US Electoral Systems

An electoral system is a system of rules for conducting elections and determining the outcome


House of Representatives
One person, One vote
  • Congressional Apportionment
    • Each state is apportioned a number of House seats, approximately corresponding to its share of the aggregate population of the 50 states, with each state guaranteed at least one seat.  
  • One person, one vote
    • One person, one vote is the rule that every person’s vote should count the same, have the same weight, have the same voting power.
  • Wesberry v Sanders
    • In Wesberry v. Sanders, the Court ruled that one person, one vote, applied to congressional districts within a state, means that the district must be approximately equal in population.
Plurality System
  • Britannica 
    • Plurality system, electoral process in which the candidate who polls more votes than any other candidate is elected. Election by a plurality is the most common method of selecting candidates for public office.
    • Advantages of the plurality system are that it is easily understood by voters, provides a quick decision, and is more convenient and less costly to operate than other methods. The main argument against it is that in an election with more than two candidates, it may result in the election of a candidate who has received only a minority of the votes cast: for example, in a closely contested election with four candidates, the total required to win by a plurality could be as little as 25 percent of the total vote plus one.
Majority System
  • Britannica
    • Under the majority system, the party or candidate winning more than 50 percent of the vote in a constituency is awarded the contested seat. A difficulty in systems with the absolute-majority criterion is that it may not be satisfied in contests in which there are more than two candidates.
  • Runoff Systems
    • Runoff Election (Georgia, Louisiana)
    • Instant Runoff / Ranked Choice Voting (Maine)
Ranked Choice Voting
  • States using ranked choice voting Fairvote
    • Alaska:
      • Adopted in 2020 for all state and federal general elections and in the 2024 Presidential election. All uses except presidential election in “Top Four” form, with open ballot primary advancing 4 candidates to the general election with RCV. First being used in a special U.S. House election in August 2022, then all offices in November 2022.
    • Maine:
      • Adopted in 2016 and first used in 2018 for all state and federal primary elections and all general elections for Congress. Extended to apply to the general election for president beginning in 2020 and presidential primary elections beginning in 2024. Elections every even year.
  • Instant Runoff Voting Wiki
    • A voting method used in single-seat elections with more than two candidates. Instead of voting for a single candidate, voters rank candidates in order of preference. Ballots are counted for each elector’s top choice, losing candidates are eliminated, and ballots for losing candidates are redistributed until one candidate wins a majority of the votes.
  • How RCV works Fairvote
    • For a single office, like for a mayor or governor, RCV helps to elect a candidate who reflects a majority of voters in a single election even when several viable candidates are in the race. Ranked choice voting is a way to ensure elections are fair for all voters. It allows voters the option to rank candidates in order of preference: one, two, three, and so forth.
    • If your vote cannot help your top choice win, your vote counts for your next choice.
    • In races where voters select one winner, if a candidate receives more than half of the first choices, that candidate wins, just like in any other election. However, if there is no majority winner after counting first choices, the race is decided by an “instant runoff.” The candidate with the fewest votes is eliminated, and voters who picked that candidate as ‘number 1’ will have their votes count for their next choice. This process continues until there’s a majority winner or a candidate won with more than half of the vote.
Ranked Choice Voting in Alaska
  • Sarah Palin’s defeat in Alaska proves ranked-choice voting works  NYT Editorial
    • Ms. Peltola received 40 percent to Ms. Palin’s 31 percent in the first round of what’s also called an instant runoff process. Under that system, Ms. Palin’s fellow Republican Nick Begich III, who received 29 percent, was eliminated from contention, and his voters had their next choices tabulated. The result: Ms. Peltola beat Ms. Palin, 52 percent to 49 percent. The same three candidates will face off again in November for a full term.
  • How second-choice votes pushed a Democrat to victory in Alaska  NYT
Ranked Choice Voting in Maine

Bangor Daily News

Janet Mills won the Democratic gubernatorial nomination in a fourth and final round of retabulation.

