After the 2012 presidential election, several allegations of vote fraud were leveled at US political parties.
This article cannot resolve these concerns; rather it demonstrates a statistical method to examine the likelihood that such an allegation is reasonable.
We take a pro forma approach to the polling statistics because any allegation could become a serious legal issue, needing more research and documentation than we can support.
Even so, this article is awash in references.
One Sample Concern: Wood County in Ohio with 108% Voter Registration
“Good News: Obama Won County in Ohio with 108% Voter Registration” raised one concern.
The important quote is “Mr. Obama won the majority of Wood County’s 108% of registered voters.”
That page also has a helpful comment by “Sluderlaw” about student voters from Bowling Green State University.
The above article links to “Ohio voter registration list nearly 500,000 smaller than in 2008: Statistical Snapshot.” Wood County’s statistics are near the bottom of the table.
There were 106,258 registered voters in 2012 versus a voting age population of 98,213 per the 2010 US Census.
- 106,258 / 98,213 = 108%, or an excess of 8%.
- 106,258 – 98,213 = 8,045 excess names.
This puzzle might best be addressed by auditing both the 2010 census and Ohio voter registration processes, but that’s outside the scope of this statistical methods article.
The “Good News” headline, above, implies that the 8,045 excess registrations led to President Obama’s victory over Mitt Romney in Wood County, Ohio.
The 2012 Presidential Election in Wood County Ohio
“Final Unofficial Results in Wood County Ohio” states that Obama received 31,596 votes or 50.9% of the vote; Romney 28,997 or 46.7%. The remaining 1,745 votes of 62,338 total were split among other candidates. Readers are welcome to provide a link to an official, final result when available.
- 50.9 – 46.7 = 4.2% margin for Obama.
- 31,596 Obama votes – 28,997 Romney votes = 2,599 lead for Obama.
A statistics-minded scientist must now test the “null hypothesis” that these results do not suggest vote fraud in Wood County.
The 108% Allegation in Wood County
The allegation, or alternate hypothesis, is that there were 8,045 excess names illegitimately registered to vote, leading to 8,045 excess votes cast for Obama in Wood County in the 2012 presidential election. Therefore removing 8,045 of Obama’s votes would correct the results.
- If you subtract those votes from the total votes, you get 54,293. (62,338 – 8,045 = 54,293)
- If you subtract those votes from Obama’s votes, you get 23,551. (31,596 – 8,045 = 23,551)
- Subtract Obama’s corrected total from Romney’s unchanged total, and you get a 5,446 vote lead for Romney. (28,997 - 23,551 = 5,446)
- Romney’s percentage of the corrected vote would be 53.4%. (28,997 / 54,293 = 53.4%)
- Obama’s percentage of the corrected vote would be 43.3$ (23,551 / 54,293 = 43.3%)
- Romney would have won the county with a corrected margin of victory of over 10%. (53.4 – 43.3 = 10.1%)