Difference between revisions of "Morning math/Voting systems"

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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.
This project is an example of formulating a '''mathematical model'''. Read more about [[Morning math/Models | mathematical models]]


For instance, if I want to represent amount of daylight in a single day, one of the simplest models might be:
==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).  
* 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--G<sub>1</sub> longitude and G<sub>2</sub> 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:
Overall questioning the "1 person, 1 vote" assumption in an effort to assess fairness and error in voting systems.


* Daylight L for any given day D is a function of location only (G<sub>1</sub> longitude and G<sub>2</sub> latitude). Now, if we construct a look-up table for daylight at any given geolocation, we'd be able to find '''L(G<sub>1</sub>, G<sub>2</sub>) = some # of seconds per day D'''.
===Variables===
 
* V<sub>a</sub> = a voting event.
==Voting systems Model==
* 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===
# For any voting event V<sub>a</sub>, there exists an overall error E<sub>V<sub>a</sub></sub>.
# For any voting event V<sub>a</sub>, there exists at least one jurisdiction J.
# For any jurisdiction J, there exists an error e<sub>J</sub>.
# For any jurisdiction J, there exists at least one vote-counting method M.
# For any jurisdiction J, there exists n number of ballots b<sub>1</sub>, ..., b<sub>n</sub>.
# For any jurisdiction J, there exists an average time to tabulate an individual ballot t<sub>M<sub>1</sub></sub>, ..., t<sub>M<sub>n</sub></sub>.
# For any ballot b, there exists some number m of voting topics, T<sub>1</sub>, ..., T<sub>m</sub>.
# For any ballot b, there exist v<sub>T<sub>1</sub></sub>, ... v<sub>T<sub>m</sub></sub> votes, each of which can be null (no vote).
# For any ballot b, there exists a corresponding method M<sub>x</sub>
# 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).

Latest revision as of 10:13, 18 December 2012

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

  • Va = 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 Va, there exists an overall error EVa.
  2. For any voting event Va, there exists at least one jurisdiction J.
  3. For any jurisdiction J, there exists an error eJ.
  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, ..., bn.
  6. For any jurisdiction J, there exists an average time to tabulate an individual ballot tM1, ..., tMn.
  7. For any ballot b, there exists some number m of voting topics, T1, ..., Tm.
  8. For any ballot b, there exist vT1, ... vTm votes, each of which can be null (no vote).
  9. For any ballot b, there exists a corresponding method Mx
  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).
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