gibson:teaching:spring-2016:math445:lab8
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gibson:teaching:spring-2016:math445:lab8 [2016/03/22 06:54] gibson [Problem 2: Simulating the 2012 Electoral College votes of a few swing states] |
gibson:teaching:spring-2016:math445:lab8 [2016/03/24 07:02] (current) gibson [Math 445 Lab 8: Predicting Presidential elections with Monte Carlo methods] |
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| * ''if-else'' statements | * ''if-else'' statements | ||
| * ''for'' loops | * ''for'' loops | ||
| - | * ''hist'' histogram plots | + | * ''histogram'' plots |
| ====Background==== | ====Background==== | ||
| Line 20: | Line 20: | ||
| * [[http://cosmiclog.nbcnews.com/_news/2012/10/30/14809227-political-forecasts-stir-up-a-storm?lite|NBC News story on Nate Silver, just prior to 2012 election]], | * [[http://cosmiclog.nbcnews.com/_news/2012/10/30/14809227-political-forecasts-stir-up-a-storm?lite|NBC News story on Nate Silver, just prior to 2012 election]], | ||
| * [[http://www.dailykos.com/story/2012/11/01/1153661/-Nate-Silver-s-Math-Based-Math|DailyKos article on Nate Silver, just prior to 2012 election]] | * [[http://www.dailykos.com/story/2012/11/01/1153661/-Nate-Silver-s-Math-Based-Math|DailyKos article on Nate Silver, just prior to 2012 election]] | ||
| - | * [[http://2012.talkingpointsmemo.com/2012/11/nate-silver-colbert-report-pundits.php?ref=fpnewsfeed|Nate Silver on the Colbert Report]] | ||
| * [[https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=nate%20silver%20controversy | google:"Nate Silver controversy" ]] | * [[https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=nate%20silver%20controversy | google:"Nate Silver controversy" ]] | ||
| * [[https://en.wikipedia.org/wiki/Electoral_College_(United_States) | Electoral College, Wikipedia]] | * [[https://en.wikipedia.org/wiki/Electoral_College_(United_States) | Electoral College, Wikipedia]] | ||
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| a random percentage of voters between -3.4% and 3.4%, and add that percent to | a random percentage of voters between -3.4% and 3.4%, and add that percent to | ||
| Obama while subtracting it from Romney. Compare the resulting percentages | Obama while subtracting it from Romney. Compare the resulting percentages | ||
| - | and declare the winner of the simulated election to whomever hads the larger | + | and declare the winner of the simulated election to whomever has the larger |
| percentage. | percentage. | ||
| Line 82: | Line 81: | ||
| - | ---- | + | ==== Problem 3: Simulating the elections in all fifty states and the likelihood that Obama or Romney wins the general election.==== |
| - | **Problem 3: Simulating the elections in all fifty states and the likelihood that Obama or Romney wins the general election.** | ||
| - | ...to be continued... | + | Now we're ready to tackle the original problem: a Monte Carlo simulation of |
| + | the 2012 Presidential election. | ||
| + | Specifically, given a list of states, the number of their electoral votes, the composite | ||
| + | polling percentages for each candidate, and the margins of error those | ||
| + | polling percentages, you are to run a large number of simulations of the | ||
| + | election and determine the likelihood that either candidate will win based | ||
| + | on the results of those simulations. For each state, start by assigning the | ||
| + | specified composite polling percentages to the two candidates. Then transfer from one | ||
| + | candidate to the other a different random number in the range between | ||
| + | ''-margin'' and ''+margin''. Compare the two percentages and award that state's | ||
| + | electoral votes to the candidate with the larger percentage of votes. Do this | ||
| + | for all fifty states (plus DC), add up all the electoral votes for each candidate, | ||
| + | and award the ''n''th election to the candidate with the majority of electoral votes. | ||
| + | Run a large number (say, 10000) of such simulated elections, keeping track of the number of | ||
| + | electoral votes for each candidate in each election. Make a histogram that | ||
| + | shows the statistical distribution of total electoral votes for one of the | ||
