The Dilemma of Bonus Points: A Conservative or Risky Decision?

In an educational setting, teachers often offer bonuses at the end of exams to encourage students to engage with the material in a deeper and more enriching way. However, the decision to opt for either 2 bonus points or 6 can be fraught with uncertainty. This article explores the decision-making process students face and provides insights into the factors that should influence their choices.

Introduction to the Scenario

Consider a teacher who, at the end of an exam, offered a bonus opportunity. For each student who opted for 6 points, all participants would lose the entire bonus. This means that the sum of choices determines whether any extra points are awarded at all. The options, therefore, are:

Selecting 2 points: Guaranteed to receive 2 points, regardless of others' choices. Selecting 6 points: Extreme risk, where if more than 10 students choose 6 points, no one gets any bonus points. This decision maximizes the potential for a 6-point bonus if more than 10 classmates choose the same, but it also riskszeros points for everyone.

Considering the Risks and Rewards

The decision to choose 2 points versus 6 points hinges on the risk of losing all potential bonus points due to the actions of others. Here are the key factors to consider:

Risk of Losing All Points

If more than 10 students choose 6 points, everyone loses all bonus points. This introduces a significant risk where you could end up with nothing regardless of your own choice. Choosing 2 points ensures a guaranteed 2 points, reducing the impact of others' decisions on your outcome.

Guaranteed Points

Selecting 2 points guarantees that you receive the bonus, regardless of the class's collective decision. This is a conservative and safer choice, as it eliminates the risk of ending up with zero points due to the actions of others.

Classroom Dynamics and Individual Decision-Making

The decision-making process can be influenced by various factors, including the size of the class, the grading scale, individual performance, and your classmates' behavior. Here's a breakdown of how these factors can impact your strategy:

Size of the Class

Small Classes (less than 20 students): In smaller classes, the variability in choices can be significant. If two or more students opt for 6 points, everyone loses. Given the small sample size, the choice becomes more critical and risky.

Large Classes (100 students): Larger classes reduce individual influence on outcomes. The probability of more than 10 students choosing 6 points is lower, making the 6-point decision less risky.

Grading Scale and Class Performance

Uncurved Classes: In an uncurved class, a score of 90 is a solid A. The extra 2 or 6 points may not significantly affect your final grade. Here, the decision to choose 2 points is simpler, as you can at least guarantee yourself some points without the high-risk, high-reward dynamic.

Curved Classes: In a curved class, your position in the grade distribution matters. The 6-point option becomes more attractive if you are close to the top and need an edge to secure a higher grade, but it also carries more risk if you are far from the top.

Individual Performance

If you are already performing exceptionally well, such as needing only 27 more points to get an A, the potential extra points become less significant. In such a scenario, choosing the 2-point option is more sensible.

Classmate Behavior and Psychological Assumptions

The choices of your classmates play a crucial role in your decision. If most people are risk-averse and choose 2 points, choosing 6 becomes a more attractive option. Conversely, if you believe others are also likely to take the higher risk by choosing 6 points, it might be worth taking the leap for a better chance of a 6-point bonus.

Consider your classmates' behavior, their general risk-taking tendencies, and their performance in class to inform your decision.

Conclusion

The decision to opt for 2 points or 6 points at the end of an exam is complex and multifaceted. It involves a careful evaluation of the risk-reward dynamic, class size, grading scale, and individual performance. Choosing the safer, 2-point option is often the wiser choice, as it guarantees some points and reduces the risk of ending up with zero. However, if you believe your classmates are likely to take the same high-risk, high-reward approach, the 6-point option may be more appealing, albeit with greater uncertainty.