POPULAR VOTES AND ELECTORAL VOTES

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POPULAR VOTES AND ELECTORAL VOTES

• The Electoral College as a Vote Counting
  Mechanism
• http//www.research.umbc.edu/nmiller/RESEARCH/PVE
  V/PVEV.htm

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The EC as a Vote Counting Mechanism

• Lets consider the Electoral College simply as a
  vote counting mechanism.
• Instead of having a single national election for
  President (in which votes are added up
  nationwide, taking no account of state
  boundaries), we have 51 separate state (and DC)
  elections for President.
• We determine the national winner by
• awarding the plurality winner in each state all
  the electoral votes of that state, and then
• adding up electoral votes across the nation to
  determine the winner,
• with an absolute electoral vote majority
  requirement,
• and a House runoff in the event no candidate
  receives the required majority.

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The EC as a Vote Counting Mechanism (cont.)

• We ignore constitutional details, e.g.,
• states might revert to legislative election of
  electors
• electors might be elected otherwise than on a
  statewide general ticket basis
• electors might violate their pledges, etc.
• Moreover, here we focus for the most part on the
  case in which there are just two serious
  candidates (who have any chance of carrying
  states) for President,
• so that (excepting a mathematically possible
  269-269 electoral vote tie) one candidate must
  receive an absolute majority of electoral votes,
  and the House runoff procedure is avoided.
• We also ignore the fact that two small states
  elect electors by district and thereby allow
  electoral votes to be divided.

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Districted Electoral Systems

• A districted election system is an electoral
  system in which voters are partitioned into
  (geographically defined) districts.
• Each district is apportioned a number of seats in
  a national electoral body.
• Parties or candidates compete for seats district
  by district.

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Districted Electoral Systems (cont.)

• Districted electoral system are extremely
  widespread.
• Most electoral democracies are parliamentary
  systems, in which the head of government (prime
  minister, premier, chancellor, etc.) is selected
  indirectly, and the general election simply fills
  the seats in the (lower house of) national
  legislature.
• All countries except the Netherlands, Israel, and
  some mini-states have districted elections,
  though some other countries have national
  adjustment seats that largely counteract the
  effect of districts.

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Districted Electoral Systems (cont.)

• Within each district, some voting rule or
  electoral formula, i.e., a specification of how
  voters declare their preferences on ballots and
  how this information on preferences is aggregated
  to fill the seats, must be used.
• Clearly, in single-member districts (SMDs), any
  formula entails a winner-take-all
  district-level outcome (since there is only one
  seat to take).
• As we have seen, several different voting rules
  can be used, e.g., Simple Plurality, (Instant)
  Runoff, Approval Voting, Borda Score, selecting
  the Condorcet Winner, etc.
• Multi-member districts (MMDs) allow a great
  variety of possible voting rules, including many
  that divide seats more or proportionally among
  competing parties (and well as other that produce
  winner-take-all, or at least winner-take-most,
  outcomes).

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Districted Electoral Systems (cont.)

• Given an electoral system that applies a (quasi-)
  proportional electoral formula on large MMDs (or
  on the undistricted nation as a whole), there
  is an essentially determinate (and proportional)
  relationship between the popular votes received
  by a party and the number of seats it wins.
• However, given an electoral system that uses SMDs
  or applies a winner-take-all formulas to MMDs,
  the relationship between overall seats and
  popular votes is complex and contingent --- in
  particular, it depends on how popular votes for a
  parties or candidates are distributed over the
  districts.

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Districted Electoral Systems (cont.)

• The British (and Canadian and other) electoral
  systems are simple winner-take-all districted
  systems, in that all districts are SMDs.
• The U.S. Electoral College system is a more
  complex winner-take-all districted electoral
  system, in that different districts (states)
  have different numbers of seats (electoral
  votes).

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Winner-Take-All Districted Systems

• A winner-take-all districted system tends to
  produce a twoparty system. Duvergers Law.
• A winner-take-all districted system tends
  nationwide to give a disproportionate number of
  seats to the leading party or candidate and to
  give few if any seats to trailing (ranked third
  or lower) parties or candidates. Exaggeration
  Effect

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Winner-Take-All Districted Systems (cont.)

• In a two-party system, the exaggeration effect
  benefits the winning party and penalizing the
  losing party.
• In winner-take-all districted systems, small
  parties (or third candidates) with
  geo-graphically concentrated support do better
  than small parties (or third candidates) with
  geographically dispersed support.

