USA election system: How much percent of popular votes does it take to win presidency?

Every majority voting system is characterized by the fact that a candidate does not necessarily need the majority of votes. For example, the most important element of the presidential election in the USA is the United States Electoral College formed by 538 electors in total. Every state has got its own amount of electors depending on its number of inhabitants. If a candidate obtains a majority in a particular state all electors belonging to it will vote for him (winner-takes-all rule). Only two states, Nebraska and Maine, do not follow the winner-takes-all rule and prefer proportional voting. The candidate who manages to reach 270 electoral votes wins the election and becomes president.

Motivated by the victory of Donald Trump in the 2016 presidential election this article aims to calculate the theoretical minimum number of votes a single candidate must get in order to take the white house - exploiting all rules of the majority voting system and the winner-takes-all rule. For that we look at the following table which depicts the distribution of electors compared to the actual population for each state (Source: Wikipedia) sorted by inhabitants per elector.

StateElectors(cumulative)Inhabitants (k)%Inhabitants per elector%
Wyoming 33563.6250.183%187.8750.061%
Washington, D.C. 36601.7220.195%200.5740.065%
Vermont 39625.740.203%208.580.068%
North Dakota 312672.5910.218%224.1970.073%
Alaska 315710.2320.230%236.7440.077%
Rhode Island 4191052.5680.341%263.1420.085%
South Dakota 322814.1790.264%271.3930.088%
Delaware 325897.9330.291%299.3110.097%
New Hampshire 4291316.4720.426%329.1180.107%
Montana 332989.4150.320%329.8050.107%
Maine 4361328.360.430%332.090.108%
Hawaii 4401360.30.441%340.0750.110%
Nebraska 5451826.340.592%365.2680.118%
West Virginia 5501852.9950.600%370.5990.120%
Idaho 4541567.5840.508%391.8960.127%
New Mexico 5592059.180.667%411.8360.133%
Nevada 6652700.5520.875%450.0920.146%
Utah 6712763.8880.895%460.6480.149%
Kansas 6772853.120.924%475.520.154%
Arkansas 6832915.9160.944%485.9860.157%
Mississippi 6892967.30.961%494.550.160%
Iowa 6953046.3560.987%507.7260.164%
Connecticut 71023574.0951.158%510.5850.165%
South Carolina 91114625.3611.498%513.9290.166%
Minnesota 101215303.931.718%530.3930.172%
Alabama 91304779.7381.548%531.0820.172%
Oklahoma 71373751.3491.215%535.9070.174%
Kentucky 81454339.3681.405%542.4210.176%
Oregon 71523831.0721.241%547.2960.177%
Colorado 91615029.21.629%558.80.181%
Washington 121736724.5362.178%560.3780.182%
Louisiana 81814533.3761.468%566.6720.184%
Wisconsin 101915686.991.842%568.6990.184%
Tennessee 112026346.1092.055%576.9190.187%
Maryland 102125773.551.870%577.3550.187%
Arizona 112236392.0122.070%581.0920.188%
Indiana 112346483.8072.100%589.4370.191%
Massachusetts 112456547.6292.121%595.2390.193%
Missouri 102555988.931.940%598.8930.194%
Georgia 162719687.6483.138%605.4780.196%
Virginia 132848001.0192.591%615.4630.199%
Michigan 163009883.6483.201%617.7280.200%
New Jersey 143148791.8882.848%627.9920.203%
Pennsylvania 2033412702.384.114%635.1190.206%
North Carolina 153499535.4853.088%635.6990.206%
Ohio 1836711536.5063.737%640.9170.208%
Illinois 2038712830.644.156%641.5320.208%
Florida 2941618801.3096.090%648.3210.210%
Texas 3845425145.558.144%661.7250.214%
New York 2948319378.096.276%668.210.216%

It becomes immediately clear that the "inhabitants per elector" value (last two columns) is anything but constant and varies from state to state. For creating a worst case scenario we need to assume that the candidate reaches a majority in "few inhabitants per elector" states starting with "Wyoming" in the first row and following the table downwards until the cumulative number of electors (third column) passes 270 at "Georgia". By doing so and building our worst case scenario on this assumption we make sure that the votes casted by less people have more impact on the overall result. If there are exactly two candidates taking part in the election one of them needs exactly 50% of the votes for wining a state. So let's further assume that the minimal candidate wins all of the 39 states from "Wyoming" to "Georgia" just by passing the 50% mark very closely and therefore wins the White House. Then we can go through every mentioned state, add the votes for our worst case candidate together and divide it through the total US population which is 308.745.288 (Wikipedia).

The result represents the minimal percentage of popular votes a candidate must have to win presidency:


Note that this value depends on the current elector distribution as well as the current population statistics. Furthermore an equal voter participation in all states was assumed. Also the rule of proportional voting in Maine and Nebraska has been neglected but should not have much impact on the overall result.

The number 21.84% seems to be surprisingly low and, in fact, does make aware the riscs and possibilities of a majority voting system like in the US. But it has to be appointed that the worst case scenario created here is not very likely to happen. Historic data reveals that in almost every US election the president won not only with a majority of electoral but also with a majority of popular votes. And in the few cases he did win with a minority of popular votes it was very close.