid catastrophic financial ruin tomorrow. But can this mathematical curve scale to the ethical weight of treating a child with cancer? Can it resolve the polarizing debates surrounding the economic costs of climate change or the implementation of nuclear power? It is unlikely, as proponents and opponents operate from fundamentally mismatched utility curves. Is there a way to merge these conflicting curves to end societal disputes? We invite you to find out more about the bell-shaped distribution and signal-to-noise ratios in Steven Pinker’s Rationality: What It Is, Why It Seems Scarce, Why It Matters, BF441.P56 2021 on June 27, 2026, from 2:00 PM to 4:00 PM.
