Why do we think we’re more likely to win at the big casino versus the small one?

 

Category Size Bias

, explained.

What is Category Size Bias?

Category size bias describes our tendency to believe outcomes are more likely to occur if they are part of a large category rather than part of a small category, even if each outcome is equally likely. While the bias is based on experimental studies that have been successfully replicated, the interpretation of the evidence remains mixed.

Where it occurs

Imagine you’re watching cross-country skiing in the Winter Olympics, a sport with a prominent field of Norwegians. You know next to nothing about cross-country skiing, but your friend points to the TV, where a woman is lining up for the race and asks you to consider the likelihood she’s the woman to win Gold. The name Ragnhild Haga appears along the bottom of the screen next to a Norwegian flag.

Regardless of Haga’s actual likelihood of winning the race, your prediction shouldn’t be influenced by the number of Norwegians also lining up for the race, yet this is an error people sometimes make. Even if the field is evenly matched, we may assume that a single outcome coming from a larger category is more likely than a smaller one.

Individual effects

Probability judgments are erroneously impacted by category size, so individuals are prone to misjudge the likelihood of a number of events. Since virtually everything belongs to some category, the ramifications of category size bias loom large.

The effects are relevant to anybody in the business of making predictions. In one study, researchers found that participants believed their chances of winning a lottery were greater when their ticket was the same color as the majority of tickets. They were willing to wager an average of 24% more for the ticket with the larger category size, despite the ticket color having nothing to do with the criteria for winning the lottery.1 Applying this result to the financial industry, one could suspect an investor to believe a stock is more likely to go up if it belongs to the sector with the most companies in the S&P 500 compared to stock from a less prominent sector.

Systemic effects

The framing of public messaging in relation to category size bias can result in unintended consequences. Additionally, knowledge of the bias can be leveraged by policymakers to promote preferred behaviors. For example, health-related messages could present preventable diseases such as lung cancer among a large number of other health risks, potentially increasing the perceived risk of lung cancer and subsequent engagement in preventative measures.1

Why it happens

It’s plausible that category size bias stems from the implicit assumption that individual category members inherit the statistical properties of their parent category. In the context of our cross-country skiing analogy, we mistake the inquiry into the likelihood that Ragnhild Haga wins the Gold, with an inquiry into the likelihood that a Norwegian wins Gold.

Why it is important

Although nobody is perfect when it comes to predictions, minimizing the biases and fallacies that can riddle our probability judgments can be crucial in various contexts. Sub-optimal predictions rooted in cognitive error can lead to negative consequences for those in the financial or medical realm. Such individuals should be aware of vulnerabilities to irrational tendencies such as the category size bias.

How to avoid it

One way to avoid the category size bias is by briefly reviewing the logic of an assumption we’ve made. Although the brain can’t compute a complex calculation to determine the actual probability of a given event, it can still leverage the common sense that we rely on outside of portability judgments. Just because a bird comes from a large flock doesn’t mean it’s a large bird. Similarly, just because Ragnhild Haga hails from a country with a lot of cross-country skiers in the race, doesn’t imply her chances of winning are greater than the next Olympian.

How it all started

Category size bias first emerged from a 2014 research paper by Matthew Isaac and Aaron Brough.1 They were the ones who conducted the study with the colored lottery tickets mentioned earlier. Their original paper included additional findings in support of the category size bias, including one involving a 26-sided die with all the letters in the alphabet. When group size was highlighted (21 consonants in the alphabet versus 5 vowels,) participants believed they would be more likely to roll a “T” versus an “A”. Additionally, Participants thought that teams were more likely to win a basketball tournament based on their mascot’s features. Teams with a mascot that resembled a greater number of others were deemed more likely to succeed.

If you’re skeptical of some of these results, you’re not alone. In 2018, Hannah Perfecto, Leif Nelson, and Don Moore published a paper titled, The Category Size Bias: A Mere Misunderstanding.2 The researchers replicated Isaac and Brough’s key findings, however follow up studies with adjusted phrasing led Perfecto and colleagues to conclude that the results that gave rise to the category size bias were mostly due to instructional confounds. In other words, participants didn’t exhibit a fundamental cognitive error, they were simply confused by the experiment’s instructions.

Example 1 - IT security threat

Another experiment from Isaac and Brough’s series of studies looked at preventive behaviors targeting IT security threats. Participants believed the risk associated with a threat that belonged to a larger group of preventive behaviors was greater than a threat that bore fewer preventive behaviors. In reality, the quantity of preventive behaviors is not indicative of the probability of the prospective threat. A password breach with a single preventive behavior (e.g., using a character-diverse password), can be more likely than a more sophisticated malware hack that may require multiple preventive initiatives.

Example 2 - Casino games

Casinos house a wide range of defined probabilities that run alongside irrational assumptions regarding such probabilities. It’s not hard to imagine how the category size bias could manifest in a casino. A gambler may perceive the “26” black pocket to be more likely than one of the green zeros. Even though both spins pose identical probabilities, “26” black belongs to a broader category (18 black numbers versus 2 green). Alternatively, a gambler may see a small group of three slot machines in the corner but would rather opt for the much larger congregation of slot machines on the other side of the casino. Although each individual slot machine would pose equal probabilities, the gambler may assume that the machines belonging to the larger group have a better chance of bearing a jackpot.

Summary

What it is

Category size bias is a mental error made when we assume outcomes are more likely when they belong to a larger category or sample group. Whether or not the bias has a psychological basis however, is still up for discussion.

Why it happens

We are erroneously associating the likelihood of a given event to the likelihood of its parent category. One might think rolling a “T” on a 26-sided die is more likely than rolling an “A” because there are more consonants than vowels.

Example 1 – IT security threat

Security risks that coincide with more preventive measures are believed to be more likely than those risks that coincide with a smaller group of measures, despite the risk and number of measures required not necessarily being predictive of each other.

Example 2 – Casino games

Casino goers may be susceptible to the category size bias. Although all slot machines in a casino may have equal probabilities, an individual may inaccurately presume the slot machines within a larger section of machines to have better odds than the ones in isolation.

How to avoid it

Reviewing the logic and causal reasoning of an assumption can mitigate the category size bias. Instead of leaning heavily on intuitive probabilities, acknowledge that such intuitions may be fallible and consider whether we may be inappropriately giving weight to category size in probability judgments.

Sources

  1. Isaac, M. S., & Brough, A. R. (2014). Judging a part by the size of its whole: The category size bias in probability judgments. Journal of Consumer Research, 41(2), 310-325.
  2. Perfecto, H., Nelson, L. D., & Moore, D. A. (2018). The category size bias: A mere misunderstanding. Judgment & Decision Making, 13(2).