The Numbers That Run Congress, From 218 to 60 to 290 to 38 and Back

If you want to understand Washington, skip the pundits and learn arithmetic. A few numbers, none of them larger than 435, decide who can pass a bill, who can stop one, who can fire a judge and who can change the Constitution. The cable panel will spend an hour on the mood of the capital. The numbers settle it in a sentence.

I am going to take them one at a time: 435, 218, 51, 60, 290, 67, 34 and 38, plus a few cousins. For each I will say where it comes from, show the arithmetic and tell you what it means for the side that finds itself outnumbered. Bring a pencil. Bring a calculator if you are a member of Congress, since the evidence suggests it is the only way some of them will find out the cost of a bill.

Which numbers are written in stone and which in sand

Before the list, a distinction that clears up most confusion. Some of these numbers come from the Constitution and can be changed only by amendment. Others come from statute, which Congress can change by passing a law. Others come from chamber rules, which each chamber can change on its own. Article I, Section 5 says that each house "may determine the Rules of its Proceedings," and that is the clause behind most of the numbers in the second and third groups.

1. Constitutional numbers: two-thirds for overrides, treaties, impeachment convictions and expulsions; two-thirds of each house and three-fourths of the states for amendments; a majority of each house for a quorum; two senators per state.
2. Statutory numbers: 435 voting House seats.
3. Rule numbers: 60 votes for cloture in the Senate; 218 signatures on a House discharge petition; many procedural thresholds in the Senate that have changed over time.

The point of keeping the categories straight is that a number from the first group is a promise that cannot be broken by the majority of the moment, and a number from the third group is only a habit that the majority could, in principle, change tomorrow. We will see why that matters to the minority.

435: the size of the House

The House of Representatives has 435 voting members. Article I, Section 2 requires representation to be apportioned among the states by population, counted every ten years, and says that there shall not be more than one representative for every thirty thousand. It does not fix the House's total size. Congress sets it by law.

The number came in steps. The Apportionment Act of 1911 set the House size that reached 435 voting members once the new states of Arizona and New Mexico were counted. After the 1920 census Congress could not agree on a new apportionment for nearly a decade. In 1929 it passed what is called the Permanent Apportionment Act, which kept the number at 435 and set up an automatic process by which the census counts would reallocate those seats every ten years. The size has stayed at 435 since, apart from a temporary rise to 437 when Alaska and Hawaii became states in 1959, which ended when the apportionment after the 1960 census took effect.

The lesson: 435 is a number set by statute, and Congress could change it. It has not, in about a century. For the constitutional basis of the count, see Actual Enumeration, What the Census Clause Requires Every Ten Years.

218: a majority of the House

A majority of 435 is the smallest whole number greater than half. Half of 435 is 217.5, so the smallest majority is 218. Check the arithmetic: 218 + 217 = 435, and 218 is more than 217.

Article I, Section 5 provides that "a Majority of each shall constitute a Quorum to do Business." In practice, a bill passes by a majority of those present and voting, so the number needed on a given day can be lower than 218 if members are absent or vacancies exist. When all 435 seats are filled and everyone votes, 218 carries a bill.

The same number shows up in a second place. Under the House's rules, a discharge petition needs the signatures of 218 members to pull a bill out of committee and force it to the floor over the wishes of the leadership. That is a rule, not a constitutional requirement, and it is the tool the minority's allies in the majority party can use when the Speaker will not schedule a vote. See 218 Signatures, How a Discharge Petition Pries a Bill Loose From the Speaker for how it works.

What it means for a minority party: 218 is the number the minority cannot reach alone. If it holds, say, 200 seats, it needs 18 members of the other side to join. The smaller the majority, the more a handful of defectors matter, which is why a narrow House majority is a fragile one.

51: a majority of the Senate

The Senate has 100 members, two from each state (Article I, Section 3, and the Seventeenth Amendment's rule on direct election). A majority is 51. If the vote splits 50 to 50, the vice president, as president of the Senate, casts the tie-breaking vote, under Article I, Section 3: "The Vice President of the United States shall be President of the Senate, but shall have no Vote, unless they be equally divided."

So a party with 50 seats and the vice presidency can pass things that need a simple majority, and a party with 50 seats and no vice president can only block. The arithmetic is exact: 50 + 50 = 100, and the tie goes to the vice president's party.

Simple majorities matter for confirmations, since under Senate precedents set in 2013 and 2017, cloture on nominations takes only a majority of those voting, and for the budget reconciliation process created in 1974, which allows certain budget bills to pass by majority vote.

60: the cloture number

To end debate on most legislation, the Senate requires a vote of three-fifths of the senators duly chosen and sworn: 60 of 100. This is Senate Rule XXII. It is a rule, not a constitutional requirement, and it has changed. The original cloture rule in 1917 required two-thirds of those voting. In 1975 the Senate lowered the bar to three-fifths of all senators sworn, which is 60 when the Senate is full.

Check the arithmetic: three-fifths of 100 is 60. Now flip it. If 60 can end a debate, then 41 can prevent it: 100 minus 60 is 40, and 40 is not enough to stop 60, but 41 leaves only 59. So 41 senators can block cloture. That is the minority's number in the Senate.

What it means for a minority party: with 41 members, a party can hold up most legislation. With fewer, it cannot, except by other procedural tools. The 41 figure is why the size of a Senate delegation matters so much more than the headline of "who has the majority." For the longer discussion, see The Filibuster After the Midterm, Why Sixty Votes Now Protect the Outnumbered.

290 and 67: two-thirds of each house

Article I, Section 7 provides that if the president vetoes a bill, Congress may override it if two-thirds of each house vote to pass it again.

