Difference between revisions of "Morning math/Voting systems"

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Revision as of 10:13, 18 December 2012

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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:
 
* 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:
 
* 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'''.


==Voting systems Model==
==Voting systems Model==
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