Load Packages:

suppressWarnings(suppressMessages(library(operators)))
suppressWarnings(suppressMessages(library(plyr)))
suppressWarnings(suppressMessages(library(ggplot2)))
suppressWarnings(suppressMessages(library(reshape2)))
suppressWarnings(suppressMessages(library(RCurl)))
suppressWarnings(suppressMessages(library(knitr)))

The data source for congressional results was is Time Magazine’s GitHub Repo. I’m grateful for their work in tidying the data and providing results for each congressional election from 2004-2012 as both as json and csv file. The link I used for the 2012 data below can be found \(\href{https://github.com/TimeMagazine/congressional-election-results.git}{here}\)

First, I loaded and cleanded the data. The file contains records of senate elections, marked as “S” in the district field, and special elections. Special elections are indicated by additional text in the district field. We will excise this info for our purposes. Those congressional districts marked “00” are at-large districts for states with only one seat.

url <- "https://raw.githubusercontent.com/TimeMagazine/congressional-election-results/master/data/results_2012.csv"
cd2012 <- getURL(url)
cd2012 <- read.csv(textConnection(cd2012))
#cd2012 <- read.csv("results_2012.csv",header=T)
cd2012$votes <- as.numeric(as.character(cd2012$votes))
## Warning: NAs introduced by coercion
cd2012 <- subset(cd2012,district != "S")
cd2012$district[cd2012$district == "01 - FULL TERM"] <- "01"
cd2012$district[cd2012$district == "04 - FULL TERM"] <- "04"
cd2012$district[cd2012$district == "10 - FULL TERM"] <- "10"
cd2012$district[cd2012$district == "11 - FULL TERM"] <- "11"
kable(subset(cd2012, state=="CA" & district=="37"))
id year name state district votes parties
138 2012_CA_37 2012 Bass, Karen R. CA 37 207039 Democratic
139 2012_CA_37 2012 Osborne, Morgan CA 37 32541 Write-In,Republican,Republican

By examining the records for the California 37th, we see that some major parties are not simply listed “Democratic” or “Republican”, but some local variation or party alliance. To simplify the results, we will lump all of the Republican and Democratic groups into their umbrella label. This will still leave a significant amount of independent and third parties in our dataset that are aligned with neither of the two.

d <- c("Democratic,Working Families","Working Families,Democratic",
       "Democratic,Progressive,Working Families","Democratic-Farmer Labor",
       "Democratic,Working Families,Independence","Democratic,Independence,Working Families",
       "Democratic-Nonpartisan League","Write-In,Democratic,Democratic","Democratic")
r <- c("Republican,Tax Revolt,Conservative,Independence","Republican,Tax Revolt,Conservative",
       "Republican,Tax Revolt","Republican,Conservative","Conservative,Republican",
       "Republican,Conservative,Libertarian","Republican,Conservative,Independence",
       "Independence,Republican","Independent Party,Republican", "Republican,Constitution",
       "Write-In,Republican,Republican","Conservative,Independence,Republican","Republican")

for (i in 1:length(cd2012$parties)){
  if (cd2012$parties[i] %in% d){
    cd2012$parties[i] <- "Democratic"
  }
  else if (cd2012$parties[i] %in% r){
    cd2012$parties[i] <- "Republican"
  }
}
kable(subset(cd2012, state=="CA" & district=="37"))
id year name state district votes parties
138 2012_CA_37 2012 Bass, Karen R. CA 37 207039 Democratic
139 2012_CA_37 2012 Osborne, Morgan CA 37 32541 Republican

The replacements worked! Now we will perform a a number of operations and aggregations to return useful dataframes.

