May 10, 2011

It is possible to win the US presidency with 21.99% of the vote

See my updated calculation here.

The insanity of the electoral college is well known, but I've never seen anyone go through and calculate the absolute most undemocratic result possible given the current US electoral setup.  What I did was take each state's population compared with its electoral votes, find the population per elector, and rank them by greatest over-representation.  Then, I added up electoral votes until I got past 270—as it turns out, 38 states + DC makes a pretty close 274.  (I imagine it would be possible to shave a few tenths off my percentage by playing with the totals, but this has to be pretty close.)  I assumed the winner got 50% + 1 votes in each of the winning states and no votes in the remaining states, giving the totals on the right.  [UPDATE: By the way, this is assuming 100% turnout!]

Now, this is clearly stupendously unlikely, but it's worth asking why it's worth keeping a system where this kind of a result is even possible.  Also, it's often repeated that it's possible to win only concentrating on the largest states, but below one can see that the most undemocratic states are usually very small.

PS: It's quite possible I made some mistake in there, I'd welcome someone double-checking my math.  OpenOffice was giving me fits when I was figuring this out.  Data from Wikipedia.

UPDATE: Yglesias adds on:
But even this is an overestimate since differential turnout is possible. You could win California with seven votes if only 13 people bothered to show up on election day.

Duly noted.  However, he adds the qualifier "two candidate" which I don't quite understand.  Clearly no matter the number of candidates, someone who still won the below states would still win the election.  More candidates, though, could lower the minimum vote needed to win these states, given that most states have a "winner take all" system.

I also recognize that Maine and Nebraska do not have that system, but so long as the congressional vote was distributed equally within each state the result would stand.  It's a reasonable assumption given our current ridiculous premises.

UPDATE II: Danny clarifies in comments that "two candidate" is to make clear that I'm only assuming two candidates.  (If you had ~308 million candidates, for example, one could win with less than 100 votes even with 100% turnout.)

UPDATE III: DOH! I knew I had a screwup in there. I mistakenly used the total US population for calculating the population percentage, forgetting that while all our various colonies (Guam, Puerto Rico, etc.) are included in the total population, they don't get counted in presidential elections (boy, speaking of unfairness...but that's another post).  Of course, this only strengthens my original point.

Here are the revised totals only counting the presidential voting electorate.

State Population Electors Population per elector Percentage of total

Wyoming 563626 3 187875 0.18%
EV total 274
Washington, D.C. 601723 3 200574 0.19%
Full percent 43.99%
Vermont 625741 3 208580 0.20%
Half percent 21.99%
North Dakota 672591 3 224197 0.22%
Remaining 56.01%
Alaska 710231 3 236744 0.23%

Rhode Island 1052567 4 263142 0.34%

South Dakota 814180 3 271393 0.26%
Winning percentage 21.99%
Delaware 900877 3 300292 0.29%

New Hampshire 1316470 4 329118 0.43%
Total population 308745538
Montana 989415 3 329805 0.32%

Maine 1328361 4 332090 0.43%

Hawaii 1360301 4 340075 0.44%

Nebraska 1826341 5 365268 0.59%

West Virginia 1852994 5 370599 0.60%

Idaho 1567582 4 391896 0.51%

New Mexico 2059179 5 411836 0.67%

Iowa 3046355 7 435194 0.99%

Kansas 2853118 6 475520 0.92%

Arkansas 2915918 6 485986 0.94%

Mississippi 2967297 6 494550 0.96%

Louisiana 4533372 9 503708 1.47%

Connecticut 3574097 7 510585 1.16%

Minnesota 5303925 10 530393 1.72%

Alabama 4779736 9 531082 1.55%

Oklahoma 3751351 7 535907 1.22%

Nevada 2700551 5 540110 0.87%

Kentucky 4339367 8 542421 1.41%

Missouri 5988927 11 544448 1.94%

Massachusetts 6547629 12 545636 2.12%

Oregon 3831074 7 547296 1.24%

Utah 2763885 5 552777 0.90%

Colorado 5029196 9 558800 1.63%

Wisconsin 5686986 10 568699 1.84%

Ohio 11536504 20 576825 3.74%

Tennessee 6346105 11 576919 2.06%

Maryland 5773552 10 577355 1.87%

South Carolina 4625364 8 578171 1.50%

Michigan 9883640 17 581391 3.20%

New Jersey 8791894 15 586126 2.85%

Indiana 6483802 11 589437 2.10%

Pennsylvania 12702379 21 604875 4.11%

Illinois 12830632 21 610982 4.16%

Washington 6724540 11 611322 2.18%

Virginia 8001024 13 615463 2.59%

New York 19378102 31 625100 6.28%

North Carolina 9535483 15 635699 3.09%

Arizona 6392017 10 639202 2.07%

Georgia 9687653 15 645844 3.14%

California 37253956 55 677345 12.07%

Florida 18801310 27 696345 6.09%

Texas 25145561 34 739575 8.14%


  1. I think the point of Matt's "two candidate" qualifier is to point out that this ridiculously low percentage of the vote doesn't involve assuming several viable candidates (like Woodrow Wilson winning the presidency with only 42% of the popular vote).

  2. That makes more sense. Yeah, thinking about it, you could posit an arbitrarily low vote percentage with an unlimited number of candidates. Thanks!

  3. By the way if all states had the same population by elector your calculation would give that 25% of the popular vote is sufficient to be elected. So equality between states is rather well respected. And sadly with ever system you can find that kind of problem (just look at the UK).

