PA_2012.html

<p><a href = "http://gerrymander.princeton.edu"><b>Gerrymandering analyzer from Prof. Sam Wang, Princeton University</b></a></p>
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Election to be analyzed:  U.S. House election of 2012 in [None]</p>
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Districts to be sampled for fantasy delegations:  U.S. House results of 2012 in all 50 states</p>
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The None delegation has 18 seats, 5 Democratic/other and 13 Republican.</p>
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Uncontested races are assumed to have been won with 25% of the vote.</p>
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The average Democratic share of the two-party total vote was 50.5% (raw)
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<b>Analysis of Intents</b></p>
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If a political party wishes to create for itself an advantage, it will pack its opponents to win overwhelmingly in a small number of districts, while distributing its own votes more thinly, but still to produce reliable wins. 
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Partisan gerrymandering arises not from single districts, but from patterns of outcomes. Thus a single lopsided district may not be an offense - indeed, single-district gerrymandering is permitted by Supreme Court precedent, and may be required for the construction of individual districts that comply with the Voting Rights Act. Rather, it is combinations of outcomes that confer undue advantage to one party or the other.
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The following two tests provide a way of quantifying any such advantage in a set of election results.
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<b>First Test of Intents: Probing for lopsided win margins (the two-sample t-test):</b> 
To test for a lopsided advantage, one can compare each partys winning margins and see if they are systematically different. 
This is done using the <a href="http://vassarstats.net/textbook/ch11pt1.html">two-sample t-test</a>. 
In this test, the party with the <i>smaller</i> set of winning margins has the advantage.</p>
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The difference between the two parties win margins meets established standards for statistical significance. 
The probability that this difference in win margins (or larger) would have arisen by partisan-unbiased mechanisms alone is less than 0.001. 
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<IMG SRC="PA_2012_Test1.png" border="0" alt="Logo"></p>
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<b>Second Test of Intents: Probing for asymmetric advantage for one party (mean-median difference and/or chi-square test):</b> 
The choice of test depends on whether the parties are closely matched (mean-median difference) or one party is dominant (chi-square test of variance).</p>
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When the parties are closely matched in overall strength, a partisan advantage will be evident in the form of a difference between the mean (a.k.a. average) vote share and the median vote share, calculated across all districts. </p>
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The mean-median difference is 7.6 % in a direction of advantage to the Republican Party. 
The mean-median difference would reach this value in 0.7 % of situations by a partisan-unbiased process. 
This difference is statistically significant (p<0.01), and in a case of suspected gerrymandering is extremely unlikely to have arisen by chance. 
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<IMG SRC="PA_2012_Test2a.png" border="0" alt="Logo"></p>
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