Misrepresentation in the House of Representatives Brookings, Feb 22, 2017
  • Despite its name, the House of Representatives is not so representative.
  • As the chart to the right shows, the total vote differential between the two parties for elections to the House in 2016 was 1.2 percent. But the difference in the number of seats is 10.8 percent, giving a total of 21 extra seats to Republicans
“Unintentional Gerrymandering: Political Geography and Electoral Bias in Legislatures,” Jowei Chen and Jonathan Rodden, Quarterly Journal of Political Science, 2013
  • Abstract
    • While conventional wisdom holds that partisan bias in U.S. legislative elections results from intentional partisan and racial gerrymandering, we demonstrate that substantial bias can also emerge from patterns of human geography.
    • We show that in many states, Democrats are inefficiently concentrated in large cities and smaller industrial agglomerations such that they can expect to win fewer than 50% of the seats when they win 50% of the votes. To measure this ‘’unintentional gerrymandering,’’ we use automated districting simulations based on precinct-level 2000 presidential election results in several states.
    • Our results illustrate a strong relationship between the geographic concentration of Democratic voters and electoral bias favoring Republicans.
  • Paper in PDF form
Proportional Representation, by Contrast
  • “Systems of proportional representation have been adopted in many countries, including Belgium, Denmark, Finland, Greece, Hungary, Israel, Italy, Luxembourg, Norway, Russia, Spain, Sweden, and Switzerland.”
  • List of 87 countries using PR (Wiki)
  • How proportional representation would work in Texas
    • Texas has 36 representatives, each representing a congressional district.  Residents of a district vote for their representative.
    • Suppose instead everyone in Texas voted for a political party: Democratic, Republican, Libertarian,  Suppose the results are: Democratic 40%, Republicans 55%, Libertarian 5%. Then the allocation of seats would be: Democrats 14 seats, Republicans 20 seats, Libertarians 2 seats.
    • A benefit is no gerrymandering problems.
    • Proportional representation, electoral system that seeks to create a representative body that reflects the overall distribution of public support for each political party. Where majority or plurality systems effectively reward strong parties and penalize weak ones by providing the representation of a whole constituency to a single candidate who may have received fewer than half of the votes cast (as is the case, for example, in the United States), proportional representation ensures minority groups a measure of representation proportionate to their electoral support
    • Proportional representation characterizes electoral systems by which divisions in an electorate are reflected proportionately in the elected body. If n% of the electorate support a particular political party, then roughly n% of seats will be won by that party. The essence of such systems is that all votes contribute to the result: not just a plurality, or a bare majority, of them.

Senate representation is the result of a compromise at the Constitutional Convention

  • Constitutional Convention (1787)
    • Virginia (Large State) Plan
      • States should be represented in proportion to their populations
    • New Jersey (Small State) Plan
      • States should be represented by the same number of representatives
    • Grand (or Connecticut) Compromise
      • Virginia Plan for the House of Representatives
      • New Jersey Plan for the Senate
  • US Senate is Undemocratic, by Noah Feldman (Bloomberg Opinion Contributor, Felix Frankfurter Professor of Law at Harvard Law School)
    • The U.S. Senate is undemocratic. Small states get the same quantity of senators as large states. It’s often added that the ratio of population between the largest and the smallest states was “only” 12 to 1 when the Constitution was first adopted. Now it is 68 to 1. (California to Wyoming, in case you’re counting.)
    • The design of the Senate is anti-democratic. In fact, it’s so undemocratic that it would be unconstitutional if it were used by the states. After the Supreme Court adopted the one person one vote principle in the 1960s, states were obligated to apply a proportional method for representation of their own senatorial districts.
    • However, the equal protection clause of the Constitution doesn’t apply to the Senate itself. That’s because the design of the Senate is baked into the Constitution – and it was baked in long before the equal protection clause was even imagined.
    • The non-representative design was a source of outrage and profound frustration to James Madison, the primary architect of the Constitution, and the other representatives of large states like New York, Pennsylvania and Virginia.
    • To understand what happened, you have to start with Madison’s initial constitutional blueprint, which was introduced in the first few days of the convention and dubbed (appropriately enough) “the Virginia plan.” Madison called for two houses in the legislature. He assumed that both would be allocated proportionately according to the population of the states.
    • Almost from the beginning, small-state delegates hinted that they would not accept proportional representation in the Senate. Madison and the other large-state delegates didn’t take the objections seriously. 
    • Realizing that the large states weren’t willing to accept their (weak) arguments for equal Senate representation, the small states played the only card they had: They staged a walkout. Their position was simple. Unless they got equal representation in the Senate, they would ensure the failure of the convention, and damn the consequences.
    • Madison was beside himself. But there was nothing he could do, and he knew it.
    • Faced with small-state intransigence, Madison and the big states compromised. It was compromise or no Constitution. They didn’t like the arrangement that emerged. But they had to live with it.
  • “The Senate has a major skew towards rural voters,” Nate Silver (538, September 20, 2020)
    • At FiveThirtyEight, our favorite way to distinguish between urban and rural areas is based on using census tracts to estimate how many people live within a 5-mile radius of you. Based on this, we can break every person in the country down into four buckets:
      • Rural: Less than 25,000 people live within a 5-mile radius of you;
      • Exurban or small town: Between 25,000 and 100,000 people within a 5-mile radius;
      • Suburban or small city: Between 100,000 and 250,000 people within a 5-mile radius;
      • Urban core or large city: More than 250,000 people within a 5-mile radius.
    • As it happens, the overall U.S. population (including Washington D.C. and Puerto Rico) is split almost exactly evenly between these buckets: 25 percent rural, 23 percent exurban/small town, 27 percent subruban/small city, and 25 percent urban core/large city.
    • But what does representation look like in the Senate? Since each state has the same number of senators, this is simple to calculate. We can take the urban/rural breakdown for each state and average the 50 states together, as in the table below:
Image Credit 538
  • Because there are a lot of largely rural, low-population states, the average state — which reflects the composition of the Senate — has 35 percent of its population in rural areas and only 14 percent in urban core areas, even though the country as a whole — including dense, high-population states like New York, Texas and California — has about 25 percent of the population in each group. That’s a pretty serious skew. It means that the Senate, de facto, has two or three times as much rural representation as urban core representation … even though there are actually about an equal number of voters in each bucket nationwide.
President and Vice President