  4. It is true that one can't cobble together a winning group of states that aren't fairly close to the population per elector average. However, looking at individual states, there are some massive discrepancies. Each Wyomingian counts almost four times as much as a Texan, each Vermontian counts about 3.5 times as much as a Floridian, etc.

    I'd be interested to see such an analysis for the UK. Link?

  5. Well, Tony Blair won his three general election with an average of 40% of the popular vote and only 35% in 2005 (wiki numbers, since there are three main parties a rough similar calculation would gives a necessary number of 17% of the popular vote).

    My point is that yes there are discrepancies but they are small in the whole (23 instead of 25) and they are common to almost every parliamentary country (with a bit more volatility for you). The confusing thing is that you call your prime minister President but you can't really call the process undemocratic.

  6. Another scenario: The 11 most populous states contain 56% of the population of the United States. Under the current system, a candidate could win the Presidency by winning a mere 51% of the vote in just these 11 biggest states -- that is, a mere 26% of the nation's votes. Under a national popular vote a candidate would win the Presidency if 100% of the voters in the 11 biggest states voted for one candidate.

    The National Popular Vote bill would guarantee the Presidency to the candidate who receives the most popular votes in all 50 states (and DC).

    Every vote, everywhere, would be politically relevant and equal in presidential elections.

    The bill would take effect only when enacted by states possessing a majority of the electoral votes–that is, enough electoral votes to elect a President (270 of 538). Then, all the electoral votes from those states would be awarded to the presidential candidate who receives the most popular votes in all 50 states (and DC).

    The bill uses the power given to each state by the Founding Fathers in the Constitution to change how they award their electoral votes for president. Historically, virtually all of the major changes in the method of electing the President, including ending the requirement that only men who owned substantial property could vote and 48 current state-by-state winner-take-all laws, have come about by state legislative action.

    The bill has passed 31 state legislative chambers, in 21 small, medium-small, medium, and large states, including one house in AR, CT, DE, DC, ME, MI, NV, NM, NY, NC, and OR, and both houses in CA, CO, HI, IL, NJ, MD, MA ,RI, VT, and WA . The bill has been enacted by DC, HI, IL, NJ, MD, MA, VT, and WA. These 8 jurisdictions possess 77 electoral votes — 29% of the 270 necessary to bring the law into effect.

  7. Well, turns out it's 22% (my mistake), but I think the key difference there is that with Blair and parliamentary systems in general there were several different candidates getting a significant fraction of the vote. Here, though, the situation is that 78% of the population voted for the losing candidate. I don't think that result is possible in parliamentary systems.

  8. I see another mistake in there--I used total population, not eligible voters. I'm tired, but maybe I'll do a correction tomorrow. Still, I don't think it would change the totals by very much.

  9. Such a scenario assumes equal turnout in each state. This is not necessarily the case. For instance, the upper Midwest (Minnesota/Wisconsin particularly) tends to vote at very high rates (partly because of pro-voting laws such as early voting and same-day registration.)

    In fact, it is theoretically possible to win the US presidency with 10 or so votes - if in California/New York/Texas/Florida/etc., for some reason, only one person voted for the candidate in question, but nobody else even voted. Not very plausible though, of course.

  10. Yeah, I think that's the point Yglesias is making about differential turnout. I suppose the absolute minimum from a percentage standpoint would be to win the above states with one vote each, then have 100% turnout in the remaining large states.

  11. The electoral college is silly. That assertion is all I can add to this discussion.

    You are a big shot blogger now. I will be able to tell people I knew you before you were a star.

  12. maybe i'm missing something here, but all you'd need is one vote from the fewest possible states that give you 270, and the other candidate gets 0 in those states, and get 100% turnout in the rest of the states for the other candidate. the winner could lose the popular vote 10's of millions to one

  13. That's of course true, but my object here by assuming 100% turnout in every state was to see how much absurdity was baked into the electoral college cake, so to speak.

  14. "Also, it's often repeated that it's possible to win only concentrating on the largest states, but below one can see that the most undemocratic states are usually very small."

    How is it more "undemocratic" for 39 small states (plus DC) - totaling 267 electoral votes in 2008 numbers - to decide who should be President but 11 large states - totaling 271 in 2008 numbers - is not? Your logic here is suspect.

    That said, I like your analysis. It is interesting to dissect the statistics to see how things add up. Looking at the 2008 election return results, using the highest winning number of votes (regardless of candidate), the 11 largest states had a popular vote of 40,756,279, while the 39 smallest (plus DC) came in with only 33,676,881. If you took away New Jersey or North Carolina (both having 15 EVs) from the 11 largest states, the large states still would have won (38.6M to 35.8M).

    Loved the statistical analysis behind the article. Keep up the good work!

  15. Glad you liked the post!

    What I mean by "undemocratic" is saying those small states have a disproportionate number of electoral votes per capita. 190,000 people gets you an electoral vote in Wyoming while it takes 740,000 people in Texas. If "one person one vote" is a decent standard for a democratic election, then those small states are indeed undemocratic.

  16. If you are looking at the Electoral Votes alone, and not what derives the number of votes (# of Senators and # of Representatives), then yes. However, if you take out the two EV's from each state, the EV:population ratio balances out. So, it's actually quite democratic, since each state receives an # of EV's based on population and an equal number of EV's due to their states as members of the Union. (I know, I know ... it's not what you were looking at.) :)