Electoral College Optimization

The US Constitution establishes an indirect system to elect the president and vice president. People elect a college (a group) of electors that then elects the president. This used to be a non-issue and non-event for ages up until in November of 2000 the election was so close in Florida that it required waiting for a few weeks and a Supreme Court decision to decide the winner. Another eventful election happened in 2016 (sans the Supreme Court intervention).

The map shows the 2016 election result by state; in blue, states won by the Democratic candidate, and in red, states won by the Republican[1].

The system

Very briefly and high level: electors are assigned to states, one for each senator and one for each representative. Washington DC, which is not a state, gets 3 electors. There are in total 538 electors and a ticket needs a simple majority of 270 votes to win.

The problem

Most states (all but two, Nebraska and Maine [2]) have chosen to assign all electors from the state to the ticket with the most votes. This is known as a winner-take-all (WTA) system.

Since every state gets a number of representatives proportional to its population but a fixed number of 2 senators, very small states get a disproportionately high number of electors relative to their population. The extreme cases: California gets an elector for every 670,000 people and Wyoming gets one per 180,000 people. So, yes, a Wyomingite (yes, a voter in Wyoming, and yes I looked up that one) carries almost 4 times the value of a Californian voter.

The opportunity

Given all of the above, one can quickly realize that it is possible to get enough electors into the college without needing to win the “popular vote”. As mentioned this effectively happened in two of the last five presidential elections. One could take this realization further and try to win the electoral college with the lowest possible number of votes. I will explore this further.

Assumptions

I am doing this for fun and to maybe make more evident how much it is wrong with this, so I am making some simplifying assumptions:

• all states are WTA states (sorry Nebraska and Maine, you are doing the right thing though, or close to it)
• I am using population and votes indistinctly. So I am assuming the proportion of the population, registered voters, and voters are about the same across states (it is complicated because electors are assigned to states according to the population but only actual voters define the WTA)

A simplistic approach

Very simply sorting the states ascending on their people-to-elector ratio (column 4) from Wyoming to California we get[3]:

(The table can be sorted by any column and the whole table will be shown by selecting “All” from the dropdown)

Taking the states in this order I start with Wyoming and I get 3 electors from a state with 563,626 people and I keep going down. Next is DC with another 3 electors and 601,723 people so a candidate getting those two states would get 6 electors from a population of 563,626+601,723=1,165,349. We keep adding electors and people until we get the needed 270 electors. We get to 271 electors by winning the top 40 states, the last one being Georgia with its 16 electors and 9,687,653 people. Yes, winning 40 states sounds like a lot but those 40 states are home to only 134,885,053 people, a mere 43% of the population! A candidate could win the electoral college by strategically losing the popular vote 43 to 57…

Shortcomings of the simplistic approach

Something to note is that in this case, the 40th state got us to 271 electors when we really needed 270 to secure a win (a very tight win). So we can wonder whether it is possible to get a better set of states that add up to 270 electors but fewer than 134,885,053 electors. One way to achieve this is to find a state with one fewer elector than Georgia (picking on Georgia only because it was the last state to squeeze in) but also at least one fewer resident.

And there is at least one such state: North Carolina, with 15 electors and 9,535,483 residents, 152,170 fewer people than Georgia. So we could replace Georgia with North Carolina and get a “better solution”: a set of states with fewer people that still let you win the electoral college.

Future work

In reality, there could be many other sets of states that also yield 270 electors and also are better than our simplistic solution. To find them and, more importantly, to find the best overall solution we should model this problem in mathematical form and formulate it as an optimization problem to be solved with mathematical programming.

I will do just that in a future post under the electoralcollege tag.

PS I noticed that the solution involves winning 40! states, another question to ask would be to see what the smallest number of states needed to win to get to 270 electors really is (guessing… 12 states?). What are other possible questions to ask?

PS2 I am using this post to learn how to add interactive tables to WordPress, I don’t like how pasted Excel tables look like. I am using TablePress. Also learning how to add maps, using SimpleMaps for this. Any better options?

Footnotes

[1] Interestingly enough, the colors were originally the opposite (red for Democrats and blue for Republicans, in the 19th century) and they remained like that for a long time until probably the mentioned election in 2000 (incredibly recent!) when all TV networks finally used the now accepted code of red for Republicans and blue for Democrats.

[2] Nebraska and Maine assign the two electors they get for their two senators as WTA and the electors they get for their representatives are voted at the representative district level. In 2016 Democrats won the 2 WTA electors in Maine but they split with Republicans for the 2 district-level electors, so Democrats won Maine 3 to 1.

[3] Change the column display o show all data, sort by the last column, and go down the table adding up the electors: with the first state you have 3, then with two 6, etc. When you get to at least 270 you stop and those are the states that allow you to win with the least population.

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