# calc total vote by state
totalVoteByState <- aggregate(votes ~ state, cd2012, sum)
# calc total vote by district
totalVoteByDistrict <- aggregate(votes ~ state + district, cd2012, sum)
totalVoteByDistrict <- totalVoteByDistrict[order(totalVoteByDistrict$state,totalVoteByDistrict$district),]
# add threshold of simple majority based on each district's vote total
totalVoteByDistrict$simpleMajority <- round(totalVoteByDistrict$votes/2 + 1,0)
kable(head(totalVoteByState,10))
state votes
AK 288840
AL 1927122
AR 1038054
AZ 2173317
CA 12204357
CO 2450839
CT 1466511
DE 388059
FL 7513534
GA 3553587 
kable(head(totalVoteByDistrict,10))
state district votes simpleMajority
1 AK 00 288840 144421
8 AL 01 196374 98188
51 AL 02 283683 141842
94 AL 03 273447 136724
132 AL 04 268777 134390
167 AL 05 290957 145480
196 AL 06 307529 153766
222 AL 07 306355 153178
9 AR 01 246843 123422
52 AR 02 286598 143300

Next, I created a dataframe for total votes for each party in each district. I added a column for each party’s percentage of the vote in the district as well as a total of the number of votes “wasted” for each party. Our critera for wasted votes are:

  1. Every vote for a losing party
  2. Every vote in excess of the simple majority for a winning party
districtParty <- aggregate(votes ~ state + district + parties, cd2012, sum)
districtParty <- districtParty[order(districtParty$state,districtParty$district),]
districtParty <- join(districtParty,totalVoteByDistrict,by=c("state","district"),type="left")
colnames(districtParty)[5] <- "totalVote"
districtParty <- districtParty[,c(1,2,5,6,4,3)]
districtParty$pctVote <- districtParty$votes/districtParty$totalVote
districtParty$wastedVote <- 0
  
for (i in 1:nrow(districtParty)){
  if (districtParty$votes[i] < districtParty$simpleMajority[i]){
  districtParty$wastedVote[i] <- districtParty$votes[i]
  }
  else if (districtParty$votes[i] >= districtParty$simpleMajority[i]){
  districtParty$wastedVote[i] <- districtParty$votes[i] - districtParty$simpleMajority[i]
  }
}
kable(head(districtParty,10))
state district totalVote simpleMajority votes parties pctVote wastedVote
AK 00 288840 144421 82927 Democratic 0.2871036 82927
AK 00 288840 144421 15028 Libertarian 0.0520288 15028
AK 00 288840 144421 5589 Non-Affiliated 0.0193498 5589
AK 00 288840 144421 185296 Republican 0.6415178 40875
AL 01 196374 98188 196374 Republican 1.0000000 98186
AL 02 283683 141842 103092 Democratic 0.3634056 103092
AL 02 283683 141842 180591 Republican 0.6365944 38749
AL 03 273447 136724 98141 Democratic 0.3589032 98141
AL 03 273447 136724 175306 Republican 0.6410968 38582
AL 04 268777 134390 69706 Democratic 0.2593451 69706

Next, I created a column to indicate which party won in each district. To do so, I iterated over every district to find which party had the highest percentage of the vote. Winners were marked with “1” in the “win” column so that we could later aggregate results by party.

allStates <- unique(districtParty$state)
allDistricts <- unique(districtParty$district)
districtParty$win <- 0 #create column to indicate wins

for (i in 1:length(allDistricts)){
  for (j in 1:length(allStates)){
    row_to_find <- data.frame(state=allStates[j], district=allDistricts[i])
    if(nrow(merge(row_to_find,districtParty))>0){
      subFrame <- subset(districtParty,state==allStates[j] & district==allDistricts[i])
      w <- which.max(subFrame$pctVote)
      districtParty[districtParty$state==allStates[j] & 
      districtParty$district==allDistricts[i],]$win[w] <- 1
    }
  }
}

Calculate total seats won by state and overall:

seatsWon <- aggregate(win ~ parties,districtParty,sum)
seatsWon <- subset(seatsWon,win!=0)
seatsWon
##       parties win
## 12 Democratic 199
## 39 Republican 234
seatsWonByState <- aggregate(win ~ state + parties,districtParty,sum)
seatsWonByState <- subset(seatsWonByState,win!=0)
seatsWonByState <- seatsWonByState[order(seatsWonByState$state,-seatsWonByState$win),]
kable(head(seatsWonByState,10))
state parties win
156 AK Republican 1
157 AL Republican 6
19 AL Democratic 1
158 AR Republican 4
21 AZ Democratic 5
159 AZ Republican 4
22 CA Democratic 38
160 CA Republican 15
161 CO Republican 4
23 CO Democratic 3

