The Multiplicative Effect of Good Collaboration in Mental Tasks

Introduction:

This post explores how effective collaboration can have a multiplicative effect on productivity in mental tasks. Unlike physical tasks, where output is often the sum of individual efforts, effective collaboration in mental tasks can lead to a ‘1 plus 1 equals 3’ effect. We use a mathematical model to explain this phenomenon and explore the underlying assumptions determining when it should and shouldn’t work. By the end, you’ll understand what constitutes constructive collaboration and what forms can be destructive.

The Observation:

In mental tasks, individuals often face challenges unrelated to time constraints or task size. People frequently get stuck on specific aspects requiring clarity, insight, or the right question. In such situations, the number of tasks completed depends on the frequency of encountering these “terminal” stuck points, which can lead to procrastination or moving on to the next task without resolving the current one.

The Power of Collaboration:

Collaboration on mental tasks reduces the likelihood of all participants getting stuck at the same point. If an individual has a 50% chance of getting stuck, then when two people collaborate, the probability of both getting stuck at the same point decreases to just 25% (0.5 \times 0.5 = 0.25). Consequently, collaborative efforts increase the chances that at least one person will have the necessary insight to overcome obstacles and maintain progress.

Real-world Example:

Consider a scenario with four tasks: A, B, C, and D. If one person works on A and B while another works on C and D, and each gets stuck on one task, only two tasks will be completed.

However, if they collaborate on A and B together, they are less likely to get stuck on the same task. They may only encounter one stuck point, allowing them to complete three out of four tasks.

This simple example shows how collaboration enables “1 plus 1 equals 3.” Working together, people can achieve more than the sum of their individual efforts. Collaboration’s multiplicative effect helps overcome obstacles and complete more work.

The Mathematical Model:

Let’s consider a scenario where a single task takes two units of time to complete. In a collaborative setting, the time required for two people to finish the task can be calculated as follows:

Probability of both people getting stuck: 0.25
Probability of at least one person having an idea to overcome the stuck point: 0.75

Therefore, the expected time to complete the task with two people collaborating is: (2 units of time) x (0.75) = 1.5 units of time

In other words, the time taken to finish one task with two people collaborating is reduced to 1.5 units of time, compared to the 2 units of time it would take for a single person.

The Assumptions and Limitations:

It’s important to note that the multiplicative effect of collaboration relies on certain assumptions and has its limitations:

Independence : The model assumes that the probability of getting stuck is independent for each individual. In reality, there may be correlations based on shared knowledge, skills, or problem-solving approaches.
Communication and coordination: Effective collaboration requires clear communication and coordination among team members. If communication breaks down or there is a lack of coordination, the multiplicative effect may be diminished.
Task complexity: The multiplicative effect is more pronounced in tasks that involve creative problem-solving and unique insights. For routine or well-defined tasks, the effect may be less significant.
Group dynamics: The model assumes a positive and productive group dynamic. If there are conflicts, power imbalances, or a lack of psychological safety, collaboration may be hindered, and the multiplicative effect may not materialize.