With several prominent politicians calling for its elimination, the Electoral College is back in the news. It’s also – nudge, nudge – in my book!
I was wary of getting too political in a volume of math jokes, but I find it the E.C. such a peculiar and compelling mathematical object that I couldn’t help myself.
A highly abridged version of the chapter follows, and then some questions. (For more, check out the book!)
What is the Electoral College?
It’s how the President becomes President!
Each state gets a certain number of Electors (the bigger the state, the more Electors). It’s these Electors, officially, who pick the president.
How does it work in practice?
States can choose Electors however they like: roulette wheel, softball match, arm-wrestling tournament. Possibilities abound!
But as it is, almost all follow this all-or-nothing electoral approach:
- Hold a statewide popular vote.
- Choose Electors who all pledge to vote for the statewide winner.
Why was the Electoral College created?
Three reasons, more or less.
First, in a big country, long before high-speed communication, it seemed unlikely that far-flung voters could knowledgeably judge national candidates.
Second, the president needed independence. Making him accountable to the House could undercut the balance of powers; but direct election could promote demagoguery. Hence, a kind of one-time CEO search committee.
Third, there had already been delicate negotiations over legislative representation. Slave states got the 3/5 clause. Small states got the Senate. The Electoral College imported these compromises into the selection of presidents.
It’s arguable whether any of these reasons still apply today. Slavery is abolished; the all-or-nothing approach has eliminated small states’ advantage (see below); and mass communication has nationalized and democratized our politics (for better or worse).
So why do we still have the Electoral College?
Replacing it never felt urgent. From 1892 to 1996, it had no discernible effect on election results. And amending the Constitution is a long, hard road.
Who benefits under the Electoral College?
One tempting answer, given 2000 and 2016 (when the Democrat won the national popular vote, but lost the Electoral College), is “the Republican Party.”
But a closer look suggests that n = 2 is too small a sample.
Who does benefit, then? That’s a tricky (and rather delicious) math question!
In general, voters in “close” states (such as Nevada, Wisconsin, and Florida) wield extra power, at the expense of voters in states with a dominant party (such as Kansas, Massachusetts, Oklahoma, and Hawaii).
Arguments that the E.C. benefits a specific, stable group – e.g., rural voters, or voters from the Midwest – don’t tend to withstand scrutiny. Such an advantage may endure for a couple of elections, but in the long term, randomness seems to reign.
What about state size? It’s complicated. A Wyoming voter has a better chance of swinging her state’s outcome than a Texas voter does. But, thanks to all-or-nothing Elector apportionment, her state has a much worse chance of swinging the election has a whole. The result is a bit of a wash.
Why do people want to replace it?
You’d have to ask them – I’m just a math teacher!
Mathematically, it seems the Electoral College gives very similar results to a popular vote, with some deviations (caused by the all-or-nothing approach) that are effectively random.
How do reformers propose to replace it?
Twelve state legislatures have passed laws to this effect:
- We pledge to give all our Electors to the winner of the national popular vote.
- This law will only take effect when a critical mass of other states pass it, too.
If the critical mass of 270 electors is reached, then the country will have a de facto popular vote, without the need for a Constitutional amendment. This is known as the National Popular Vote Interstate Compact.
You’re a math teacher. Do you have some exercises for math students?
Why, sure! Here are two strings of problems.
ELECTORS PER CAPITA: WHAT DOES IT TELL US?
The formula for your state’s number of Electors is roughly this: Population/700,000 + 2, rounded to the nearest whole number. Assume that the winner within each state gets all of its Electors.
1. Compute the number of electors for Alaska (737,000 people), South Dakota (882,000 people), Mississippi (2,986,000 people), and Alabama (4,887,000 people).
2. Now, compute the number of electors per capita for Alaska, South Dakota, Mississippi, and Alabama.
3. Under this system, which sorts of states will have the most Electors per capita?
4. Which will have the fewest?
5. Who do you think is more powerful – voters in small states, voters in big ones, or does it not matter? Explain.
Let’s imagine the country were made of 2 states: Megastate, with a population of 1.4 million, and the State of Moe, with a single resident named Moe.
6. How many Electors does each state receive?
7. How many Electors per capita does each state have?
8. Whose vote has a better chance of swinging the election: Moe’s, or a voter’s in Megastate? Think carefully, and explain!
9. What does this two-state scenario tell us about the usefulness of “Electors per capita” as a measure of power?
10. What is another way we could measure a voter’s power?
SYSTEMS OF APPORTIONMENT: DO THEY MATTER?
Currently, 48 out of 50 states apportion their Electors on an all-or-nothing basis: the winner of the statewide vote gets all of the Electors.
Imagine if states switched to a proportional system, whereby if you win X% of the vote in a state, you get X% of the Electors (rounded to the nearest whole number).
1. Suppose that Minnesota votes 68% for A, 30% for B, and 2% for C. How should it apportion its 10 electors? Explain.
2. Suppose that Minnesota votes 53% for A, 44% for B, and 3% for C. How should it apportion its 10 electors? Explain.
3. How would the effect of this change be different for big states like California (with 55 electors) than for small states like Vermont (with 3 electors)?
4. Imagine going to Hawaii (which usually votes Democrat) and asking a Democrat and a Republican whether they support this change. What do you think they would say, and why?
Imagine if states switched to a district-by-district system. For example, if a state has 5 electors, it breaks its voters into 5 districts, and assigns an elector to the winner of each.
5. Suppose that in Massachusetts, this has no effect on the electors. What does that tell us about Massachusetts? Be specific.
6. Suppose that in New Hampshire, this has a big effect: instead of winning all 4 electors, the Democrat now wins only 2. What does this tell us about New Hampshire? Be specific.
7. Suppose a Republican and a Democrat in New Hampshire are each asked to divide the state into districts. Do you think they’d make similar divisions? Why or why not?