A quick detour to get a rough comparison of the total votes and wasted votes by party:

totalWastedVoteByParty <- aggregate(wastedVote ~ parties, districtParty, sum)
totalWastedVoteByParty <- totalWastedVoteByParty[order(-totalWastedVoteByParty$wastedVote),]
totalVoteByParty <- aggregate(votes ~ parties, districtParty, sum)
totalVoteByParty <- totalVoteByParty[order(-totalVoteByParty$votes),]
kable(head(totalWastedVoteByParty,6))
parties wastedVote
12 Democratic 33763208
39 Republican 25146263
21 Libertarian 1302730
16 Independent 485517
25 No Party Affiliation 374428
14 Green 342912 
kable(head(totalVoteByParty,6))
parties votes
12 Democratic 59637698
39 Republican 58265212
21 Libertarian 1302730
16 Independent 485517
25 No Party Affiliation 374428
14 Green 342912

Phenomenal! By looking at the at the aggregate, we see that Democrats and Republicans received roughly the same number of votes nationally. Although Democrats received 1,372,486 more votes, Republicans won a 35 seat majority in the House of Representatives. We also see that there are far more wasted votes for Democrats - 8,616,945 more to be precise - just about a third more wasted votes than for Republicans.

Now we will start to create our misapportionment metric by diving into the data for wasted votes for each party by state.

numDistricts <- data.frame(table(totalVoteByDistrict$state))
colnames(numDistricts) <- c("state","number")
numDistricts[9,2] <- 27 # correct, missing two from redistricting
sum(numDistricts$number) # check all 435 are there
## [1] 435
totalWastedVoteByPartyByState <- aggregate(wastedVote ~ state + parties, districtParty, sum)
totalVoteByPartyByState <- aggregate(votes ~ state + parties, districtParty, sum)
totalVoteByPartyByState <- totalVoteByPartyByState[order(totalVoteByPartyByState$state,-totalVoteByPartyByState$votes),]
totalWastedVoteByPartyByState <- totalWastedVoteByPartyByState[order(totalWastedVoteByPartyByState$state,-totalWastedVoteByPartyByState$wastedVote),]
kable(head(totalVoteByPartyByState,10))
state parties votes
156 AK Republican 185296
18 AK Democratic 82927
104 AK Libertarian 15028
146 AK Non-Affiliated 5589
157 AL Republican 1233624
19 AL Democratic 693498
158 AR Republican 637591
20 AR Democratic 304770
70 AR Green 57706
105 AR Libertarian 37987 
kable(head(totalWastedVoteByPartyByState,10))
state parties wastedVote
18 AK Democratic 82927
156 AK Republican 40875
104 AK Libertarian 15028
146 AK Non-Affiliated 5589
19 AL Democratic 540320
157 AL Republican 423234
20 AR Democratic 304770
158 AR Republican 118560
70 AR Green 57706
105 AR Libertarian 37987

Our first attempt will take a simplified look at the results by ignoring third parties. We will subset the dataframe to only include Democrats and Republicans and then join it with the number of districts and total vote for each state. This will let us create new columns for the efficiency gap and the number of seats misapportioned.

The efficiency gap is calculated by the absolute value in the difference of wasted votes for each party, divided by the total number of votes in the state. The number of misapportioned seats is a product of the efficiency gap and the number of seats/districts in the state.

