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In many counties in certain states, there are vastly more votes for the Republican candidate in precincts where more people voted. In these same states there are few or no counties where there are more votes for the Democratic candidate in precincts where more people voted.

We find this extremely perplexing.

Our analysis looks at the relationship between the number of votes cast at each polling place in a given county and the percentage of votes cast for a given candidate at that polling place.

There is usually no clear demographic reason for larger precincts in urban and suburban areas to be strongly associated with any political preference.

The term “precinct” refers to the geographical region that is assigned to an individual polling place. Unlike congressional districts, the size and political leaning of voting precincts is simply a function of the density and demographics of the surrounding population. The political leaning of a given voting precinct should not be strongly related to its size, except for the observation that very small precincts tend to be located in rural areas, which historically have voted more conservatively.

In general, as the vote count is tallied for a given county starting with the smallest precincts and moving to the larger ones, we would expect the percent of votes for a given candidate to quickly stabilize at or near the final outcome, unless for some reason there is a strong bias toward one candidate in larger precincts. A more thorough explanation of the reason for this is here.

We see these patterns of increasing Republican votes with increasing precinct size most strongly at the county level. When all the counties in a state are aggregated together, these strong patterns often cancel each other out, resulting in smoother or flatter lines. Because of this our analysis examines election results county by county.

We invented a very simple metric – deltaM* – to describe how “flat” one of these sets of lines is. This estimates numerically the extent to which there is a change in vote margin as we move from adding only smaller precincts to adding larger precincts to the totals. We arrive at this margin by first identifying the median precinct size – where half the precincts are smaller and half the precincts are larger. We then add up the votes for the two candidates in all of the precincts below and including the median to see how different the vote outcome would be if we stopped counting votes after we added only the results from the smaller precincts. If the outcome for all precincts compared to that for only the smaller half of the precincts favors the Republican candidate, deltaM is positive. If the final outcome compared to the “smaller precincts only” outcome favors the Democratic candidate, deltaM is negative.

DeltaM represents the distance between the vote lines at the far right of the graph compared to the distance between the lines at the middle of the graph.

County by County
Santa Clara County CA displays an expected pattern of cumulative vote percent as precincts are added by size:

Notice that at the far left of the graph there is a bit of “noise”, but that the line quickly goes flat as you move toward the right. This means that precincts of all sizes are scattered fairly evenly about this large and diverse county. This is what one would generally expect to see for most large counties.

In the graph above, deltaM is zero. There is no difference in election outcome if you count only the smaller precincts.


The graph below displays a very different pattern – one that we find hard to explain demographically:

Milwaukee CVT Graph - deltaMLink to interactive graph

In Milwaukee County, WI, the percent of Republican votes rose from below 20% for precincts at or below the median size, to over 30% for all precincts at the far right of the graph, a change of 10%. The percent of Democratic votes fell a corresponding 10% from the median to the far right of the graph, making our deltaM (change in margin) 20.2%.

Notice that the average percent of Republican votes for precincts with fewer than 953 voters is just over 20%, while for precincts with fewer than 1151 voters the average percent is nearly 25%. Why would so many more Republicans cast their votes at precincts at the larger end of that very narrow range?

Also notice that the red line starts its upward slope far to the left of the center of the graph. In fact the line begins to climb upward when the Republican percent of the vote is around 15%. This indicates that our deltaM calculation is conservative. As many as 30% of the votes in this county were affected by this rising line.

To estimate the number of votes affected by a non-zero deltaM we multiply deltaM by the total number of ballots cast in the county. You can see the number of votes cast above the deltaM number in the top left corner of the graphs. In the case of Milwaukee county when we multiply the 20.2% deltaM margin by the 428650 votes cast, we conservatively estimate 85,000 votes were cast that differ from what would be expected had the patterns of votes cast in larger precincts been consistent with the patterns in smaller precincts. We will refer to this number as “deltaMxV”.

In other words, if the lines had become flat at the center of the graph, as the Law of Large Numbers predicts they should, the Republican candidate would have had a margin of at least 85,000 votes(deltaMxV) less than the reported results indicated, in this county alone.

This recurring pattern of rising red lines that do not conform to what the Law of Large Numbers would lead us to expect, has become known as the “red shift” among statisticians and election analysts.**

State by State
If you look at just one county it is difficult to definitively prove that a “red shift” is not simply due to some kind of odd demographic distribution with respect to precinct size. This would mean that where there is a notable red shift, as in Milwaukee County WI, most of the larger precincts are found in heavily Republican areas. This seems unlikely, but is not necessarily impossible.

For this reason, we look at all the large counties in a state to get a clearer sense of whether a red shift like the one we see above is simply a statistical fluke of some sort.

