(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 182288, 4324] NotebookOptionsPosition[ 180710, 4267] NotebookOutlinePosition[ 181053, 4282] CellTagsIndexPosition[ 181010, 4279] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Duverger\[CloseCurlyQuote]s Law", "Title", CellChangeTimes->{{3.776600831050974*^9, 3.7766008318453026`*^9}, { 3.7770707783137817`*^9, 3.7770707814944534`*^9}}], Cell["Adam Rumpf, 7/22/2015", "Text", CellChangeTimes->{{3.7766008347881403`*^9, 3.776600838290375*^9}, { 3.777070775570448*^9, 3.7770707767908287`*^9}}], Cell[CellGroupData[{ Cell["Introduction", "Section", CellChangeTimes->{{3.7766008459498987`*^9, 3.776600848547045*^9}}], Cell["\<\ This is an implementation of the simple behavioral model that Duverger\ \[CloseCurlyQuote]s Law is based on. We begin with a set of political parties \ lying at various points on a political spectrum, each with a given amount of \ initial support. We then simulate a sequence of election cycles. After each \ cycle, if a voter\[CloseCurlyQuote]s preferred candidate did not win, then \ they will consider changing their support to the most successful candidate on \ their half of the political spectrum, with centrist supporters being willing \ to move in either direction.\ \>", "Text", CellChangeTimes->{{3.776600856235587*^9, 3.776600860481224*^9}, { 3.7770721222701683`*^9, 3.7770722467988195`*^9}}], Cell[TextData[{ "The main function defined below is ", StyleBox["votecycle[]", "Code"], ", and accepts the following arguments:" }], "Text", CellChangeTimes->{{3.777072251950158*^9, 3.7770722733687553`*^9}, { 3.777072825982736*^9, 3.777072827404539*^9}}], Cell[CellGroupData[{ Cell[TextData[{ Cell[BoxData[ FormBox["p", TraditionalForm]], FormatType->"TraditionalForm"], " (mandatory): A list of the initial support for each political party, \ ordered from left to right. The length of this list implicitly determines the \ number of parties." }], "ItemNumbered", CellChangeTimes->{{3.777072285017068*^9, 3.777072343445828*^9}}], Cell[TextData[{ Cell[BoxData[ FormBox["t", TraditionalForm]], FormatType->"TraditionalForm"], " (mandatory): Number of election cycles to simulate." }], "ItemNumbered", CellChangeTimes->{{3.777072285017068*^9, 3.777072361974415*^9}}], Cell[TextData[{ Cell[BoxData[ FormBox["d", TraditionalForm]], FormatType->"TraditionalForm"], " (optional, default ", Cell[BoxData[ FormBox["0.9", TraditionalForm]], FormatType->"TraditionalForm"], "): The fraction of voters that abandon their current party in favor of the \ most successful neighbor after each cycle. A lower value causes a more \ gradual change." }], "ItemNumbered", CellChangeTimes->{{3.777072285017068*^9, 3.7770724340610704`*^9}}], Cell[TextData[{ Cell[BoxData[ FormBox["s", TraditionalForm]], FormatType->"TraditionalForm"], " (optional, default 0): A switching threshold, expressed as a percent. \ Voters will only consider switching to a party that has beaten their current \ party by a margin least ", Cell[BoxData[ FormBox["s", TraditionalForm]], FormatType->"TraditionalForm"], " percent." }], "ItemNumbered", CellChangeTimes->{{3.777072285017068*^9, 3.7770725325708447`*^9}}], Cell[TextData[{ Cell[BoxData[ FormBox["r", TraditionalForm]], FormatType->"TraditionalForm"], " (optional, default 0): Random drift between neighboring parties. After \ each iteration, for each party, a random number of supporters chosen \ uniformly from ", Cell[BoxData[ FormBox[ RowBox[{"[", RowBox[{"0", ",", "r"}], "]"}], TraditionalForm]], FormatType->"TraditionalForm"], " will move to a neighboring party." }], "ItemNumbered", CellChangeTimes->{{3.777072285017068*^9, 3.7770725656692367`*^9}, { 3.77707261939861*^9, 3.7770726959983315`*^9}, {3.7770727376884623`*^9, 3.777072740701502*^9}}] }, Open ]], Cell["\<\ This function produces a four-part plot based on the given parameters. The \ top two bar plots show the initial and final amount of support for each \ party. The lower left line plot shows each party\[CloseCurlyQuote]s support \ over the election cycles. 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