I also created columns for the advantage given to either party. This advantage is simply the seat misapportionment in their favor. The seat advantage for each state is determined by the party with fewer wasted votes.

twoPartyModel <- subset(totalWastedVoteByPartyByState,parties=="Democratic" | totalWastedVoteByPartyByState$parties=="Republican")
twoPartyModel <- dcast(twoPartyModel,state ~ parties,value.var="wastedVote")
# bind number districts and total vote
twoPartyModel <- join(twoPartyModel,numDistricts,by="state",type="left")
twoPartyModel <- join(twoPartyModel,totalVoteByState,by="state",type="left")
twoPartyModel$efficiency.gap <- abs(twoPartyModel$Democratic-twoPartyModel$Republican)/twoPartyModel$votes
twoPartyModel$seats.misapportioned <- twoPartyModel$efficiency.gap*twoPartyModel$number
colnames(twoPartyModel)[2:5] <- c("w.votes.D","w.votes.R","seats","total.votes")
twoPartyModel$adv.R <- 0 
twoPartyModel$adv.D <- 0

for (i in 1:nrow(twoPartyModel)){
  if (twoPartyModel$w.votes.D[i] < twoPartyModel$w.votes.R[i]){
    twoPartyModel$adv.D[i] <- twoPartyModel$seats.misapportioned[i]
  }
  else if (twoPartyModel$w.votes.R[i] < twoPartyModel$w.votes.D[i]){
    twoPartyModel$adv.R[i] <- twoPartyModel$seats.misapportioned[i]
  }
}


sum(twoPartyModel$adv.R)
## [1] 37.18521
sum(twoPartyModel$adv.D)
## [1] 8.228584

By summing the total advantages for each party, we see that the Republicans have roughly a 29 seat advantage based on the efficiency gap. This measure is remarkably close to the excess number of seats Republicans hold in proportion to their share of the vote.

# Republican Seats in proportional system
(58265212/sum(totalVoteByParty$votes))*435
## [1] 208.982
# Libertarian Seats in proportional system
(1302730/sum(totalVoteByParty$votes))*435
## [1] 4.672549

We calculated above that Republicans won 234 seats in the 2012 election, but we see here that in a strictly proportional system they would have won 209. Of course, seats in the House of Representatives aren’t meant to be proportionally allocated, but here we may be able to disprove the notion that the Republican advantage is the product of political advantage in many smaller, less-populated districts. Our measure of the efficiency gap shows that they hold 29 seats more than they should. This demonstrates how perfect political symmetry - parity in wasted votes - differs from strict proportionality. We demonstrate that Republicans hold 29 seats more than they should, which would actually put them at 4 seats fewer than a strictly proportional allotmment. We see here that symmetry in wasted votes does not manifest strictly proportional outcomes. Some symmetric elections may benefit one of the two major parties at the cost of the other, but it appears in this case that the Republicans picked up most of the five seats Liberatarians would have won.

Now we will add some metrics to our two-party model to see how a symmetric election may have turned out.