If these red shifts were statistical flukes, one would expect them to be canceled by corresponding “blue shifts” if you look at all the counties in a large state.

Thus for each race in each state we calculate the deltaM for each county that has more than 50 precincts/polling places. We then multiply the deltaM by the number of votes cast in each county to estimate the votes associated with the lines’ deviations from horizontal to get deltaMxV*.

In order to identify the proportion of votes at the state level that are associated with this phenomenon, we then sum all of the deltaMxV’s for all eligible counties in the states. We will call this statewide sum “deltaMxV_S.” A positive deltaMxV_S represents a statewide increases in Republican votes and a negative deltaMxV_S represents a statewide decrease in Republican votes. We can then divide deltaMxV_S by the total number of votes cast in the state to see what proportion (deltaM_S) of the state’s total votes have been affected by this phenomenon.

In the tabs for each state under the “Elections by State” tab you will see a table displaying the deltaM for each of its counties – simply click the plus sign to display the table. The colors indicate whether that county voted Republican or Democrat, and the intensity of the colors indicate how strongly the vote favored the winning candidate.

If the shifts were simply statistical flukes, one would expect “red shifts” to be canceled by corresponding “blue shifts” in other counties in the state. This would cause the overall deltaM for the state to stabilize near zero for each race.
Indeed we do see a near zero deltaM in a few states.

The table below shows the overall deltaM_S and deltaMxV_S values for the races within states we have analyzed so far.

Of the six races we have analyzed, there are four strongly positive statewide deltaM_S values (favoring Republicans). All four of these are in “swing states”.

Click any column header to sort the table below.

2016 - Presidential Races

StateRaceDatedeltaMdeltaMxV
CAPresident2016-11-08-0.3%-38,549
COPresident2016-11-081.5%42,136
MIPresident2016-11-086.3%297,421
NCPresident2016-11-084.8%75,589
OHPresident2016-11-087.5%389,799
PAPresident2016-11-088.7%526,749
WAPresident2016-11-08-1.7%-51,423
WIPresident2016-11-085.2%148,967

2016 - Swing State Counties with Delta M greater than 5%

StateCountyRaceDatedeltaMdeltaMxV
WIRACINEPresident2016-11-0838%35,300
OHCUYAHOGAPresident2016-11-0824.4%141,777
NCFORSYTHPresident2016-11-0823%14,096
MIMUSKEGONPresident2016-11-0822.1%17,123
PALANCASTERPresident2016-11-0821.5%52,052
NCORANGEPresident2016-11-0821.4%3,993
WIKENOSHAPresident2016-11-0821.4%15,994
PALEHIGHPresident2016-11-0820.4%32,837
WIMILWAUKEEPresident2016-11-0820.2%86,383
MIGENESEEPresident2016-11-0819.9%38,823
PABEAVERPresident2016-11-0819.1%15,994
PAMERCERPresident2016-11-0818.6%9,724
PABERKSPresident2016-11-0818.4%33,657
PAERIEPresident2016-11-0818.3%22,602
PAALLEGHENYPresident2016-11-0816.5%106,962
PAYORKPresident2016-11-0815.3%29,368
OHMONTGOMERYPresident2016-11-0814.9%36,307
OHLUCASPresident2016-11-0814.9%27,662
OHLORAINPresident2016-11-0814.3%19,103
OHCLARKPresident2016-11-0814.3%8,378
NCMECKLENBURGPresident2016-11-0814.1%22,796
NCBUNCOMBEPresident2016-11-0814%4,537
NCDURHAMPresident2016-11-0813%3,954
OHSTARKPresident2016-11-0812.8%21,305
PADELAWAREPresident2016-11-0812.8%38,090
NCGASTONPresident2016-11-0812.7%3,351
MIBERRIENPresident2016-11-0812.6%8,985
MICALHOUNPresident2016-11-0812.5%7,325
PABLAIRPresident2016-11-0812.4%6,758
MIKENTPresident2016-11-0812.3%37,376
PANORTHAMPTONPresident2016-11-0812.1%17,420
PAMONTGOMERYPresident2016-11-0811.1%47,930
OHALLENPresident2016-11-0810.9%4,751
WIBROWNPresident2016-11-0810.2%12,835
NCNEW HANOVERPresident2016-11-0810.1%3,609
OHSUMMITPresident2016-11-0810%24,612
WISHEBOYGANPresident2016-11-0810%5,837
MIWAYNE (OTHER)President2016-11-0810%51,199
OHRICHLANDPresident2016-11-089.4%4,963
MIOAKLANDPresident2016-11-089.4%62,189
OHPORTAGEPresident2016-11-089.3%6,700
OHBUTLERPresident2016-11-089%14,803
NCCABARRUSPresident2016-11-088.9%3,575
NCGUILFORDPresident2016-11-088.6%6,779
WIWAUKESHAPresident2016-11-088.5%19,767
MIJACKSONPresident2016-11-088.4%5,826
PAFAYETTEPresident2016-11-088.3%4,448
OHHAMILTONPresident2016-11-088.3%32,007
OHLAWRENCEPresident2016-11-088.2%2,117
MIOTTAWAPresident2016-11-088.2%11,480
NCUNIONPresident2016-11-088.2%2,500
PAWASHINGTONPresident2016-11-088.2%8,312
OHMAHONINGPresident2016-11-087.9%8,773
OHSANDUSKYPresident2016-11-087.5%1,965
PACAMBRIAPresident2016-11-087.4%4,690
MIWASHTENAWPresident2016-11-087.1%13,295
PACENTREPresident2016-11-087.1%5,372
OHSCIOTOPresident2016-11-086.6%1,947
WILA CROSSEPresident2016-11-086.6%4,069
MIKALAMAZOOPresident2016-11-086.4%7,992
PACHESTERPresident2016-11-086.3%16,984
OHJEFFERSONPresident2016-11-086.2%1,894
PAARMSTRONGPresident2016-11-086.1%1,914
OHLAKEPresident2016-11-086%6,564
MIST. CLAIRPresident2016-11-085.8%4,535
NCWAKEPresident2016-11-085.8%11,256
PAWESTMORELANDPresident2016-11-085.2%9,519
OHTUSCARAWASPresident2016-11-085.2%2,023
PABUTLERPresident2016-11-085.1%4,920
OHROSSPresident2016-11-085%1,457
OHWAYNEPresident2016-11-085%2,375
OHGEAUGAPresident2016-11-08-5.7%-2,743
PACLEARFIELDPresident2016-11-08-6%-2,055
PAHUNTINGDONPresident2016-11-08-6.7%-1,312
WIOUTAGAMIEPresident2016-11-08-7.7%-6,961
NCCUMBERLANDPresident2016-11-08-9%-3,760
PAINDIANAPresident2016-11-08-10.3%-3,440
WIMARATHONPresident2016-11-08-10.5%-6,615
WIDODGEPresident2016-11-08-11.2%-4,746
WIGRANTPresident2016-11-08-12.1%-2,870