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The Swing Ratio

• The magnitude of the exaggeration effect is
  reflected by the swing ratio.
• A swing ratio of 3, for example, means that a
  party that increases its national vote share by
  1 can expect to increase its seat share by about
  3.
• The claim that such systems have exagger-ation
  effects is simply to say that the swing ratio is
  greater than one.

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Reversal of Winners

• Any districted electoral system can produce a
  reversal of winners.
• That is, the candidate or party that wins the
  most popular votes may fail to win the most seats
  or electoral votes (and there-fore lose the
  election).
• Such outcomes are actually more common in many
  parliamentary systems than in U.S. Presidential
  elections.

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Historical Overview of EC as a Vote Counting
System

• The following chart is a scattergram that plots
  the relationship between popular votes and
  electoral vote from 1928 through 2004.
• 1948 and 1968 are excluded because third
  candidates with concentrated electoral support
  won substantial electoral votes in those years.

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But evidently the translation of popular votes
into electoral votes is cannot be entirely
linear.
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Evidently EC has no systematic tendency to
produce wrong winners
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Limitations of the Historical Approach

• Trade-off between number of elections to include
  (plotted points in scattergram) and uniformity of
  the political environment.
• In any case, we are limited to about 50 data
  points.
• We can get as many data points from a single
  election using a cross-sectional approach.

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The Cross-sectional or Uniform National Swing
Approach

• This analytical technique allows us to identify
  the swing ratio, the wrong winner interval, and
  other characteristics of the translation of
  popular votes into electoral votes in individual
  elections.
• We use state-by-state popular vote data to
  profile the electoral landscape that
  character-ized a particular election.
• Then we let the political tides in favor of one
  or other party/candidate rise and fall in a
  uniform national swing.

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Uniform National Swing1988 as an Example

• In the 1988, the Democratic ticket of Dukakis and
  Bentsen received 46.10 of the two-party national
  popular vote and won 112 electoral votes (though
  one of these was lost to a faithless elector).
• Given state-by-state popular vote totals, we can
  display the relationship between Democratic
  popular and electoral votes in 1988, if we take
  the actual state-by-state vote totals as the
  starting point and then consider how states would
  tip into or out the Democratic column in the face
  of a uniform national swing of varying magnitudes
  for or against the party.
• For example, a uniform national swing of 2.50 in
  favor of the Democrats would increase their
  national popular vote percent to 48.60 and would
  shift every state they lost by less than 2.50
  into the Democratic column.

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1988 List

• The first column lists the states (plus DC)
  ordered in terms of the performance of the
  Democratic ticket in the 1988 Presidential
  election.
• The second (D2PC) column shows the Democratic
  percent of the two-party presidential vote (i.e.,
  excluding votes casts for minor parties) in each
  state.
• The third column (DSWG) is equal to 50 - D2PC.
• Each negative entry represents the magnitude of a
  uniform national swing against the Democrats that
  would just cost them the state in question.
• For example, Dukakis carried his home state of MA
  with 53.98 of the 2-party vote. Thus Dukakis
  would still carry MA in the face of a uniform
  national swing against him of up to 3.98 but
  would lose MA in the face of a larger national
  swing.
• Each positive entry represents the magnitude of a
  uniform national swing in favor of the Democrats
  that would just gain them the state in question.
• For example, Dukakis lost CA with 48.19 of the
  vote. Thus Dukakis would still lose CA with a
  uniform national swing in his favor of anything
  less than 1.81 but would win CA with any larger
  favorable national swing.

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1988 List (cont.)

• The fourth column (DPOP) is equal to 46.10
  DSWG.
• It represents the Democratic national popular
  vote given a national swing just big enough to
  tip the state.
• For example, the 3.98 national swing against the
  Democrats just sufficient to tip MA into the
  Republican column results in a 42.12 national
  popular vote for the Democrats
• For example, the 1.81 swing in favor of the
  Democrats just sufficient to tip CA into the
  Democratic column results in a 47.91 national
  popular vote for the Democrats.
• The fifth column (EVCM) is the total electoral
  vote for the Democratic ticket cumulating from
  their strongest to weakest state.
• The fourth and fifth columns together allow us to
  examine the relationship between popular votes
  and electoral votes, taking the actual
  state-by-state 1988 vote as a baseline and
  considering uniform national swings in both
  directions from this baseline.