View Electoral College

One person, not necessarily one vote
One person one vote
  • A basic principle of democracy is one person, one vote, that every vote should have the same weight.   This means that voting districts should be the same same size.  As Chief Justice Earl Warren said in Reynolds v. Sims about congressional districts within a state:
    • “Whatever the means of accomplishment, the overriding objective must be substantial equality of population among the various districts, so that the vote of any citizen is approximately equal in weight to that of any other citizen in the State.”
  • Thus districts with equal populations have votes with equal weight.  Conversely, votes in districts with unequal populations have different weights. A vote in a district with 100 members, for instance, has 10 times the weight of a vote in a district with 1000 members.
  • The underlying principle is:
    • The weight of a vote in a district = 1 / population of the district
  • The weight of a vote in a district with 100 members is 1/100.  The weight of a vote with 1000 members is 1/1000.  (1/100) / (1/1000) = 10. Therefore the weight of a vote in the smaller district is ten times the weight of a vote in the larger.
  • We thus have a method for weighing people’s votes for senators and president across states and for representatives across congressional districts: divide the number of elected officials by the population.
House of Representatives
  • The graph shows the weight of a vote for each of the 435 representatives, relative to a baseline of 1, where each vote has the same weight.
  • Here’s how it works.  Take the rightmost vertical bar, for example, representing Wyoming’s single district. The absolute weight of a vote in the district is 1 / 581,024, since Wyoming’s population is 581,024.
  • If all 435 congressional districts had the same number of members, every vote would have the same weight of 435 / 330,000,000.
    • The District of Columbia has no representatives.
  • So the weight of a vote in Wyoming’s single district relative to the ideal equal weight is:
    • (1 / 581,024 ) / (435 / 330,000,000) = 1.30566, as shown on the graph.
  • The relative weights are pretty close to 1. This is due to the 1964 Supreme Court ruling in Wesberry v Sanders that “as nearly as practicable one man’s vote in a congressional election is to be worth as much as another’s.”
  • There are anomalies, nevertheless, e.g. a vote in RI 2nd has twice the weight of a vote in Montana’s single district.  Such anomalies are due to the algorithm for apportioning house seats to the states, explained in Computing Apportionment.
  • The graph shows the weight of a vote for senator in each of the 50 states, relative to a baseline of 1, where each vote has the same weight.
  • The weight of votes for Senators differ substantially from state to state.  For example, a vote in WY has 68 times the weight of a vote in CA.  This is because state populations vary greatly, though each state has the same number of senators.
  • The absolute weight of a vote for senator in a particular state equals 2 divided by the state’s population. So the absolute weight of a vote in WY equals 2 / 577,719.
  • The hypothetical equal weight of a vote for senator is 100 / 330,000,000.
    • The District of Columbia has no senators.
  • Thus the relative weight of a vote in WY is
    • (1/577719) / (50/330000000) = 11.42, as shown on the graph.
  • The graph shows the weight of a vote for president in each of the 50 states, relative to a baseline of 1, where each vote has the same weight.
  • The weight of a vote for president differs from state to state, but not nearly as much for Senators.  For example, a vote in WY has 3.5 times the weight of a vote in CA.  This is because, while senators have an expanding effect on the difference in electoral votes, representatives have a moderating effect.
    • The number of a state’s electors equals the number of the state’s representatives plus the number of senators. 
  • The absolute weight of a vote for president in a particular state equals the number of the state’s electoral votes divided by the state’s population. So the absolute weight of a vote in WY is 3 / 577,719.
  • The hypothetical equal weight of a vote for president is 538 / 330,000,000.
    • 538 electoral votes = 435 representatives + 100 senators + 3 D.C.electoral votes.
      • The District of Columbia has 3 electoral votes, though no senators or representatives. This is thanks to the 23rd Amendment, which allocates to D.C. the number of electoral votes equal to the number of the least-populated state (meaning 3).
  • Thus the relative weight of a vote in WY is
    • (3 / 577,719) / (538 / 330,000,000.) = 3.1852
Not every vote counts the same: Quick Take
  • Not every vote counts the same. For example, because of the difference in populations, a vote for senator in WY has 68 times the weight of a vote in CA
  • The population difference also biases the presidential vote. A vote for president in WY has 3.5 times the weight of a vote in CA. Thus, Bush in 2000 and Trump in 2016 won with fewer popular votes.
  • Differences in state populations also indirectly impact the Supreme Court. Trump, for instance, though losing the popular vote, appointed three SC justices.

View One person, not necessarily one vote