• House: two-thirds of 435 is 290. Check: 435 times 2 is 870, divided by 3 is 290 exactly. So a veto override needs 290 votes if all members vote.
• Senate: two-thirds of 100 is 66.67, so the smallest whole number is 67.

These are the numbers for overrides, for proposing a constitutional amendment (Article V: two-thirds of both houses), for the Senate's consent to a treaty (two-thirds of senators present, Article II, Section 2), for convicting a person after impeachment (two-thirds of senators present, Article I, Section 3) and for expelling a member (two-thirds of that house, Article I, Section 5). Note the phrase "present." For a treaty and for impeachment, the requirement is two-thirds of the senators present, so if all 100 are there it is 67, and if only 90 are there it is 60.

Now flip the arithmetic for the minority.

• In the House, 290 are needed to override, so 146 can sustain a veto. Check: 435 minus 145 is 290, so if 145 vote no, 290 vote yes and the override succeeds. With 146 no votes only 289 remain, and it fails. So the number is 146.
• In the Senate, 67 are needed, so 34 can sustain a veto or block a treaty. Check: 100 minus 33 is 67, so with 33 no votes the override carries; with 34 it fails.

That is why a president whose party holds one-third plus one of either house can make a veto stick, and why the Founders designed the veto as a real check. It is not a number a simple majority can overcome. See Two-Thirds of the Senate, How the Treaty Clause Was Built to Be Hard.

38: the states needed to ratify

Article V provides two paths to propose an amendment: two-thirds of both houses of Congress, or a convention called on the application of two-thirds of the state legislatures. Either way, ratification requires three-fourths of the states, by their legislatures or by conventions, as Congress chooses.

• Three-fourths of 50 is 37.5, so the smallest whole number is 38.
• A convention on the application of two-thirds of the states needs 34, since two-thirds of 50 is 33.33.
• To block an amendment, you need 13 states. Check: 50 minus 12 is 38, so if only 12 states object, 38 ratify and the amendment passes. With 13 states objecting, only 37 remain.

Those figures explain why only twenty-seven amendments have been ratified. The process is intentionally steep. See Twenty-Seven Amendments Out of Over Eleven Thousand Proposals, by the Numbers.

The cousins

A few related numbers belong here.

• 2: two senators per state, a number protected unusually well. Article V provides that "no State, without its Consent, shall be deprived of its equal Suffrage in the Senate." That clause cannot be amended away without the state's own agreement.
• 9: the number of justices on the Supreme Court, set by statute (the Judiciary Act of 1869), not by the Constitution.
• 270: the number of electoral votes needed to win the presidency, because the Electoral College has 538 members (435 representatives, 100 senators and 3 for the District of Columbia under the Twenty-Third Amendment), and a majority of 538 is 270. Check: 538 divided by 2 is 269, so a majority is 270.
• 7: the number of members of the House's oversight committee who can, under a federal statute (5 U.S.C. 2954), demand information from executive agencies. This one, often called the seven-member rule, is explained in The Seven Member Rule and Other Oversight Tools a Congressional Minority Keeps.

Who can change what

Now the central question for the minority. If you are outnumbered, which numbers can the majority change against you?

1. The constitutional numbers cannot be changed by a majority at all. Two-thirds is two-thirds. A majority that is annoyed at a veto cannot lower the bar to override it, and cannot change the three-fourths rule for amendments without an amendment.
2. The statutory numbers can be changed by a majority of both houses and the president. The size of the House, the number of justices and the statutes giving minority-party members oversight rights are all in this group. A majority could change them, subject to the veto.
3. The rule numbers can be changed by each chamber alone. The cloture threshold, the discharge petition's 218 and the thresholds for nominations are all in this group. The Senate has changed its rule in 1917, 1949, 1959 and 1975, and by precedent in 2013 and 2017 for nominations.

The majority-of-the-moment finds the third group the easiest to change and the first the hardest, and the minority has the opposite interest. That is why the claim "it's just a Senate rule" is both true and beside the point. A rule is a promise that the majority makes to the minority, and a majority that breaks it today is a minority tomorrow.

What each number means for the minority

Let us put it together in a table.

The pattern is that every threshold has a mirror, and the mirror is the minority's power. A member who looks at a vote and sees only the majority number has read half the page. For the same reason, a new member of the minority should memorize 41, 34, 146 and 13, because they are the numbers that turn a lost election into a seat at the table.

The Founders' reasoning

Why did they set the numbers where they did? A simple majority for ordinary legislation, because a republic must be able to govern. Two-thirds for overrides, treaties and amendments, because those are the acts that either override a considered decision or bind the nation for a long time, and they should require broad agreement.

Madison wrote in Federalist 10 that a majority can be a faction. The higher thresholds are the answer: they make a majority prove it is more than the temper of an election. You can read the Founding documents at the Constitution page. And for the same argument in satire, see If a Majority Could Never Be Slowed, a Satirical Tour of the 51-Vote Republic.

The case in brief

1. The House has 435 voting seats by statute, so a majority is 218; the Senate has 100, so a majority is 51 with the vice president breaking ties.
2. The Senate's 60-vote cloture threshold is a rule, adopted at two-thirds in 1917 and lowered to three-fifths in 1975, and it lets 41 senators block most bills.
3. Two-thirds thresholds in the Constitution mean 290 House votes and 67 Senate votes, and the mirror numbers 146 and 34 let a minority sustain a veto or block a treaty.
4. Amendments need three-fourths, or 38 of 50 states, so 13 states can block one.
5. The Constitution fixes the thresholds the majority cannot change; the chambers set the rest, and every threshold has a mirror that is the minority's power.

What you can do: write down your own representatives' and senators' party and the numbers above, then use the representatives finder to see which of them sit on the margin of a close vote.