HOUSE SIZE, APPORTIONMENT, AND DISTRICTING

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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.

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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.

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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

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House Size (at Apportionment) by Decade
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Electoral Vote Floor to EV Total
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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).

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• 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.

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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
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• 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 Gores
  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

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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.

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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.

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Hamiltons Method Largest Remainders

• Fix the size of the House, e.g., at 105.
• Determine each states 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 (NYs 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.
• Hamiltons method round all quotas down, then
  allocate remaining seats to states according to
  the size of their remainders.

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Hamiltons Method (cont.)

• Hamiltons 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 Hamiltons method is subject to a number of
  paradoxes.
• The Alabama Paradox increasing the size of the
  House can reduce a states seats, all else equal.
• The Population Paradox even if state As
  population grows faster than state Bs, 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.

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Divisor Methods

• All divisor methods award House seats
  sequen-tially to states on the basis of their
  priority for an additional seat.
• Initially, every states priority is determined
  by its population, so the first seat is awarded
  to the largest state.
• Thereafter, a states 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.

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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 states 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

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Jeffersons 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., n1.
• With respect to the alternate characterization,
  Jeffersons rounding rule is to round all
  quotients down to the nearest integer.

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Jeffersons Method (cont.)

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

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Jeffersons Method (cont.)

• Thus Jeffersons 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.

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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.

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Apportionment Legislation

• When it first passed the 1790 Apportion-ment
  Bill, Congress used the Hamilton Method.
• Washington rejected the bill (on Jeffer-sons
  urging), exercising the first Presi-dential veto
  in history.
• Congress failed to override the veto and passed a
  new Apportionment Bill based on Jeffersons
  method.

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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.

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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.

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Other Variations on Election 2000

• Using the actual (Hill-Huntington) apportionment
  formula on 1990 Census
• Bush 271 Gore 267
• Using Jeffersons 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.

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Districting

• Article 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).

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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.

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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.

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Such gerrymandering can produce undoubtedly
weirdly shaped districts
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Closer to home
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• 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

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