Simulation exercises on outlier analysis
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Lilliputia is a tiny state that looks like a 6 x 3 grid. Each square of the grid has the same number of voters, who all vote for either the "1 Party" or the "0 Party".
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We want to divide Lilliputia into 6 districts. There are 170 different ways to do this; you can see all of them at the bottom of this page.
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Depending on where the 1-voters and the 0-voters live, different plans give different results. The table below gives a summary.
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1
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1
Number of plans in which 1 wins...
Percentage:
6
0 districts:
00%
7
1
1 districts:
170100%
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1
2 districts:
00%
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3 districts:
00%
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4 districts:
00%
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5 districts:
00%
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6 districts:
00%
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TOTAL PLANS:
170100%
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Experiment with different possible distributions of 0 and 1 voters in Lilliputia.
1) Can you find a situation where 1/3 of the voters are 1's, but a random districting plan is more likely to give them no districts than two districts? (Two out of six is what they would get if you had proportional representation.)
2) Can you find a situation where 1/3 of the voters are 1's, but this time a plan where they win no districts looks very suspicious? (Give an example of such a plan.)
3) Can you find a situation where 1/3 of the voters are 1's, and this time a plan where they win 3 districts looks suspicious? (Give an example of such a plan.)
4) Can you find a situation where 1/3 of the voters are 1's, but there is simply no way for them to win more than one district?
5) Now experiment with situations where half the voters are 1's. Which arrangements of their voters are most advantageous for Party 1?
Which are least advantageous? Are there arrangements that are hard to gerrymander in either direction?
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