| + | candidates, using bins of width 10 between 0 and 540 (0-9.99 for bin 1, 10-14.99 for | ||
| + | bin 2, etc). If you can figure out how, color the bins corresponding to Romney | ||
| + | wins red and the bins corresponding to Obama wins blue, or else just draw a vertical | ||
| + | line at the magic number of 270 electoral votes needed to win the election outright. | ||
| + | === Questions === | ||
| + | Then answer the following questions (again, pretending that it's still Tuesday, November 6th 2012 and the real outcome is unknown). | ||
| + | |||
| + | - Who is most likely to win the presidential election? | ||
| + | - What is the probability that the most likely winner will actually win? | ||
| + | - What is the most likely range of electoral votes for the winner? (among the bins of width 10 specified above) | ||
| + | - What is the likelihood of a 269-269 electoral vote tie? | ||
| + | |||
| + | Turn in print-outs of your codes, your histogram, and your answers to the above questions. | ||
| + | |||
| + | |||
| + | === Tips === | ||
| + | |||
| + | * Start with a small number of simulated elections (say 100) and then increase to a large number (say 10,000) when you're confident your code is working correctly. | ||
| + | * Try to use as few for-loops as possible. If you are really on fire, you can do it with just one for-loop that loops over the number of trials. | ||
| + | * Changing the colors of histogram bins in Matlab is not as easy as one might hope. You'll need to take data returned from the **hist** function and replot it with the **bar** command. See http://www.mathworks.com/matlabcentral/newsreader/view_thread/290534 for an example of how to do this. | ||
| + | |||
| + | === Data === | ||
| + | |||
| + | Here's the 2012 polling data, taken from [[http://fivethirtyeight.blogs.nytimes.com]] on 2012-11-01. You can load this into Matlab as a matrix ''P'' by cutting and pasting the data into a text file ''P.asc'' and running ''load P.asc'' within Matlab. If you don't believe this polling data, feel free to use something you trust more. | ||
| + | |||
| + | <file matlab P.asc> | ||
| + | % Composite 2012 Presidential election polling numbers | ||
| + | % from http://fivethirtyeight.blogs.nytimes.com | ||
| + | % 2012-11-01 1am | ||
| + | % | ||
| + | % O == Obama percentage | ||
| + | % R == Romney percentage | ||
| + | % M == margin of error | ||
| + | % EV == electoral votes | ||
| + | % | ||
| + | % O R M EV state | ||
| + | 36.8 62.7 3.8 9 % AL | ||
| + | 38.8 59.7 6.0 3 % AK | ||
| + | 46.2 53.0 3.3 11 % AZ | ||
| + | 38.7 59.7 3.8 6 % AR | ||
| + | 58.2 40.5 2.9 55 % CA | ||
| + | 50.9 48.2 3.0 9 % CO | ||
| + | 56.7 42.4 3.3 7 % CT | ||
| + | 59.6 39.7 5.5 3 % DE | ||
| + | 93.1 6.3 3.2 3 % DC | ||
| + | 49.9 49.7 2.7 29 % FL | ||
| + | 45.5 54.1 2.7 16 % GA | ||
| + | 66.5 32.6 3.9 4 % HA | ||
| + | 32.2 66.1 4.4 4 % ID | ||
| + | 59.9 39.5 3.0 20 % IL | ||
| + | 45.3 53.9 3.0 11 % IN | ||
| + | 51.2 47.8 3.2 6 % IA | ||
| + | 38.0 61.0 6.1 6 % KA | ||
| + | 40.4 58.7 4.5 8 % KY | ||
| + | 39.4 59.8 3.5 8 % LA | ||
| + | 56.1 42.7 3.7 4 % ME | ||
| + | 61.0 38.0 3.0 10 % MD | ||
| + | 59.1 39.8 3.7 11 % MA | ||
| + | 53.1 45.8 2.7 16 % MI | ||
| + | 53.8 45.0 2.9 10 % MN | ||
| + | 39.4 60.1 5.3 6 % MS | ||
| + | 45.6 53.6 2.8 10 % MO | ||
| + | 45.3 53.1 3.9 3 % MT | ||
| + | 40.5 58.8 3.3 5 % NE | ||
| + | 51.9 47.2 2.9 6 % NV | ||
| + | 51.5 47.8 3.4 4 % NH | ||
| + | 55.6 43.4 3.3 14 % NJ | ||
| + | 54.2 44.6 3.6 5 % NM | ||
| + | 62.5 36.9 2.8 29 % NY | ||
| + | 48.9 50.5 2.6 15 % NC | ||
| + | 42.1 56.5 3.9 3 % ND | ||
| + | 51.4 47.6 2.7 18 % OH | ||
| + | 33.9 65.8 3.8 7 % OK | ||
| + | 53.7 44.0 3.6 7 % OR | ||
| + | 52.6 46.5 2.6 20 % PA | ||
| + | 61.9 36.3 4.3 4 % RI | ||
| + | 43.3 56.0 4.6 9 % SC | ||
| + | 42.6 56.1 4.2 3 % SD | ||
| + | 41.4 57.7 3.9 11 % TN | ||
| + | 41.3 58.1 3.1 38 % TX | ||
| + | 27.8 70.5 4.1 6 % UT | ||
| + | 50.8 48.6 2.5 13 % VA | ||
| + | 66.3 32.5 4.8 3 % VT | ||
| + | 56.2 42.5 3.5 12 % WA | ||
| + | 41.4 57.4 4.7 5 % WV | ||
| + | 52.5 46.8 2.9 10 % WI | ||
| + | 30.9 67.6 6.0 3 % WY | ||
| + | </file> | ||
gibson/teaching/spring-2016/math445/lab8.1458654876.txt.gz · Last modified: 2016/03/22 06:54 by gibson
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