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1988 PVgtEV Chart

• A scattergram (with the points connected)
  plotting EVCM against DPOP produces the
  monotonically increasing (i.e., never decreasing)
  PVEV step function shown in the following chart.
• The plot is monotonic because it assumes the
  increase in the Democratic national popular is
  uniform across states.
• It is a step function because electoral votes do
  not increase continuously with popular votes but
  rather in discrete increments (of no less than
  three votes) whenever another state tips into the
  Democratic column.
• Dukakis actually won 46.1 of the popular vote,
  which translated into 112 electoral votes. This
  is shown in the chart by the dashed green
  vertical and horizontal reference lines that
  intersect at the actual election outcome (DPOP
  46.1, EVCM 112).

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Political Landscape vs. Political Tides

• The PVEV function may be said to depict the
  political landscape in a given election.
• We then examine what happens as PV goes up or
  down (as political tides wax or wane) as a
  result of uniform national swings of varying
  magnitude.

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1988 PVEV Chart

• Note that the general pattern of the 1988 chart
  broadly resembles that of the historical chart
  (especially the curvilinear variant).
• However, the slope of the function in the middle
  of the chart is considerably steeper.
• Indeed, the tidal version of the chart shows
  that, while Dukakis got 112 electoral votes (and
  416 for Bush) with about 46 of votes, with 54
  he would have gotten about 390 electoral votes
  (and 148 for Bush).
• Note that the 1988 PVEV function is not quite
  symmetric about DPOP 50, at least at 50 4.
• Thus an 8 swing in the popular vote would have
  gained Dukakis 278 electoral votes (34.75
  electoral votes for each 1 of the popular vote,
  implying a swing ratio of about 6.5.

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Wrong Winners in PVEV Charts

• Such a chart can partitioned into four equal
  quadrants by vertical and horizontal lines
  located at DPOP 50 and EVCUM 269.
• An election outcome located at the intersection
  of these lines is a perfect tie, with respect to
  both popular and electoral votes.
• An outcome (including the actual 1988 outcome) in
  the south-west quadrant (Rep Winner) is one in
  which the Democrats lose both the popular and
  electoral votes.
• An outcome in the northeast quadrant (Dem
  Winner) is one in which the Democrats win both
  the popular and electoral vote.
• An outcome in the northwest quadrant entails a
  Democratic electoral vote victory with less than
  half of the two-party popular vote, i.e., the
  Democrat is a wrong winner.
• An outcome in the southeast quadrant entail a
  Democratic electoral vote loss despite a popular
  vote majority, i.e., the Republican is a wrong
  winner.

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Wrong Winners in PVEV Charts (cont.)

• Assuming uniform national swings from the actual
  state-by-state popular vote, an Electoral College
  wrong winner (or reversal of winners or
  misfire) can occur if and only the PVEV
  function fails to pass precisely through the
  perfect tie point at the center of the chart
  (50.000 gt 269).
• It is evident that, given any landscape, the
  electoral vote function almost always fails to
  pass through the perfect tie point, so the
  probability of a wrong winner approaches 50 as
  the popular vote division approaches a perfect
  tie.
• Because the PVEV step function is monotonic, it
  can pass through only one of the two wrong winner
  areas.
• So for a given electoral landscape, only one
  candidate can be a potential wrong winner.

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The Wrong Winner Interval in 1988

• The 1988 chart suggests that that the 1988
  popular vote split would have had to be a
  virtually perfect tie in order to produce a wrong
  winner (and it isnt evident from the full-sized
  chart which candidate it might be).
• We can examine this with precision if we go back
  to the data on which the chart is based.
• We see that if there had been a wrong winner, it
  would have been Bush (but this outcome would have
  been very unlikely even if the election had been
  much closer).

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The Wrong Winner Interval in 1988

• We see that, if Dukakis had won precisely 50 of
  the popular vote, he would have lost the election
  with only 252 electoral votes.
• If Dukakis had won 50.05 of the popular vote,
  Colorado would have tipped to the Democrats, but
  he still would have lost with only 260 electoral
  votes.
• But if Dukakis had reach 50.08 of the popular
  vote, Michigan would have tipped, giving him an
  electoral vote majority of 280.
• Thus in 1988 there would have been a wrong
  winner Bush if (under the uniform swing
  assumption) Dukakis had received between 50.0000
  and 50.0765 of the popular vote.

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The Wrong Winner Interval in 1988

• The following chart zooms in on the critical
  region in the vicinity of DPOP 50 to show the
  "wrong winner interval in 1988, i.e., the DPOP
  interval from 50.0000 to 50.0765.

