The Mathematics of the Electoral College

E. Arthur Robinson, Jr.(with Daniel Ullman)

Dec 1, 2010

Because we had it last election, and it wasn’t changed.

Why do we have an Electoral College?

Because it’s in the Constitution.

Why did we have the Electoral College last election?

Because, in the 18th century: communication and transportation

were primitive; the US was vast and sparsely

populated; campaigning was regarded as

inappropriate; a public mandate was regarded as

dangerous.

Why did our founding parents devise an Electoral College system?

Are senators elected directly?

Yes, they are now. Not in the original Constitution. Were appointed by state legislatures. Changed by 17th Amendment (1913). Justice Scalia: This “mistake” started

a “decline in so-called states rights” (Nov. 13, 2010, Texas Tech. Law School).

Yes. Failure of anonymity. Not every voter has the same

degree of influence over the final decision, violating the principle of “one person, one vote”.

Other concerns: Focus on swing states; Discourages turnout.

Is there a problem with the Electoral College?

¾ of the states must ratify a Constitutional amendment.

Most states are small. Electoral college perceived to favor

small states. They are unlikely to ratify an

amendment that removes their “advantage”.

Why hasn’t the Electoral College been abolished?

The Electoral Map

The Election of 2008

The same picture, in Electoral units

The Election of 2008

2004 Electoral map

2000 Electoral map

When has Electoral College differed from “Popular Vote”?

1876: Rutherford B Hayes wins EC 185 to 184. Samuel J. Tilden won 51.5% of popular vote.

1888: Benjamin Harrison wins EC 201 to 200. Grover Cleveland wins plurality in popular vote.

2000: George W Bush wins EC 271 to 267. Al Gore wins majority of popular vote (Supreme Court gives Florida’s 25 votes to Bush).

National Popular Vote Interstate Compact (began 2007).

States agree to allocate their electoral votes according to national popular election winner.

Article II gives states right to appoint electors as they see fit.

Six states have joined. MD, NJ, IL, HW, WA, MA.

Takes effect when states with 270 votes join.

What’s wrong with “caucusing”?

Example: The Supreme Court (9 justices)

How 5 Justices can dominate the Court.

How 3 Justices can dominate the Court.

How 2 Justices can dominate the Court.

What’s wrong with “weighted voting”?

Example: The European Economic Community of 1958.

Votes: France 4, Germany 4, Italy 4, Belgium 2, The Netherlands 2, and Luxembourg 1.

12 votes out of 17 were needed to pass resolutions in the Council.

How do we measure voter “power”?

How important is your vote? When does your vote really matter?

How likely is it that your vote actually matters in the end?

(Not very.) What is the probability that a voter

in a state with population p casts a deciding vote?

Banzhaf power

Invented by John Banzhaf, now GW Law Professor in 1960’s.

Used to analyze Nassau County, NY Board of Supervisors.

Lawsuit on behalf of some citizens who believed they were under-represented.

Later applied analysis to Electoral College.

Banzhaf power

Assume not all voters have same “power”.

Collect voters who favor one candidate into a coalition.

Coalition is winning if it has the votes to elect its candidate.

Winning coalition member is critical if his/her vote is necessary to win.

European Economic Community of 1958. 12 votes to win.

Country Votes

France 4

Germany 4

Italy 4

Belgium 2

Netherlands 2

Luxembourg 1

Winning Coalitions

European Economic Community of 1958. 12 votes to win.

Country Votes Banzhaf Power

France 4 10

Germany 4 10

Italy 4 10

Belgium 2 6

Netherlands 2 6

Luxembourg 1 0

Senate 2001

Senate starts with 50 Democrats and 50 Republicans + 1 (VP Dick Cheney--Republican)

Jim Jeffords (R-Vt) becomes Indepandent

New count: 50 Democrats, 50 Republicans, 1 Independent

51 votes needed to pass bill.

Jim Jeffords’ Senate

Senate 2001

Party Votes Banzhaf Power

R 49+1 2

D 50 2

I 1 2