twoPartyStateTotals <- subset(totalVoteByPartyByState,parties=="Democratic" | totalVoteByPartyByState$parties=="Republican")
twoPartyStateTotals <- dcast(twoPartyStateTotals,state ~ parties,value.var="votes")
colnames(twoPartyStateTotals)[2:3] <- c("d.votes","r.votes")
twoPartyModel <- join(twoPartyModel,twoPartyStateTotals,by="state",type="left")
# calculate projected seats
twoPartyModel$proj.D.seats <- (twoPartyModel$d.votes/twoPartyModel$total.votes)*twoPartyModel$seats
twoPartyModel$proj.R.seats <- (twoPartyModel$r.votes/twoPartyModel$total.votes)*twoPartyModel$seats
display <- twoPartyModel
#display[,2:9] <- round(display[,2:9],2)
kable(display[,c(1,4,7,12,13)])
state seats seats.misapportioned proj.D.seats proj.R.seats
AK 1 0.1455893 0.2871036 0.6415178
AL 7 0.4252985 2.5190341 4.4809659
AR 4 0.7175349 1.1743898 2.4568703
AZ 9 0.2580921 3.9216304 4.6863697
CA 53 1.2802878 32.1043754 19.6725347
CO 7 0.3431882 3.0859546 3.2668698
CT 5 0.9623896 3.2433476 1.7057151
DE 1 0.1903164 0.6440593 0.3343744
FL 27 2.9047930 12.1906488 13.7506657
GA 14 0.9293826 5.7080820 8.2894754
HI 2 0.3019603 1.3490258 0.6509742
IA 4 0.1096082 2.0121201 1.8925944
ID 2 0.3749705 0.6558284 1.2808642
IL 18 1.0471468 9.7638073 7.8567970
IN 9 1.3883687 4.0266283 4.7639194
KS 4 0.0627830 0.7393317 2.8021317
KY 6 0.7122713 2.3539121 3.5324701
LA 6 0.7682076 1.2635545 4.0209273
MA 9 0.3879411 6.4761451 2.1714945
MD 8 0.5785490 5.0451608 2.6620387
ME 2 0.5334815 1.2332614 0.7667386
MI 14 2.3112845 7.1244616 6.3863620
MN 8 0.1169094 4.4474870 3.4486441
MO 8 0.9638537 3.3470728 4.3756075
MS 4 0.0277807 1.3620477 2.3295797
MT 1 0.3946763 0.4271876 0.5325134
NC 13 2.7841548 6.5786734 6.3378995
ND 1 0.3682878 0.4178849 0.5495987
NE 3 0.6455137 1.0727520 1.9272480
NH 2 0.4085112 0.9997537 0.9138644
NJ 12 2.0638059 6.5609951 5.2300038
NM 3 0.2758823 1.6976062 1.2998526
NV 4 0.2595020 1.8621360 1.8782758
NY 27 2.0979047 17.2385141 9.3760276
OH 16 3.6932604 7.5091061 8.1559140
OK 5 0.8161184 1.5473006 3.2311991
OR 5 0.7597368 2.7839943 2.0164479
PA 18 4.3056870 9.0498016 8.7794030
RI 2 0.6688927 1.0889133 0.7577967
SC 7 1.4879715 2.9022655 4.0092606
SD 1 0.3510095 0.4255027 0.5744973
TN 9 0.2157263 3.1389991 5.3973430
TX 36 1.8254567 13.8561480 20.8049834
UT 4 0.2132312 1.2986684 2.5943536
VA 11 2.3454557 5.3209992 5.5294050
VT 1 0.0130324 0.7201472 0.2331779
WA 10 0.3250112 5.4443818 4.5556182
WI 8 1.1720342 4.0386575 3.9184214
WV 3 0.0323316 1.2026167 1.7973833
WY 1 0.0486101 0.2386891 0.6900852

Add actual seats won to the model and plot the results:

seatsWonByState <- dcast(seatsWonByState,state ~ parties,value.var="win",fill="0")
seatsWonByState$Democratic <- as.numeric(as.character(seatsWonByState$Democratic))
seatsWonByState$Republican <- as.numeric(as.character(seatsWonByState$Republican))
colnames(seatsWonByState)[2:3] <- c("act.D.seats","act.R.seats")
twoPartyModel <- join(twoPartyModel,seatsWonByState,by="state",type="left")
twoPartyModel$proj.diff <- abs(twoPartyModel$proj.R.seats - twoPartyModel$proj.D.seats)
twoPartyModel$act.diff <- abs(twoPartyModel$act.R.seats - twoPartyModel$act.D.seats)
ggplot(twoPartyModel) + 
  geom_point(aes(x=state, y=proj.D.seats),color="red") +
  geom_point(aes(x=state, y=proj.R.seats),color="black")

ggplot(twoPartyModel) + 
  geom_point(aes(y=efficiency.gap, x=act.diff),color="black") +
  geom_point(aes(y=efficiency.gap, x=proj.diff),color="white")

ggplot(twoPartyModel) + 
  geom_point(aes(x=state, y=seats.misapportioned),color="black") +
  geom_point(aes(x=state, y=adv.R),color="red") +
  geom_point(aes(x=state, y=adv.D),color="blue") +
  ylim(0.5,5) + 
  ggtitle("Misapportioned Congressional Districts Seats By Party")
## Warning: Removed 24 rows containing missing values (geom_point).
## Warning: Removed 32 rows containing missing values (geom_point).
## Warning: Removed 42 rows containing missing values (geom_point).

