Latest / Behavioral Economics with Fexingo: Decision Making, Bias, and How People Really Spend / Why Your Brain Overweights Small Probabilities
Transcript
- Lucas: Luna, quick question: if I offered you a 1-in-100 chance to win a hundred dollars, how much would you pay for that ticket? Luna: I'd probably go... I don't know, maybe two or three dollars? Definitely not more than five. Lucas: Right. So the expected value is one dollar — a hundred times one percent. But you just said you'd pay two or three. That's the gap we're talking about today. Luna: So I'm paying more than the ticket is mathematically worth. Why does my brain do that? Lucas: It's a phenomenon Kahneman and Tversky called probability weighting. In their prospect theory, we don't perceive probabilities linearly. We overweigh small chances and underweigh large ones. Luna: Meaning a 1-in-100 chance feels more like, say, 1 in 20 in our heads? Something like that? Lucas: Exactly. Their experiments showed that people treat a 1 percent probability as though it's about 5 or 6 percent. That's a huge distortion. And the flip side: a 99 percent chance feels like only 91 or 92 percent. Luna: So we overpay for long shots and underpay for near-certainties. That explains a lot about gambling. Lucas: It explains the entire lottery industry. Take a typical state lottery ticket: you pay two dollars for a 1-in-300-million chance at a jackpot. Expected value is maybe 50 cents. Yet millions of people buy them every week. Luna: Because that tiny chance feels bigger. The dream of winning hijacks the math. Lucas: And it's not just lotteries. Insurance works on the same principle in reverse. You pay a premium that's higher than the expected loss because the small probability of a big disaster feels scarier than it should. Luna: So probability weighting makes us buy both lottery tickets and insurance. That's almost contradictory — one is for upside, the other for downside. But the same bias drives both. Lucas: Exactly. Kahneman and Tversky called it the fourfold pattern. For small probabilities of gain, we're risk-seeking — we gamble. For small probabilities of loss, we're risk-averse — we buy insurance. Both are driven by overweighing those small chances. Luna: Okay, I want to test this on a real example. Think about the Powerball jackpot that hit 1.5 billion a few years back. People drove across state lines to buy tickets. Were they all just bad at math? Lucas: Not exactly. Many knew the odds were terrible. But the emotional weight of 'what if I win' overrides the calculation. Plus there's social proof — seeing others buy tickets makes the chance feel more plausible. Luna: So probability weighting plus social proof is a dangerous cocktail. Luna: What about the opposite side? Underweighing near-certainties — where does that show up? Lucas: One big place is in preventive healthcare. A vaccine might have a 99.9 percent chance of preventing a disease, but people skip it because that 0.1 percent failure chance feels bigger than it is. Or they focus on rare side effects. Luna: So the near-certain benefit gets discounted, and the tiny risk gets amplified. That's exactly the pattern. Lucas: Another example: investing. People hold onto losing stocks because they overweight the small chance it'll bounce back. Meanwhile, they sell winners too early because the near-certain gain feels less exciting than the tiny chance of a bigger loss. Luna: Disposition effect, right? That's the tendency to sell winners and hold losers. Probability weighting is one driver. Lucas: Exactly. And it's not just individuals. Fund managers do it too. They chase high-risk, high-reward bets near the end of the quarter if they're trailing benchmarks, overweighing the small chance of a turnaround. Luna: So this bias is pervasive. Are there ways to correct for it? Lucas: The first step is awareness. When you're considering a long-shot bet, ask yourself: what is the expected value? Literally multiply the outcome by the probability. If it's negative, your brain is lying to you. Luna: But that's hard to do in the moment. Especially when there's emotion involved. Lucas: That's why some people use decision journals. Write down the odds before you make a choice. Then later you can see how often your gut overweighed small chances. Luna: Or you can reframe the probability. Instead of '1 in 100', think '99 out of 100 you lose'. That shifts the emotional weight. Lucas: That's a great technique. It's called 'frequency framing'. Psychologists have shown that presenting odds as frequencies — '9 out of 10' instead of '90%' — reduces the overweighting effect. Luna: I wonder if policy makers could use this. Like, when they communicate risks of a disease or benefits of a treatment, they could use frequency framing to help people make better decisions. Lucas: Some already do. The U.K. National Health Service, for example, presents screening benefits as 'for every 1,000 women screened, 3 deaths are prevented' rather than '0.3% reduction in mortality'. That small change makes the benefit feel real. Luna: So it's not about eliminating the bias — it's about working around it. Lucas: Right. And speaking of working around things, I realized something while we were talking about lotteries: if this episode has made a single concept click for you, it's probably worth the price of a coffee. And honestly, if it was, you can find the show at buy me a coffee dot com slash fexingo. Luna: Yeah, listener support is what keeps this show ad-free and independent. We don't run sponsors, so every little bit helps us keep digging into these biases. Lucas: Exactly. No pressure — just if it was worth it to you. Now, back to probability weighting. One question I get often is: does this bias change with age or experience? Luna: I've read that older adults might be less susceptible to some framing effects. Is that true for probability weighting? Lucas: Some studies suggest that with age, the emotional response to small probabilities diminishes, possibly due to changes in dopamine systems. But other research shows that financial literacy matters more than age. Luna: So you can train yourself to think in expected value terms, even if the gut feeling doesn't go away. Lucas: Exactly. Professional poker players are a good example. They constantly calculate pot odds — comparing the chance of winning a hand to the size of the pot. Over time, that calculation becomes automatic, overriding the gut. Luna: But they still feel the thrill of a big win. They just don't act on it. Lucas: Right. The bias doesn't disappear, but you can build systems to counter it. Like, before you buy a lottery ticket, ask: would I rather have this two dollars, or a 1-in-300-million chance? The answer becomes obvious. Luna: Okay, let's look at one more real-world case: insurance deductibles. When people choose a lower deductible, they pay a higher premium to avoid a small chance of a big out-of-pocket cost. Is that overweighing the risk? Lucas: Often, yes. The expected value usually favors a higher deductible with lower premiums. But people overweigh the small chance of a big claim and choose the low-deductible plan, paying more on average. Luna: So insurance companies make money off probability weighting — on both sides. They sell policies that overweigh loss, and they invest premiums in assets that overweigh gain. Lucas: That's a really sharp observation. And it's not malicious — it's just how the market responds to our biases. The same bias that makes us buy lottery tickets also makes us buy overpriced insurance. Luna: So what's the takeaway? When you're facing a decision with a small probability of a big outcome, stop and do the math. Lucas: And if the math doesn't support the choice, ask yourself: is my brain inflating this chance? Because odds are, it is. Luna: That's a good note to end on. Thanks, Lucas. Lucas: Thanks, Luna. See you next time.