2016 - Non-Swing State Counties with Delta M greater than 5%

StateCountyRaceDatedeltaMdeltaMxV
WAKITTITASPresident2016-11-0822.5%4,256
COPUEBLOPresident2016-11-0817.4%13,477
CAFRESNOPresident2016-11-0812.3%32,425
CAMADERAPresident2016-11-0811.2%4,542
CALASSENPresident2016-11-088.3%809
CAKERNPresident2016-11-087%15,922
WASTEVENSPresident2016-11-086.8%1,539
COEL PASOPresident2016-11-085.4%16,848
CANEVADAPresident2016-11-08-5%-2,473
WAWHATCOMPresident2016-11-08-5%-5,491
WAGRAYS HARBORPresident2016-11-08-5.4%-1,487
CASAN JOAQUINPresident2016-11-08-5.4%-11,383
CANAPAPresident2016-11-08-5.5%-3,098
CATUOLUMNEPresident2016-11-08-5.6%-1,330
COMESAPresident2016-11-08-6.1%-4,554
CASANTA CRUZPresident2016-11-08-6.3%-7,384
CAPLACERPresident2016-11-08-6.3%-10,691
WASKAGITPresident2016-11-08-6.4%-3,562
CASAN DIEGOPresident2016-11-08-6.7%-81,072
COADAMSPresident2016-11-08-7.6%-14,451
WAPIERCEPresident2016-11-08-8%-27,565
CASONOMAPresident2016-11-08-9%-18,894
CABUTTEPresident2016-11-08-9.5%-8,203
WAFRANKLINPresident2016-11-08-9.5%-2,253
CASUTTERPresident2016-11-08-10.3%-3,231
CASISKIYOUPresident2016-11-08-12.5%-2,314
WAWHITMANPresident2016-11-08-17.6%-3,038
CASAN BENITOPresident2016-11-08-17.9%-3,634
CAYOLOPresident2016-11-08-19.5%-14,438
CAMERCEDPresident2016-11-08-20%-13,226
CASOLANOPresident2016-11-08-20.5%-31,664
CAIMPERIALPresident2016-11-08-46.5%-19,487

 


 

* Acknowledgments
Our deltaM and deltaMxV metrics were developed with much guidance and feedback from Dr. Laura Little and Dr. Tracy Simpson of the University of Washington.

** References
How Trustworthy are Electronic Voting Systems in the US? (Beth Clarkson)
Republican Primary Election 2012 Results – Amazing Statistical Anomalies