Now we calculate Democrat:Republican vote ratio and plot against efficiency gap. Now we want to look at the distribution for the efficiency gap based on who has more votes in a state. States with a DR ratio less than 1 have more Republican votes, and those with a ratio greater than 1 have more Demcratic voters

twoPartyModel$marg.victory <- abs(twoPartyModel$d.votes-twoPartyModel$r.votes)/twoPartyModel$total.votes
twoPartyModel$voteratio <- ifelse(twoPartyModel$r.votes<twoPartyModel$d.votes,
                          twoPartyModel$r.votes/twoPartyModel$d.votes,
                          twoPartyModel$d.votes/twoPartyModel$r.votes)
twoPartyModel$majority <- ifelse(twoPartyModel$r.votes>twoPartyModel$d.votes,"R","D")
ggplot(twoPartyModel,aes(x=voteratio, y=efficiency.gap)) + 
  geom_point(aes(colour=majority)) + 
  scale_colour_manual(values=c("blue","red")) + 
  stat_smooth(se=TRUE,level=0.95) + 
  ylim(-0.2,0.4) + xlim(1,4) 
## Warning: Removed 50 rows containing non-finite values (stat_smooth).
## Warning: Removed 50 rows containing missing values (geom_point).

ggplot(twoPartyModel,aes(x=voteratio, y=efficiency.gap,colour=majority)) + 
  geom_point() + 
  scale_colour_manual(values=c("blue","red")) + 
  geom_smooth(se=FALSE,method=lm,level=0.95) 

ggplot(twoPartyModel,aes(x=marg.victory, y=efficiency.gap,colour=majority)) + 
  geom_point() + 
  scale_colour_manual(values=c("blue","red")) + 
  geom_smooth(se=FALSE,method=lm,level=0.95) 

rgap <- subset(twoPartyModel,voteratio<1)
dgap <- subset(twoPartyModel,voteratio>1)
summary(rgap$efficiency.gap)
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
## 0.006945 0.049450 0.124300 0.133100 0.191900 0.394700
summary(dgap$efficiency.gap)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 
twoPartyModel[,c(1,6,10,11,20)]
##    state efficiency.gap d.votes r.votes majority
## 1     AK    0.145589254   82927  185296        R
## 2     AL    0.060756921  693498 1233624        R
## 3     AR    0.179383731  304770  637591        R
## 4     AZ    0.028676903  946994 1131663        R
## 5     CA    0.024156373 7392703 4530012        D
## 6     CO    0.049026884 1080454 1143796        R
## 7     CT    0.192477929  951281  500290        D
## 8     DE    0.190316421  249933  129757        D
## 9     FL    0.107584926 3392402 3826522        R
## 10    GA    0.066384473 1448869 2104098        R
## 11    HI    0.150980146  285008  137531        D
## 12    IA    0.027402051  772387  726505        D
## 13    ID    0.187485241  208297  406814        R
## 14    IL    0.058174825 2743702 2207818        D
## 15    IN    0.154263188 1142554 1351760        R
## 16    KS    0.015695743  195505  740981        R
## 17    KY    0.118711889  684744 1027582        R
## 18    LA    0.128034606  359190 1143027        R
## 19    MA    0.043104563 2080594  697637        D
## 20    MD    0.072318627 1626872  858406        D
## 21    ME    0.266740751  427819  265982        D
## 22    MI    0.165091749 2327985 2086804        D
## 23    MN    0.014613678 1560984 1210409        D
## 24    MO    0.120481707 1119554 1463586        R
## 25    MS    0.006945186  411398  703635        R
## 26    MT    0.394676283  204939  255468        R
## 27    NC    0.214165756 2218357 2137167        D
## 28    ND    0.368287790  131869  173433        R
## 29    NE    0.215171226  276239  496276        R
## 30    NH    0.204255606  340925  311636        D
## 31    NJ    0.171983824 1794407 1430386        D
## 32    NM    0.091960755  422189  323269        D
## 33    NV    0.064875501  453310  457239        R
## 34    NY    0.077700175 4128031 2245236        D
## 35    OH    0.230828775 2412451 2620251        R
## 36    OK    0.163223687  410324  856872        R
## 37    OR    0.151947354  949660  687839        D
## 38    PA    0.239204835 2793538 2710070        D
## 39    RI    0.334446368  232679  161926        D
## 40    SC    0.212567357  742805 1026129        R
## 41    SD    0.351009465  153789  207640        R
## 42    TN    0.023969590  796513 1369562        R
## 43    TX    0.050707131 2949900 4429270        R
## 44    UT    0.053307799  324309  647873        R
## 45    VA    0.213223247 1806025 1876761        R
## 46    VT    0.013032386  208600   67543        D
## 47    WA    0.032501116 1636726 1369540        D
## 48    WI    0.146504274 1445015 1401995        D
## 49    WV    0.010777199  257101  384253        R
## 50    WY    0.048610103   57573  166452        R