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The Wrong Winner Area in 1988

• We can also determine the "wrong winner area
  rectangle of the electoral vote function,
  i.e., the rectangle with its southwest corner at
  50 and 252 and its northwest corner at 50.0765
  and 280.
• The width of this rectangle is the wrong winner
  interval and its height is the Dukakiss gain in
  electoral votes over this interval.
• In 1988, this rectangle occupies about 0.000042
  of the total area in the full chart (i.e., 100
  538)
• It occupies 0.000333 of the maximum wrong winner
  rectangle.
• This maximum in turn is equal to 1/8 of the full
  chart ignoring apportionment effects well
  return to this later.

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Symmetry of the PVEV Function

• Call a PVEV (almost) symmetric if it is true
  that, if the Democratic candidate would win X
  electoral votes with Y of the popular vote, then
  the Republican candidate would likewise win
  (almost) X electoral with Y of the popular vote.
• Clearly if PVEV is (almost) symmetric, there is
  (almost) no possibility of a wrong winner.
• We have seen that, while Dukakis got 112
  electoral votes with about 46 of votes, Bush
  would have gotten 148 electoral votes with 46 of
  the popular vote, so in this respect the 1988
  PVEV function was somewhat asymmetric.

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Symmetry of the PVEV Function (cont.)

• We can observe the overall degree of symmetry by
  superimposing the PVEV function for one party
  over that for the other.
• The 1988 PVEV function is actually highly
  symmetric,
• except In the vicinity of D2PC 50 3-4
• except for the distinctive case of DC.

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Two Sources of Wrong Winners

• This PVEV visualization makes clear that there
  are two distinct ways in which wrong winners may
  occur.
• First, a wrong winner may occur is as a result of
  the (non-systematic) rounding error (so to
  speak) necessarily entailed by the fact that the
  electoral vote function moves up and down in
  discrete steps.
• In this event, a particular electoral landscape
  may allow a wrong winner of one party but small
  perturbations of that landscape allows a wrong
  winner of the other party.
• Second, a wrong winner may occur as result of
  (systematic) asymmetry or bias in the general
  character of the PVEV function.
• In this event, smaller perturbations of the
  electoral landscape will not change the partisan
  identity of potential wrong winners.
• Such asymmetry or bias in turn results from two
  distinct phenomena
• apportionment effects and
• distribution effects.

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Wrong Winners Produced by Rounding Error

• The 1988 landscape provides a clear illustration
  of a possible wrong winner due to rounding
  error only.
• While the general path of the electoral vote
  function takes it through the perfect tie point,
  the stepwise character of the precise path means
  that it almost certainly misses the perfect tie
  point.
• Thus a wrong winner interval occurs in a narrow
  popular vote interval on one or other side of the
  50 popular vote mark.

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Wrong Winners Produced by Asymmetry

• The second source of possible wrong winners is
  substantial asymmetry or bias in the PVEV
  function such that its general path clearly
  misses the perfect tie point and it passes
  through either through the northwest quadrant or
  the southeast quadrant.
• In times past (e.g., in the New Deal era and
  earlier), there was a clear asymmetry in the PVEV
  function that result primarily from the electoral
  peculiarities of the old Solid South namely
• its overwhelmingly Democratic popular vote
  percentages, combined with
• its strikingly low voting turnout.

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Wrong Winners Produced by Asymmetry (cont.)

• The asymmetry of the PVEV function is most
  extreme (and favored the Democrats with respect
  to landslide elections, but this is without
  consequence for determining the winner.
• What might easily have affect the outcome of
  elections in this period is the smaller asymmetry
  in the vicinity of D2PC 50.
• This bias against the Democrats was such that the
  electoral vote function would have regularly
  produced a wrong Republican winner if the
  Democratic ticket received between 50 and about
  51.5 of the vote.
• The Democratic Party was dominant in Presidential
  elections during this period despite this
  unfavorable electoral landscape because it
  benefited from consistently favorable high
  political tides.
• In 1940, the wrong winner interval runs from
  50.00 to 51.51, almost 20 times wider than in
  1988
• In the 1940, the wrong winner area is 38 times
  larger than in 1988.

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Wrong Winner in 2000

• Potential wrong winner outcomes all recent
  elections are due to rounding errors in
  essentially symmetric PVEV functions.
• The wrong winner interval extended from D2PC
  50 to D2PC 50.2716 (about 3.5 times wider than
  in 1988 but less than 1/5 as wide as in 1940.
• The wrong winner outcome in 2000 occurred because
  the actual D2PC fell just within this interval,
  i.e., D2PC 50.2664.

