Johns Hopkins University
Mathematics and Democracy Teach Out
Johns Hopkins University

Mathematics and Democracy Teach Out

Ed Scheinerman

Instructor: Ed Scheinerman

Gain insight into a topic and learn the fundamentals.
Beginner level

Recommended experience

12 hours to complete
3 weeks at 4 hours a week
Flexible schedule
Learn at your own pace
Gain insight into a topic and learn the fundamentals.
Beginner level

Recommended experience

12 hours to complete
3 weeks at 4 hours a week
Flexible schedule
Learn at your own pace

What you'll learn

  • Mathematics of voting

  • Theories of democracy

Details to know

Recently updated!

July 2024

Assessments

4 assignments

Taught in English

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There are 4 modules in this course

This module sets the stage for the entire Teach Out. We begin by discussing the nature of mathematics (as opposed to arithmetic) and develop a workable abstract model for democracy: a function that takes individual preferences and returns a group decision. We then look closely at different methods for two-party elections, fairness criteria we want these functions to have, and conclude that only the Simple Majority method satisfies those criteria.

What's included

6 videos1 reading1 assignment2 discussion prompts

This module builds on the work from Module 1 by considering elections with three (or more) candidates. We examine various decision functions (such as Plurality and Borda Counts) as well as properties we want those functions to have. We conclude with Arrow’s Theorem that shows that there are no decision functions satisfying basic fairness criteria.

What's included

7 videos1 reading1 assignment2 discussion prompts

In the previous modules we assumed that each voter ranks the candidates from most to least desirable; these individual rankings are the inputs to the decision functions. In this module we question the viability of asking voters to rank both for psychological reasons (it is very difficult to rank a long list of options) and—more to the point of this Teach Out—for mathematical reasons. We model preference using a simple game played with dice that illustrates non-transitive preference: A is better than B, B is better than C, but C is better than A!

What's included

3 videos1 reading1 assignment1 discussion prompt

This module considers mathematical issues arising in representative democracy in which elected officials make decisions for the larger population. In the United States House of Representatives, the number of representatives from a given state is proportional to the population of that state. However, since the number of representatives from a state must be a whole number, and the total number of representatives is 435, we need a method by which seats are allocated to states. We present the apportionment methods of Hamilton and Jefferson, and discuss problems arising with these methods. We conclude with a theorem of Balinsky and Young that shows there are no apportionment methods satisfying basic fairness conditions.

What's included

7 videos3 readings1 assignment1 discussion prompt

Instructor

Ed Scheinerman
Johns Hopkins University
1 Course83 learners

Offered by

Recommended if you're interested in Math and Logic

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