HOUSE SIZE, APPORTIONMENT, AND DISTRICTING

• All of these factors, which pertain directly to House elections, are also relevant to Presidential elections.– House size and apportionment determine the

number of electoral votes for each state.– The Maine/Nebraska system of awarding

electoral voters in based on Congressional Districts.

HOUSE SIZE

• Not fixed by the Constitution, except that “the number of Representatives shall not exceed one for every thirty thousand, but each state shall have at least one Representative.”

• Each state has electoral votes equal to its total represen-tation in Congress, i.e., number of House seats + 2, so– each state has a guaranteed a “floor” of 3 electoral votes,– which entails a systematic small-state advantage.

• The Constitution specified a provisional apportionment of 65 House seats, – in turn implying 65 + 26 = 91 electoral votes.

Failed First Amendment After the first enumeration required by the first article of

the Constitution, there shall be one Representative for every thirty thousand, until the number shall amount to one hundred, after which the proportion shall be so regulated by Congress, that there shall be not less than one hundred Representatives, nor less than one Representative for every forty thousand persons, until the number of Representatives shall amount to two hundred; after which the proportion shall be so regulated by Congress, that there shall not be less than two hundred Representatives, nor more than one Representative for every fifty thousand persons.

[Sent to the states for ratification along with the Bill of Rights and Amendment 27]

House Size (at Apportionment) by Decade

Electoral Vote Floor to EV Total

Implications of Increasing House Size for Electoral Votes

• Increasing the number of House seats allows a more precise apportionment among the states.

• Increasing the number of House seats reduces the impact of the 3-electoral vote floor relative to the total number of electoral votes.

• On both counts, increasing the size of the House increases proportionality in the allocation of Electoral Votes and, in particular, reduces the small state advantage.

• Changing House size can change the outcome of Presidential elections (all else equal).

• In 2000, Bush carried 30 states and Gore 21 (including DC), so– On the basis of “House” Electoral Votes only, Gore

would have beaten Bush: • Bush: 271 – 60 = 212• Gore: 267 – 42 = 225

• 2000 was the first time since 1916 that an electoral vote victory turned on “Senatorial” electoral votes.

• And it was the first time since 1876 that a popular vote loser became an electoral vote winner on the basis of “Senatorial” electoral votes.

Moreover, Gore carried most of the biggest states, while Bush carried most of the middle-size states and the

smallest states were divided about equally

• As a result, a larger House size could have given Gore an overall [House + Senatorial] Electoral Vote victory.

• But, perhaps surprisingly, the relationship between increasing House size and Gore’s electoral college advantage was not “monotonic.”– See M. G. Neubauer and J. Zeitlin, “Outcomes of Presidential

Elections and House Size,” PS: Politics and Political Science, October 2003

The Apportionment Clause

• Article I, Section 2, Clause 3• Representatives [and direct Taxes] shall be apportioned

among the several States which may be included within this Union, according to their respective Numbers [which shall be determined by adding to the whole Number of free Persons, including those bound to Service for a Term of Years, and excluding Indians not taxed, three fifths of all other Persons]. The actual Enumeration shall be made within three Years after the first Meeting of the Congress of the United States, and within every sub-sequent Term of ten Years, in such Manner as they shall by Law direct.

The Apportionment Problem

• But the Constitution does not specify a mathe-matical formula by which this apportionment would be calculated.

• When Congress took up the first Apportionment Bill in 1790, it discovered that solving this prob-lem was not straightforward.

• Two rival apportionment formulas were proposed.

Hamilton’s Method [Largest Remainders]

• Fix the size of the House, e.g., at 105.• Determine each state’s proportion of the apportionment

population.– For example, New York had 9.77685% of the population. Given

a House of 105 members, NY would ideally have 9.77685% x 105 = 10.26569 seats (NY’s quota).

• But NY and every state must have a whole number of House seats.

• The most obvious remedy is to round off quotas in the normal manner; but such rounded whole numbers may not add to 105.

• Hamilton’s method: round all quotas down, then allocate remaining seats to states according to the size of their “remainders.”

Hamilton’s Method (cont.)• Hamilton’s Method is a “quota method” of

apportionment.• Accordingly it “stays in quota,” i.e., it gives every

state its quota rounded either up or down.• But Hamilton’s method is subject to a number of

“paradoxes.”– The Alabama Paradox: increasing the size of the House can

reduce a state’s seats, all else equal.– The Population Paradox: even if state A’s population grows

faster than state B’s, A can lose seats to B in the later apportion-ment, all else equal.

– The New State Paradox: admitting a new state, even while expanding the size of the House so that the “old” states together have the same number seats as before, can redistribute those seats among the “old” states.

Divisor Methods

• All divisor methods award House seats sequen-tially to states on the basis of their “priority” for an additional seat.

• Initially, every state’s priority is determined by its population, so the first seat is awarded to the largest state.

• Thereafter, a state’s priority is determined by its population divided by some function of n, where n is the number of seats it has already been awarded.

• Different divisor methods use different functions of n.

Divisor Methods (Alternate Characterization)

• Select a divisor approximately equal to the total population of all states divided by the total number of House seats, i.e., the average CD population.

• Divide each state’s population by this divisor and round off the resulting quotient by some rule to produce an provisional apportionment.

• Different divisor methods use different rounding rules.

