Introduction
As someone who works as an educator at the University of Michigan, I know how vexed a statement this is, but it's incredibly difficult to
ignore the hard truth: it is immensely profitable for students to cheat on exams and projects. I obviously do not condone this behavior
and reprimand it in my lab sections should I discover it happening, but over time I have grown more sympathetic of college students struggling
with the choice to cheat or remain honest, regardless of their histories with academic integrity.
The concepts I explain here can be applied to situations outside of academia. A prominent, similar example includes using white text in resumes to trick Applicant Tracking Systems (ATSs) into tricking the system not to filter your resume despite the qualifications not being fulfilled. For example, if a job listing states that one must know AWS in order to apply, one can circumvent the automated filtering process by writing AWS in small white text, and have the resume looked at by a human. This maximizes the chances of a human reviewing the resume and proceeding to the next step, where as an honest applicant without AWS experience would either apply and immediately get filtered out or would not apply altogether.
This post aims to illustrate where the motivation to violate academic integrity stems from, create a framework that can quantify the mechanism of cheating, and what we can do to mitigate future violations.
Note: This post will utilize concepts in game theory to analyze cheating incentives. An extensive knowledge in game theory is not required and I will try to explain the relevant principles as we build up the model. I have included external links when mentioning important concepts in the event you would like to read more about them.
The concepts I explain here can be applied to situations outside of academia. A prominent, similar example includes using white text in resumes to trick Applicant Tracking Systems (ATSs) into tricking the system not to filter your resume despite the qualifications not being fulfilled. For example, if a job listing states that one must know AWS in order to apply, one can circumvent the automated filtering process by writing AWS in small white text, and have the resume looked at by a human. This maximizes the chances of a human reviewing the resume and proceeding to the next step, where as an honest applicant without AWS experience would either apply and immediately get filtered out or would not apply altogether.
This post aims to illustrate where the motivation to violate academic integrity stems from, create a framework that can quantify the mechanism of cheating, and what we can do to mitigate future violations.
Note: This post will utilize concepts in game theory to analyze cheating incentives. An extensive knowledge in game theory is not required and I will try to explain the relevant principles as we build up the model. I have included external links when mentioning important concepts in the event you would like to read more about them.
Game Theory
Using Game Theory, we can create a scenario where a student needs to make a decision about whether to cheat or not and
make this decision based on how beneficial it is for said student. To create this framework we will use the following assumptions.
This table seems to suggest that cheating is a dominated strategy, i.e. there is no penalty to cheating. Obviosuly, this is not the case; so far we have just demonstrated
how we can neatly evaluate the payout structures.
Now that we understand how the table is created, we need to relax the assumption of cheaters never getting caught and incorporate that into our model.
It is important to acknowledge that many students cheat and get away with it. This means that if all cheaters are treated equally, they each have the same
random chance of getting caught (though this ignores the intelligence of those executing the cheat). Let's denote the probability of getting caught by \(p\).
So, for a random cheater, they have a \((1 - p)\) probability of getting away with it and getting a reward of \( r \). However, what reward (penalty really) needs to be given in the event
the cheater gets caught? For now, we will denote it by \( t \), but we should note that cost of getting caught is going to be significantly higher than the
reward of a few extra points on an assessment. Many universities have strict academic integrity policies (for example, here's mine) and getting caught will nearly always result
in more pain than the reward is ever worth.
Lastly, we need to address that for every additional random student that decides to cheat, the probability of getting caught increases. We will denote the increase in probability of getting caught by \( \delta \).
If we update the payout matrix to reflect these developments, it looks something like this.
With this game now fully established, we can start understanding the different payoffs associated with each \( (\delta, p, r, t) \) tuple.
You can use the sliders provided to play around with the various combinations and see how they influence the outcome. Note that \( p + \delta \)
is constrained to take on a maximum value of 1, since a probability cannot exceed the value of 1.
- The student pool is large enough where we can realistically analyze one student cheating at a time, even though many cheating efforts take multiple people. Therefore, the players in this game are "Random Student" and "All Other Students."
- If a student decides to cheat, it doesn't take away from the scores of other students - it simply adds to the cheaters score.
- Students make their decisions simultaneously, but are aware of the payout structure.
- For now, cheaters will not get caught in this exercise. We will relax this assumption later.
| Student Cheating | |||
Lastly, we need to address that for every additional random student that decides to cheat, the probability of getting caught increases. We will denote the increase in probability of getting caught by \( \delta \).
