Absentee ballot outcomes contrasted with machine ballots, cast in Pennsylvania State Senate elections, selected districts, 1982-1993.
A data frame with 22 observations on the following 8 variables.
a numeric vector, year of election, 19xx
a numeric vector, Pennsylvania State Senate district
a numeric vector, absentee ballots cast for the Democratic candidate
a numeric vector, absentee ballots cast for the Republican candidate
a numeric vector, votes cast on voting machines for the Democratic candidate
a numeric vector, votes cast on voting machines for the Republican candidate
a numeric vector, Democratic margin among absentee ballots
a numeric vector, Democratic margin among ballots case on voting machines
In November 1993, the state of Pennsylvania conducted elections for its state legislature. The result in the Senate election in the 2nd district (based in Philadelphia) was challenged in court, and ultimately overturned. The Democratic candidate won 19,127 of the votes cast by voting machine, while the Republican won 19,691 votes cast by voting machine, giving the Republican a lead of 564 votes. However, the Democrat won 1,396 absentee ballots, while the Republican won just 371 absentee ballots, more than offsetting the Republican lead based on the votes recorded by machines on election day. The Republican candidate sued, claiming that many of the absentee ballots were fraudulent. The judge in the case solicited expert analysis from Orley Ashenfelter, an economist at Princeton University. Ashenfelter examined the relationship between absentee vote margins and machine vote margins in 21 previous Pennsylvania Senate elections in seven districts in the Philadelphia area over the preceding decade.
Ashenfelter, Orley. 1994. Report on Expected Absentee Ballots. Typescript. Department of Economics, Princeton University.
Ashenfelter, Orley, Phillip Levine and David Zimmerman. 2003. Statistics and Econometrics: Methods and Applications. New York: John Wiley and Sons.
Jackman, Simon. 2009. Bayesian Analysis for the Social Sciences. Wiley: Hoboken, New Jersey. Examples 2.13, 2.14, 2.15.
data(absentee) summary(absentee) denom <- absentee$absdem + absentee$absrep y <- (absentee$absdem - absentee$absrep)/denom * 100 denom <- absentee$machdem + absentee$machrep x <- (absentee$machdem - absentee$machrep)/denom *100 ols <- lm(y ~ x, subset=c(rep(TRUE,21),FALSE) ## drop data point 22 ) ## predictions for disputed absentee point yhat22 <- predict(ols, newdata=list(x=x), se.fit=TRUE, interval="prediction") tstat <- (y-yhat22$fit[,"fit"])/yhat22$se.fit cat("tstat on actual outcome for obs 22:",tstat,"\n") cat(paste("Pr(t>",round(tstat,2),") i.e., one-sided:\n",sep="")) cat(1-pt(tstat,df=yhat22$df),"\n") ## make a picture xseq <- seq(min(x)-.1*diff(range(x)), max(x)+.1*diff(range(x)), length=100) yhat <- predict(ols,interval="prediction", newdata=list(x=xseq)) plot(y~x, type="n", axes=FALSE, ylim=range(yhat,y), xlim=range(xseq),xaxs="i", xlab="Democratic Margin, Machine Ballots (Percentage Points)", ylab="Democratic Margin, Absentee Ballots (Percentage Points)") polygon(x=c(xseq,rev(xseq)), ## overlay 95% prediction CI y=c(yhat[,"lwr"],rev(yhat[,"upr"])), border=FALSE, col=gray(.85)) abline(ols,lwd=2) ## overlay ols points(x[-22],y[-22],pch=1) ## data points(x,y,pch=16) ## disputed data point text(x,y, "Disputed\nElection", cex=.75, adj=1.25) axis(1) axis(2)