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# We use a lognormal income distribution to simulate the income distribution in the USA in 2008. |
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# The parameters are chosen so that the median income comes out to about $30,000, |
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# the gini index comes out to about 0.35, and the 90/10 ratio comes in at about 6:1, |
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# as in the Luxembourg Income Study figures for 2010. |
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# See the key figures here: http://www.lisdatacenter.org/data-access/key-figures/inequality-and-poverty/ |
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incomes <- rlnorm(300000,meanlog=log(30000),0.55) |
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require(reldist) # to calculate the gini index |
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gini(incomes) |
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# should come out around 0.3, which is a bit lower than the 0.37 the LIS gives for the USA in 2010 |
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# Voting system parameters. x is the sensitivity of the system to income inequality |
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# (the "disenfranchisement parameter"); n is the number of classes of voters. |
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# With n = 10, we have deciles; with x = 1, we have voting power inversely proportional to income. |
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n <- 10 |
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x <- 1 |
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# We now calculate the median income of each class of voters |
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spacing <- 1/n |
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first.midpoint <- spacing/2 |
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midpoints <- quantile(incomes,seq(first.midpoint, |
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1-first.midpoint, |
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spacing)) |
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# And we are now ready to calculate the relative weight of votes in each class |
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votes <- (midpoints[1]/midpoints)^x |
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# Here we approximate the democratic vote shares per decile, using this data from ANES: |
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# http://electionstudies.org/nesguide/2ndtable/t9b_1_1.htm. (This is not exact). |
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# Lowest decile voted about 75% democratic; highest decile voted about 33% democratic |
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dem.vote.shares.08 <- seq(from=0.75, |
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by=-0.04234, |
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length.out=n) |
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# Here we approximate the turnout per decile, using this data from ANES: |
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# http://electionstudies.org/nesguide/2ndtable/t6a_2_2.htm. (This is not exact). |
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# Lowest decile had turnout of about 65%; highest decile had turnout of about 89%. |
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# This is probably overstated. |
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turnout.08 <- seq(from=0.65,by=0.02,length.out=10) |
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# This is the Democratic share of the vote we would expect with the existing voting system |
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original.result <- weighted.mean(dem.vote.shares,turnout.08) |
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# should be about 0.55, which is close to the 54% of the vote that the Democrats actually got in |
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# the 2008 congressional election. See http://electionstudies.org/nesguide/toptable/tab9b_1.htm |
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# This is the Democratic share of the vote we would expect with an inverse income voting system, |
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# not taking differential turnout into account |
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result.no.turnout <- weighted.mean(dem.vote.shares.08,votes) |
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# should be about 0.62 (62%), about 7% points bigger than the actual Democratic share |
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# This is the Democratic share of the vote we would expect with an inverse income voting system, |
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# taking actual differences in turnout in 2008 into account |
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result.with.turnout <- weighted.mean(dem.vote.shares.08,votes*turnout.08) |
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# should be about 0.61 (61%) |
