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winner-take-all-distortion.nb
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winner-take-all-distortion.nb
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(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
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Notebook[{
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Cell["Winner-Take-All Distortion", "Title",
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Cell[TextData[{
"This Notebook defines a set of functions for demonstrating how the results \
of elections can be distored when evaluated as a collection of aggregated \
winner-take-all races instead of simply counting every individual vote. \
Specifically, we have a ",
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" array of voters, each of which is affiliated with one party. Taken \
individually, this can be imagined as an array of ",
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"."
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"Next, we try grouping people into ",
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" districts, resulting in a ",
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" array of districts, and instead of giving each person a direct vote, we \
instead hold a vote within each individual district and evaluate all of the \
district-wide results. Within a district, the candidate with the most votes \
wins the entire district (with ties being broken arbitrarily). This could be \
thought of as introducing a congress of ",
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"After that we group people into ",
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" districts in a ",
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is a single-winner election like a presidential election."
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"For each collection of districts we display a pie chart of the \
congressional makeup as well as a \[OpenCurlyDoubleQuote]misrepresentation \
score\[CloseCurlyDoubleQuote], calculated as the sum over all parties of the \
difference between their individual-level support and their overall \
district-level support (in percentage points, \[OpenCurlyDoubleQuote]",
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having exactly ",
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", then the misrepresentation score would be ",
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": the sum of red\[CloseCurlyQuote]s 10 pp overrepresentation and blue\
\[CloseCurlyQuote]s ",
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"The main function defined below is ",
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" (default ",
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"): A list of party support weights. The initial array is generated by \
randomly assigning each voter to a party, and the weight list determines the \
relative likelihood that any given voter belongs to each party. The length of \
this list implicitly determines the number of parties. Since the array is \
randomly generated, evaluating the function repeatedly with the same inputs \
will generally yield different results."
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" (default 0): If set to 0, displays only an array, pie chart, and \
misrepresentation score as described above. If set to 1, then for each row it \
also displays a pie chart and misrepresentation score of the results which \
would come from using a proprotional system instead of using district-level \
results."
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Cell["\<\
As expected, misrepresentation score tends to increase as the number of \
districts decreases, sometimes quite rapidly, and the misrepresentation of \
the proportional system will always be a lower bound to the misrepresentation \
of the winner-take-all district system. Also observe what happens to smaller \
political parties as the number of districts decreases.\
\>", "Text",
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