The summary stats for the two efficiency gaps show that the two parties have roughly the same distributions. The mean for the Democratic efficiency gap is a just short of the Republican, but the median efficiency gap for Dems is higher. The Republican efficiency gap, however, is skewed higher given three states where the efficiency gap exceeds 0.35. (Intepretation: roughly one-third of the seats in those states are misapportioned towards Republicans).

Sampling - first create simulated results

sim <- data.frame(a=1:99,b=99:1)
sim$wasted.b <- ifelse(sim$b>=51,sim$b-51,sim$b)
sim$wasted.a <- ifelse(sim$a>=51,sim$a-51,sim$a)
sim$margin <- abs(sim$a-sim$b)
sim$vote.ratio <- ifelse(sim$a<sim$b,sim$a/sim$b,sim$b/sim$a)
sim$efficiency.gap <- abs(sim$wasted.a-sim$wasted.b)/100
# split at 0.33 and 0.93
packed <- sim[sim$vote.ratio<0.33,]
cracked <- sim[sim$vote.ratio>0.33 & sim$vote.ratio<0.93,]
competitive <- sim[sim$vote.ratio>0.93,]
f1 <- lm(efficiency.gap~vote.ratio,packed)
f2 <- lm(efficiency.gap~vote.ratio,cracked)
f3 <- lm(efficiency.gap~vote.ratio,competitive)

The linear regression fits we get for this model gives us the piecewise function:

\[Vote\:Ratio = VR\] \[ Efficiency\:Gap = \begin{cases} 0.467 - 1.51 \times VR, & VR < 0.33 \\ -0.224 + 0.782 \times VR, & 0.33 \leq VR \leq 0.93 \\ 0.510 - 0.510 \times VR, & 0.93 < VR \leq 1 \end{cases} \]

# efficiency gap by district
foo <- dcast(districtParty,state + district + totalVote ~ parties,value.var="wastedVote",fill=0)
foo$efficiency.gap <- abs(foo$Democratic-foo$Republican)/foo$totalVote
foo <- foo[,c("state","district","totalVote","Republican","Democratic","efficiency.gap")]
colnames(foo)[4:5] <- c("w.votes.R","w.votes.D")
bar <- dcast(districtParty,state + district ~ parties,value.var="votes",fill=0)
bar <- bar[,c("state","district","Republican","Democratic")]
colnames(bar)[3:4] <- c("votes.R","votes.D")
bar$vote.ratio <- ifelse(bar$votes.D<bar$votes.R,bar$votes.D/bar$votes.R,bar$votes.R/bar$votes.D)
foo <- join(foo,bar,by=c("state","district"),type="left")
foo$majority <- ifelse(foo$votes.R>foo$votes.D,"R","D")
foo$margin <- (abs(foo$votes.R-foo$votes.D)/foo$totalVote)*100
e2 <- aggregate(efficiency.gap~state,foo,mean) # agg. mean efficiency gap by state based on all districts
colnames(e2)[2] <- "mean.efficiency.gap"
twoPartyModel <- join(twoPartyModel,e2,by="state",type="left")