• Adjust the divisor up or down until the required number of seats has been apportioned

Jefferson’s Method [Greatest Divisors]• Fix the size of the House, e,g., at 105.• House seats are awarded sequentially.• The first House seat is awarded to the largest state.• The second House seat is also awarded to the largest

state if its population divided by 2 is greater than the population of the second largest state; otherwise it is awarded to the second largest state.

• In general, each additional seat is awarded to the state with the “strongest claim” to the seat, where this claim is determined by the population of the state divided by the number of seats it has already been awarded plus one, i.e., n+1.

• With respect to the alternate characterization, Jefferson’s rounding rule is to round all quotients down to the nearest integer.

Jefferson’s Method (cont.)

• Jefferson’s method (like other divisor methods) is not subject to the Alabama, Population, or New State Paradox.

• But Jefferson’s method (like other divisor methods) does not stay in quota. In particular (for Jefferson),– a big state may get more than its quota

rounded up, and– a small state may get less than its quota

rounded down.

Jefferson’s Method (cont.)

• Thus Jefferson’s Method exhibits bias (to the advantage of big states and disadvan-tage of small states).

• NOTE: all apportionment methods may have to be adjusted to comply with the constitutional requirement that every state have at least one House seat.

Other Divisor Methods

• John Adams advocated the divisor rule that rounds all quotients up to the nearest integer.– It is the divisor rule most favorable to small states.

• Daniel Webster advocated the divisor rule at the midpoint between Jefferson and Adams, i.e., that rounds all quotients up or down to the nearest integer in the normal manner.– It is the divisor rule least biased toward either big or

small states.

• The Hill-Huntington divisor method is the apportionment method now in effect.– It is slightly biased toward small states.

Apportionment Legislation

• When it first passed the 1790 Apportion-ment Bill, Congress used the Hamilton Method.

• Washington rejected the bill (on Jeffer-son’s urging), exercising the first Presi-dential veto in history.

• Congress failed to override the veto and passed a new Apportionment Bill based on Jefferson’s method.

Apportionment Legislation (cont.)

• Throughout the 19th Century, in each Apportionment Bill Congress always changed (almost always increased) the House size and often changed the apportionment method.

• Congress discovered the Alabama Paradox while debating 1870 bill and never used Hamilton Method thereafter.

• Congress established a “permanent” House size of 435 in 1913.

Apportionment Legislation (cont.)• Congress prescribed a “permanent” appor-

tionment method (the Hill-Huntington “Method of Equal Proportions” in the 1940 Apportionment Bill.

• Thus, since 1940, apportionment has been on “automatic pilot” and Congress no longer passes a new Apportionment Bill each decade.– The definitive work on this subject is by M. Balinski

and H. P. Young, Fair Representation.– The authors argue that the optimal apportionment formula is the

divisor method proposed by Daniel Webster.

Other Variations on Election 2000

• Using the actual (Hill-Huntington) apportionment formula on 1990 Census

– Bush 271 Gore 267• Using Jefferson’s apportionment formula on 1990 Census

– Bush 266 Gore 272• Using Hill-Huntington on the 2000 Census

– Bush 280 Gore 258• Using Jefferson on the 2000 Census

– Bush 277 Gore 261• Under all variations above, Gore wins on the basis of

“House” electoral votes only, because Bush has an 18 vote advantage based on “Senate” electoral votes only.

DistrictingArticle I, Section 4, Clause 1

The times, places and manner of holding elections for Senators and Representatives, shall be prescribed in each state by the legislature thereof; but the Congress may at any time by law make or alter such regulations, except as to the places of choosing Senators.

Since 1967 (and at various earlier times as well) Congress has pre-scribed that the “manner” of holding elections for Representative shall be by Single-Member Districts (SMDs), thereby producing “single-winner” elections in each district.

All states with two or more Representatives are therefore required to divide themselves into a number Congressional Districts (CDs) equal to their House seat apportionment.

Districting is either done by the state legislature or by another body prescribed by state law (or by courts when legal issues arise).

Districting (cont.)• In Maine and Nebraska, Presidential electors are

elected by district, rather than statewide.• Any state is free to adopt such a system and

several other states (including Florida) have considered the district system.

• Under the Maine/Nebraska system, the two “Senatorial” electors are elected statewide, while the remaining “House” electors are elected from CDs (on an SMD basis).

• Thus creating CDs is relevant to Presidential selection in Maine and Nebraska and potentially in other states as well.

Districting Controversies• Since 1964 Supreme Court rulings have

required that CDs within each state have (virtually) equal populations.

• District boundaries must cut across natural and jurisdictional boundaries to comply with these court rulings.

• Computer technology and geographic informa-tion systems make it possible to readily deter-mine the likely political effects of alternative districting plans.

• As a result, district boundaries have been drawn in increasing weird ways.

Such “gerrymandering” can produce undoubtedly weirdly shaped districts

Closer to home

• It is commonly claimed that such “gerry-mandering” produces districts that are safe for one or other party and therefore non-competitive.

• If this is true, and if CDs were used to elect Presidential electors, then presi-dential election campaigns would focus on a relatively few “battleground” CD.

• However, CDs are not nearly as safe for one party or the other as the outcomes in House elections seem to suggest.– House elections vs. Presidential vote by CD