Discrete Mathematics for Computer Science (CS 20) – Spring 2023

Module Topic: Graph Theory & Testimonial Injustice
Module Author: Daniel Belgrad

Course Level: Lower-level undergraduate
AY: 2022-2023

Course Description: “Widely applicable mathematical tools for computer science, including topics from logic, set theory, combinatorics, number theory, probability theory, and graph theory. Practice in reasoning formally and proving theorems.” Course link.

Semesters Taught: Spring 2021, Spring 2022, Spring 2023

Tags

• Graph theory [CS]
• Peripheral nodes [CS]
• Testimonial injustice [phil]
• Epistemic injustice [phil]
• Social structures [phil]
• Testimony [phil]
• Information [CS]

Module Overview

Students learn how to model social structures using graphs. Then they learn how information flow can change through those graphs depending on testimonial injustices. Finally, they brainstorm ways to adjust the graphs to limit the impact of testimonial injustice.

    Connection to Course Technical Material

The module builds directly on the graph theory material taught in the three weeks prior.

Goals

Module Goals

1. Learn about testimonial injustice as a general concept
2. Illustrate testimonial injustice in group exercises that utilize graph theory
3. Understand, in a more nuanced manner, what testimonial injustice is and why it is wrong

    Key Philosophical Questions

1. What is testimonial injustice?
2. How can we use graph theory to inform our understanding of testimonial injustice?
3. How can we use graph theory to combat testimonial injustice?

Materials

    Key Philosophical Concepts

• Testimonial injustice: hearer takes the speaker’s word as less reliable due to prejudice
• Epistemic injustice
• Social networks
• Power structures

    Assigned Readings

• “Me Too”: Epistemic Injustice and the Struggle for Recognition.

Implementation

    Class Agenda

1. Lecture: Defining Testimonial Injustice (20 mins)
2. Group Activity #1 (20 mins)
3. Group Discussion #1 (5 mins)
4. Group Activity #2 (20 mins)
5. Final Discussion (10 mins)

    Sample Class Activity

Part 1: Students model two graphs at their table (presented in a handout). One node is a testifier who is trying to share information that is not morally loaded. The person who is listening to their testimony has a certain probability that they will “believe” the person’s testimony. They roll dice, which determines whether they believe. All other nodes in the graph have the same probability. They model information flow to see whether the testimony spreads around the full graph.

Part 2: Students model three graphs, of the same shape as the two initial graphs but now certain nodes are much less likely to believe the testimony than others (due to testimonial injustice). The first graph has the testifier isolated and generally disbelieved. The second has the testifier less isolated but still disbelieved. The final graph has the testifier less isolated and less disbelieved. The three graphs show the progression of how one could handle testimonial injustice in a social network (while not addressing the injustice itself).

    Module Assignment

As you read in Jackson’s “Me Too”: Epistemic Injustice and the Struggle for Recognition, The Me-Too Movement involved thousands of women in different industries coming forward with experiences of sexual harassment and assault. This movement became a “consciousness-raising event” where testimony about sexual harassment was taken more seriously than it had been in the past and perpetrators suffered the consequences. Creating a directed graph as an aid in your explanation, what features of the movement contributed to this outcome? Please consider the number of nodes, the number of testifiers, and the number and probability of edges between nodes

Lessons Learned

• The material was very closely connected to the course material, and students were engaged.
• A class-wide graph would have been a compelling way to close the session