If we update the payout matrix to reflect these developments, it looks something like this.
| Student Cheating | |||
| Student Cheating | |||
\( \delta \):
\( p \):
\( r \):
\( t \):
A positive outcome means that an entity gained points by cheating whereas a negative outcome means an entity lost points by cheating. An outcome of 0 simply means the party did not cheat and therefore, does not receive a penalty or reward. The question remains what values each of these variables should take on. Several sources indicate that the probability of students getting caught is small at only around 5%1 2. Additionally, we can identify from this Unicheck report that 61% of 71,300 sampled undergraduates believe it is ethical to cheat on some sort of academic assessment and that a whopping 95% of them had cheated in the past. By plugging in \( p = 0.5 \) into our sliders above, even if a student receives no credit for an assessment (\( t = -100 \)) if caught, even at an egregious \( \delta = 0.05 \), the reward needs to only be 12 points for a student to be incentivized to cheat. If \( \delta \) drops to 0.01, then the reward only needs to be 7 to make cheating a dominated strategy.Solutions
So, if students are clearly incentivized to cheat, how do we prevent it? Personally, I have tunnel vision on a singular solution; however, to make this seem less
biased, I have included a few solutions in increasing order of effectivenes (obviously from a subjective point of view).
1. Make Punishments More Severe (Rating: 2/10)
One suggestion posited by the paper How College Students Cheat On In-Class Examinations: Creativity, Strain, and Techniques of Innovation is that a threat of severe punishment is effective for cheating prevention. This is equivalent to driving \( t \) lower. While it's obvious from the game theory perspective that increasing the punishment lowers the reward of cheating, more stringent punishments will likely ignore if this is a student's first offense. The first offense is not even solely restricted to cheating either; for some students, violating academic integrity might be their first real experience with making a consequential mistake. Increasing punishments may certainly prevent cheating, but may also disincentivize a correction or recovery process for students who have been caught. After all, while we want to protect academic integrity, protecting the future of admitted students is also a responsibility of academic institutions. Therefore, it is possible that there exists a better solution that has fewer negative side effects.
2. Increase Vigilance for Cheating Detection (Rating: 2/10)
Though this solution seems remarkably similar to Solution 1, it only increases the chances of getting caught, but not the punishment for it. This would be the equivalent of increasing \( p \) in our model.
3. Create Cheating-Robust Environments (Rating: 5/10)
This one is slightly different from the first solution in that the preventative measures are taken before an assessment takes place and, therefore, before any cheating can take place. This sidesteps the false accusations issue and makes the barrier of entry to cheating signficiantly higher. While this could be effective with smaller class sizes, this setup could take a tremendous amount of effort to execute and the difficulty of setup increases somewhat exponentially with class size. This difficulty
4. Do Away with Time Sensitive Assessments (Rating: 8/10)
Based on the ratings (that are obviously super detailed) I like this solution the best.
The obvious drawback behind this solution is that the assessments themselves become more time consuming for both the students to complete and for the instruction staff to grade. This can definitely be strenuous for large class sizes that would otherwise have a facile grading process of grading only a handful of relatively short assessments. However, this alleviates many of the other concerns
1. Make Punishments More Severe (Rating: 2/10)
One suggestion posited by the paper How College Students Cheat On In-Class Examinations: Creativity, Strain, and Techniques of Innovation is that a threat of severe punishment is effective for cheating prevention. This is equivalent to driving \( t \) lower. While it's obvious from the game theory perspective that increasing the punishment lowers the reward of cheating, more stringent punishments will likely ignore if this is a student's first offense. The first offense is not even solely restricted to cheating either; for some students, violating academic integrity might be their first real experience with making a consequential mistake. Increasing punishments may certainly prevent cheating, but may also disincentivize a correction or recovery process for students who have been caught. After all, while we want to protect academic integrity, protecting the future of admitted students is also a responsibility of academic institutions. Therefore, it is possible that there exists a better solution that has fewer negative side effects.
2. Increase Vigilance for Cheating Detection (Rating: 2/10)
Though this solution seems remarkably similar to Solution 1, it only increases the chances of getting caught, but not the punishment for it. This would be the equivalent of increasing \( p \) in our model.
3. Create Cheating-Robust Environments (Rating: 5/10)
This one is slightly different from the first solution in that the preventative measures are taken before an assessment takes place and, therefore, before any cheating can take place. This sidesteps the false accusations issue and makes the barrier of entry to cheating signficiantly higher. While this could be effective with smaller class sizes, this setup could take a tremendous amount of effort to execute and the difficulty of setup increases somewhat exponentially with class size. This difficulty
4. Do Away with Time Sensitive Assessments (Rating: 8/10)
Based on the ratings (that are obviously super detailed) I like this solution the best.
The obvious drawback behind this solution is that the assessments themselves become more time consuming for both the students to complete and for the instruction staff to grade. This can definitely be strenuous for large class sizes that would otherwise have a facile grading process of grading only a handful of relatively short assessments. However, this alleviates many of the other concerns