Iain Dunning

Contact: iaindunning at gmail, @iaindunning, github/IainNZ

› Representation, Filibusters and the US Senate

First posted: Nov 22, 2013

The Senate is one half of the legislative branch of the government of USA. It has 100 members, 2 from each state. Each of the 2 senators are elected separately on a simple majority basis (although some states have runoff elections if no candidate wins a majority). The consequence of these two decisions is that any two senators can represent widely different numbers of people.

Consider first Wyoming, which on July 1st, 2012 was estimated to have a population of 576,412 people, making it the smallest state. Assuming for the sake of simplicity that all these people can vote, to become a senator for Wyoming you would thus need to obtain at least 288,207 votes. On the other hand California, on the same date, was estimated to have a population of 38,041,430 people, so to become a senator for California would require 19,020,716 people to vote for you (under our assumption). The point is that a senator from California represents at least 66 times as many people as a senator from Wyoming. If everyone in California voted for the same senator, that senator could directly represent up to 132 times as many people as a senator from Wyoming that only just obtained a majority of the votes.

A majority of 51 votes is required to pass a measure in the Senate . In the event of a tie, the Vice President of the USA can step in to break the tie (John Adams did this 29 times!). However, an interesting “feature” of the Senate is the ability to filibuster, which means to essentially delay even having a vote by means of various tactics, typically by simply speaking indefinitely on the matter. There is a way around this tactic though: “three-fifths of the Senators duly chosen and sworn” (typically 60 votes) can agree to end the filibuster and move to vote. The filibuster has been in the news because the Senate recently decided to limit the ability to use it - now a simple majority is sufficient to stop a filibuster for some measures (such as appointing judges to certain courts).

The question I want to ask is - how representative or unrepresentative is the Senate with and without the filibuster?

With the filibuster

Although a minority of Senators cannot pass measures, they can still block them. Suppose there are two parties, the Apple party and the Orange party, and suppose there are 41 senators from the Orange party. If all 41 Orange senators agree to, they can filibuster endlessly as the Apple senators can never get the required 60 votes to end a filibuster. How many votes does the Orange party need to get 41 senators?

Lets start with Wyoming, the smallest state. As stated before, the population of Wyoming is 576,412, so the Orange party would need only to convince 288,207 people to vote for their candidates to gain two senators (again using our simplifying assumption that all people can vote). Let us repeat this process for the 20 smallest states, and also pick up another senator from the 21st smallest state, Iowa.

State Population Majority Running Total Percent Total Population Senators So Far
North Dakota6996283498159510280.36
South Dakota83335441667817334310.610
Rhode Island10502925251473219696116
New Hampshire132071866036038800561.218
West Virginia185541392770769663822.226
New Mexico2085538104277089369152.930
Iowa 3074186 1537094 17691102 5.6 41

We can see that the support of 5.6% of the population (or of voters, if the proportion of people who can vote in each state is similar) is sufficient to block a measure in the Senate.

Without the filibuster

Without the filibuster, and assuming the President is a member of the Apple Party, the Orange Party needs to have majority of 51 votes to block measures. We’re going to need another ten Senators then from the next 10 smallest states:

State Population Majority Running Total Percent Total Population Senators So Far

We can see that the support of 8.9% of the population (or of voters, if the proportion of people who can vote in each state is similar) is sufficient to block a measure in the Senate even without the filibuster.

Real life

While the above numbers look (and are) worrying, the real situation is surely not so bad. In the US Senate right now there are 53 Democratic Party senators, 45 Republican Party senators, and two independents - thus the Republican Party can filibuster the Democratic Party, and the Democratic Party can block any measure of the Republican Party. How representative are these 100 senators of the total population? One way to answer this question is the following:

  • If both senators are from same party then the population of that state is allocated to that party.
  • If the senators are from different parties then each party is allocated half the population of that state.
  • Angus King, Senator for Maine, and Bernie Sanders, Senator for Vermont, generally work with the Democratic Party so we will treat them as members.

If you do the math using this list you will find that the Democratic Party + independents represent 58.2% of the population, and the Republican Party represents 41.8%. That seems like a reasonable enough outcome, but there is a catch.

Suppose, for arguments sake, that each Republican senator won their seat by getting 50%+1 of the votes. What percentage of the population would you need to get those same 45 senate spots they currently hold? It turns out to be only 20.9%. Likewise, the Democratic Party (+ independents) only need to convince 29.1% of the population to vote for them to hold their current 55 spots.

Another interesting question is: only 41 Republicans are required to filibuster - so if we remove the four Republican senators who represent the most people, how many people do the remaining 41 senators represent at best (assume whole state voted for them) and at worst (assuming they barely won)? Texas has 2 Republican senators, Florida has one, and Illinois has one. Using the same method of apportioning people we used before, those 41 Republican senators represent the wishes of “at best” 28% of the population, and “at worse” only 14%.


The Senate does not represent the voices of the people. The argument for its existence and creation is usually claimed to be a check against the “tyranny of the majority” (the House, being a more representative body, represents the “majority” in this case). However, one must question whether this notion makes sense in the modern day and, even if it does, whether the degree to which a minority can block measures (with or without the even more “unrepresentative” filibuster) is a price worth paying.

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