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Wrong Winner in 1860

• The grand daddy of all wrong winners was
  occurred in 1860.
• This electoral landscape exhibits the same kind
  of bias as 1940 (produced by extreme Republican
  weakness in the South) but in even more extreme
  degree.
• It is well known that with slightly less than 40
  of the national popular vote, Lincoln won a
  comfortable electoral vote majority (180 out of
  303) against a divided opposition.
• But this victory was quite different from (for
  example) Wilsons electoral vote majority (435
  out of 531) victory against divided opposition in
  1912.

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Wrong Winner in 1860 (cont.)

• Even if he had confronted a single non-Republican
  candidate able to assemble all Douglas,
  Breckinridge, and Bell votes, Lincolns electoral
  vote total would have been only slightly reduced
  (whereas Wilson would have lost badly against a
  similarly united opposition).
• The only states that Lincoln actually won but
  would have lost against united opposition were
  California and Oregon (which he won by a
  pluralities against a divided opposition).
• He would have held every other state that he
  actually carried, because he carried them with an
  absolute majority of the popular vote.
• Though Douglas is credited with a popular
  plurality in New Jersey, Lincoln (for peculiar
  reasons) won four of its seven electoral votes.
• Even if we shift these four electoral votes out
  of the Lincoln column along with the seven
  electoral votes from California and Oregon,
  Lincoln wins 169 electoral votes (with 39.8 of
  the popular vote) against 134 electoral votes
  (with 60.2 of the popular vote) for the united
  opposition.
• The 1860 PVEV function for this scenario displays
  extraordinary asymmetry.

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Factors Producing PVEV Asymmetry and Systematic
Wrong Winners

• Two distinct characteristics of districted
  electoral systems can produce asymmetry or bias
  in contribute to reversals of winners
• apportionment effects and
• distribution effects.
• Either effect alone can produce a reversal of
  winners.

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Apportionment Effects

• A perfectly apportioned districted electoral
  system is one in which each states electoral
  vote is precisely proportional to its popular
  vote in every election (and apportionment effects
  are thereby eliminated).
• It follows that, in a perfectly apportioned
  system, a party (or candidate) wins X of the
  electoral if and only if it wins states with X
  of the total popular vote.
• Note that this say nothing about the popular vote
  margin by which the party/candidate wins (or
  loses) state.
• Therefore this does not say that the party wins
  X (or any other specific ) of the popular vote.
• An electoral system can be perfectly apportioned
  in advance of the election (in advance of knowing
  the popular vote in each state).

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Apportionment Effects (cont.)

• In highly abstract analysis of its workings, Alan
  Natapoff (an MIT physicist) largely endorsed the
  workings Electoral College (particularly its
  within-state winner-take-all feature) as a vote
  counting mechanism but proposed that each states
  electoral vote be made precisely proportional to
  its share of the national popular vote.
• This implies that
• electoral votes would not be apportioned until
  after the election, and
• would not be apportioned in whole numbers.
• Such a system would eliminate apportionment
  effects from the Electoral College system (while
  fully retaining its distribution effects).
• Reversal of winners could still occur under
  Natapoffs perfectly apportioned system.
• Natapoffs perfectly apportioned EC system would
  create perverse turnout incentives in
  non-battleground states.
• Alan Natapoff, A Mathematical One-Man One-Vote
  Rationale for Madisonian Presidential Voting
  Based on Maximum Individual Voting Power, Public
  Choice, 88/3-4 (1996).

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Imperfect Apportionment

• The U.S. Electoral College system is
  (substantially) imperfectly apportioned, in many
  ways that we have noted.
• House (and electoral vote) apportionments are
  anywhere from two (e.g., 1992) to ten years
  (e.g., 2000) out of date.
• House seats (and electoral votes) are apportioned
  on the basis of total population, not on the
  basis of
• the voting age population, or
• the voting eligible population, or
• registered voters, or
• actual voters in a given election (and turnout
  varies considerably from state to state).
• House seats (and electoral votes) must be
  apportioned in whole numbers and therefore cant
  be precisely proportional to anything.
• Small states are guaranteed a minimum of three
  electoral votes.
• Similar imperfections apply (in lesser or greater
  degree) in all districted systems.

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Perfect Apportionment (cont.)