ggplot(sim) + geom_point(aes(x=margin,y=efficiency.gap))

ggplot(sim) + geom_point(aes(x=vote.ratio,y=efficiency.gap)) # interesting piece-wise function

ggplot() + 
  geom_point(data=sim, aes(x=vote.ratio,y=efficiency.gap)) +
  geom_point(data=foo, aes(x=vote.ratio,y=efficiency.gap,color=majority)) +
  scale_colour_manual(values=c("blue","red")) # +

 # geom_point(data=twoPartyModel, aes(x=voteratio,y=mean.efficiency.gap,color=majority)) 
sampleState <- function(stateAbbrev){
  record <- subset(twoPartyModel,state==stateAbbrev)
  margin <- record["marg.victory"]
  s <- as.numeric(record["seats"])
  # create vector with "D","R",and "I" each repeated for number of votes in state
  u <- c(rep("D",record["d.votes"]),rep("R",record["r.votes"]),
                          rep("I",record["total.votes"]-record["d.votes"]-record["r.votes"]))
  # randomize
  u <- sample(u)
  # split
  chunk <- split(u, ceiling(seq_along(u)/(length(u)/12))) 
}

x = data.frame(num = 1:26, let = letters, LET = LETTERS) set.seed(10) derp <- split(x, sample(rep(1:2, 13)))

Here we’ll delve briefly into the results for third parties:

thirdParties <- subset(districtParty,districtParty$parties!="Democratic" & districtParty$parties!="Republican")
thirdParties$pctVote <- round(thirdParties$pctVote*100,1)
summary(thirdParties$pctVote)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   0.800   2.000   3.095   3.375  46.000

There are a remarkable number of independent candidates picked up more than 10% of the vote. California and Florida each have four district where third parties picked up a significant votes. The Green Party also picked up 16% of the vote in the Arizona 3rd and Liberatarian parties fared vary well in districts in AZ, KS, LA, and TX.

kable(subset(thirdParties,thirdParties$pctVote>10))
state district totalVote simpleMajority votes parties pctVote wastedVote win
26 AR 03 245660 122831 39318 Green 16.0 39318 0
54 AZ 07 127827 63914 23338 Libertarian 18.3 23338 0
85 CA 13 288582 144292 38146 No Party Preference 13.2 38146 0
103 CA 23 216003 108002 57842 No Party Preference 26.8 57842 0
116 CA 29 150281 75142 38994 No Party Preference 25.9 38994 0
122 CA 33 318520 159261 146660 No Party Preference 46.0 146660 0
181 CO 05 307237 153620 53318 Unaffiliated 17.4 53318 0
221 FL 04 315470 157736 75236 No Party Affiliation 23.8 75236 0
262 FL 20 244285 122144 29553 No Party Affiliation 12.1 29553 0
265 FL 21 284400 142201 63137 No Party Affiliation 22.2 63137 0
271 FL 25 200229 100116 48763 No Party Affiliation 24.4 48763 0
337 IL 02 297712 148857 40006 Independent 13.4 40006 0
411 KS 03 293762 146882 92675 Libertarian 31.5 92675 0
442 LA 04 249531 124766 61637 Libertarian 24.7 61637 0
445 LA 05 260216 130109 37486 No Party Affiliation 14.4 37486 0
447 LA 06 306713 153358 32185 Libertarian 10.5 32185 0
448 LA 06 306713 153358 30975 No Party Affiliation 10.1 30975 0
469 MA 07 252836 126419 41199 Independent 16.3 41199 0
630 MS 03 293322 146662 58605 Reform 20.0 58605 0
993 TN 06 241241 120622 34766 Independent 14.4 34766 0
1059 TX 17 179262 89632 35978 Libertarian 20.1 35978 0
1064 TX 19 192063 96032 28824 Libertarian 15.0 28824 0