The Electoral College & Gerrymandering

A Mathematical Exploration of Issues of Representation in the United States

Callie Gardella Overview

1. How is representation determined? 2. What is Gerrymandering? 3. What is the Electoral College?

Guiding Question: Is there a mathematical method that could be used to address issues of representation and bias in determining apportionment and redistricting? The Federal Legislative Branch

Senate: 100 seats, 2 per state

House of Representatives: 435 seats, assigned according to population Apportionment

Dividing the 435 seats of congress between the 50 states

Occurs every ten years, coinciding with the Census

Rules: 1. Every state gets at least 1 representative 2. The Census must provide the state populations within 9 months of collection 3. The President must inform Congress of these numbers within one week of their next session 4. Congress has 15 days to determine the number of representatives per state Historical Methods

The Hamilton/Vinton Method: Assign each surplus seat: to the state with the highest fractional component

The Jefferson Method: Assign each surplus seat to the state with the largest critical divisor

The Webster Method: Round up if the fractional component is ≥.5, round down otherwise Current Mathematical Method

Huntington-Hill Method, used since 1941 mathematically determined priority listing of states

Priority calculated by dividing the population of each state by the geometric mean of its current and next seats P - represents a state's total population n - represents the current number of seats per state+1 Redistricting

Traditional Criteria to be met: Compactness Contiguity Preservation of counties and other political subdivisions Preservation of communities of interest Preservation of cores of prior districts Avoiding pairing incumbents Gerrymandering

Manipulating district lines to favor one particular group Examples

Arizona

Illinois Shortest Split Line Method

ShortestSplitLine( State, N ){ If N=1 then output entire state as the district; A = floor(N/2); B = ceiling(N/2); find shortest splitline resulting in A:B pop ratio; Use it to split the state into the two HemiStates SA and SB; ShortestSplitLine( SB, B ); ShortestSplitLine( SA, A ); } 15 people 5 districts 15 people 5 districts Example: Virginia

What is the Electoral College?

Established in the U.S. Constitution the formal body which elects the President and Vice President

States get electors according to their number of House and Senate Seats

DC gets 3 electors Who do the Electors vote for?

Depends on the state

Most states are Winner-Take-All for whoever gets the plurality

Maine and Nebraska use a district system: 2 electors vote for the state’s popular plurality 1 elector votes for each congressional district’s popular plurality Faithless electors Mathematical Issues

Least Represented: Texas (755,312/EC vote)

Most Represented: Wyoming (192,579/EC vote) How to Win the Presidency with a Minority of the Votes Year Popular Vote Electoral College

1876 Samuel Tilden Rutherford B. Hayes

1888 Grover Cleveland Benjamin Harrison

2000 Al Gore George W. Bush 2016 Hillary Clinton Donald J. Trump

Error: 4/58= 7% Videos for More Information https://www.youtube.com/playlist?list=PL3-mmEh5T5EvrU8OqOkc4jp SlolWNdQUm

Spreadsheet https://www.cgpgrey.com/blog/the-sneaky-plan-to-subvert-the-electo ral-college Sources https://www.census.gov/topics/public-sector/congressional-apportionment/about/computing.html https://www.visitthecapitol.gov/sites/default/files/documents/resources-and-activities/CVC_HS_Activ itySheets_CongApportionment.pdf https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1084767/pdf/pnas01901-0017.pdf https://www.census.gov/history/www/reference/apportionment/methods_of_apportionment.html https://history.house.gov/Institution/Electoral-College/Electoral-College/ http://www.math.wisc.edu/~robbin/141dir/propp/COMAP/Guidefor1stTimeInstructors/o_FAPP07_F TI_14.pdf https://faculty.math.illinois.edu/~cliu32/JeffersonMethod.pdf https://journals.sagepub.com/doi/pdf/10.1177/1536867X1201200303 https://www.wired.com/2017/04/gerrymandering-illegal-mathematicians-can-prove/ https://www.cgpgrey.com/blog/gerrymandering-explained.html https://rangevoting.org/SplitLR.html https://2020census.gov/en/important-dates.html https://www.ncsl.org/research/redistricting/redistricting-criteria.aspx https://redistricting.lls.edu/who.php https://www.270towin.com/historical-presidential-elections/