Morning math/Voting systems

A mathematical model can be very simple or very complex. The goal is to represent a system or process using precise definitions and mathematical relationships. One way to create a model is to simply start building it, acknowledging it won't be perfect, but trying to improve the model along the way. Eventually you should arrive at a basic (fairly simple) model, which you can then make more complex (and perhaps more accurate) by elaborating in areas that previously were glossed over.

For instance, if I want to represent amount of daylight in a single day, one of the simplest models might be:

• For any given day D, some percentage of that day occurs in which there is measurable daylight L.

However, I can improve this model and make it more complicated by:

• Measuring daylight L as hours, minutes, seconds, milliseconds (or similarly as some percentage up to a particular decimal point e.g. 49.255%) of some day.
• Adding new variables, such as a geolocation--G₁ longitude and G₂ latitude, since daylight is a function of where on the earth measurement is taken. Or, allowing daylight to be more than a percentage, represented by an additional variable for luminosity U (imagine clouds reducing the impact of daylight).

However, perhaps some of the complications are not relevant given the context, so one may want to simplify the model to simply be:

• Daylight L for any given day D is a function of location only (G₁ longitude and G₂ latitude). Now, if we construct a look-up table for daylight at any given geolocation, we'd be able to find L(G₁, G₂) = some # of seconds per day D.

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).