Morning math/Voting systems

This project is an example of formulating a mathematical model. Read more about mathematical models

Voting systems Model

There are three sections to this model: variables (our basic definitions), relationships (attempts to represent a more complex understanding of the components of our model), and the side-line (items that will complicate the model further, to be tackled later, as we go).

Overall questioning the "1 person, 1 vote" assumption in an effort to assess fairness and error in voting systems.

Variables

• V_a = a voting event.
• E = overall error
• e = error
• T = a topic to be voted upon
• b = a single ballot
• v = a vote (a choice)
• J = jurisdiction (a geographic boundary)
• M = a vote counting method
• t = tabulation time

Relationships

1. For any voting event V_a, there exists an overall error E_Va.
2. For any voting event V_a, there exists at least one jurisdiction J.
3. For any jurisdiction J, there exists an error e_J.
4. For any jurisdiction J, there exists at least one vote-counting method M.
5. For any jurisdiction J, there exists n number of ballots b₁, ..., b_n.
6. For any jurisdiction J, there exists an average time to tabulate an individual ballot t_M1, ..., t_Mn.
7. For any ballot b, there exists some number m of voting topics, T₁, ..., T_m.
8. For any ballot b, there exist v_T1, ... v_Tm votes, each of which can be null (no vote).
9. For any ballot b, there exists a corresponding method M_x
10. For any ballot b, there exists a ballot type y.

Side-line

• Rank-choice? -- Other voting styles, multiple votes per voter
• Anecdotal secrete ballot
• Some voters may require assistance (potential introduction to error?)
• Vote-counting is functional
• What about predictions?
• Errors on basis of discernable intent of the registered voter.
  • We are not concerned with human intermediaries (e.g. volunteers).