• With perfect apportionment, the PVEV function
  looks essentially the same as a typical PVEV
  function.
• It remains a step function and follows the same
  S-curve form.
• See following to compare the actual and perfect
  apportionment PVEV functions for 1988.

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Distribution Effects

• Distribution effects in districted electoral
  system result from the winner-take-all at the
  district/state level character of these systems.
• Such effects can be powerful even in
• simple districted (one district-one
  seat/electoral vote) systems, and
• perfectly apportioned systems.
• One candidates or partys vote may be more
  efficiently distributed than the others,
  causing a reversal of winners independent of
  apportionment effects.
• Here is the simplest possible example of
  distribution effects producing a reversal of
  winners in a simple and perfectly apportioned
  district system.
• There are 9 voters partitioned into 3 districts,
  and candidates D and R win popular votes as
  follows (R,R,D) (R,R,D) (D,D,D)
• Popular Votes Electoral Votes
• D 5 1
• R 4 2
• Rs votes are more efficiently distributed, so R
  wins a majority of electoral votes with a
  minority of electoral votes.

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The 25-75 Rule

• What is the most extreme logically possible
  example of a wrong winner in perfectly
  apportioned system?
• One candidate or party wins just over 50 of the
  popular votes in just over 50 of the (simple)
  districts or in complex districts that
  collectively have just over 50 of the electoral
  votes.
• These districts also have just over 50 of the
  popular vote (because apportionment is perfect).
• The winning candidate or party therefore wins
  just over 50 of the electoral votes with just
  over 25 (50 of 50) of the popular vote and
  the other candidate with almost 75 of the
  popular vote loses the election.
• If the candidate or party with the favorable vote
  distri-bution is also favored by imperfect
  apportionment, a reversal of winners could be
  even more extreme.

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Distribution Effects (cont.)

• A proposal to reform the Electoral College that
  was actually considered seriously in the 1950s
  was the Lodge-Gossett Plan.
• The existing apportionment of electoral votes
  would be maintained.
• The office of elector would be abolished.
• In each state, candidates would be awarded
  electoral votes exactly proportional to their
  popular vote share in the state.
• Under this plan, the PVEV function would be
  (essentially) smooth and would generally follow
  the EV PV line, but it would wander a bit from
  side to side.
• Reversal of winners could still occur (favoring
  candi-dates who do exceptionally well in small
  and/or low turnout states).

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Apportionment vs. Distribution Effects in 1860

• The 1860 election was based on highly imper-fect
  apportionment.
• The southern states (for the last time) benefited
  from the 3/5 compromise pertaining to
  apportionment.
• The southern states had on average smaller
  popula-tions than the northern states and
  therefore benefited disproportionately from the
  small state guarantee.
• Even within the free population, suffrage was
  more restricted in the south than in the north.
• Turnout among eligible voters was lower in the
  south than the north.

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Apportionment vs. Distribution Effects in 1860
(cont.)

• But all these apportionment effects favored the
  South and therefore the Democrats.
• Thus the pro-Republican reversal of winners was
  entirely due to distribution effects.
• The magnitude of the reversal of winners in 1860
  the wrong winner interval of about 10 points
  would have been even greater in the absence of
  the countervailing apportionment effects.

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Apportionment vs. Distribution Effects in 1860
(cont.)

• Lincoln was the majority winner in all northern
  states except NJ, CA, and OR.
• Thus he also would have carried these states
  against a united opposition.
• These states together held a (modest) majority of
  the electoral votes.
• Lincoln carried many of these states (especially
  the more populous ones) by modest margins in the
  50-55 range.
• Lincoln received almost no votes in any southern
  (slave) states (and literally none in most of
  them).

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Apportionment vs. Distribution Effects in 1860
(cont.)

• Thus the popular vote distribution closely
  approximated the 25-75 pattern.
• Lincoln carried the northern states that held a
  bit more than half the electoral votes (and a
  larger majority of the free population),
  generally by modest popular vote margins.
• On the other hand, the anti-Lincoln opposition
• carried the southern states with a bit less than
  half of the electoral votes (and substantially
  less than half of the free population by
  essentially 100 margins and
• lost all other states other than NJ, CA, and OR
  by relatively narrow margins.

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Sterling Diagrams

• First, we construct a bar graph of state-by-state
  popular and electoral vote totals, set up in the
  following manner.
• The horizontal axis represents all states
• ranked from the strongest to weakest for the
  winning party where
• the thickness of each bar is proportional to the
  states electoral vote vote and
• the height of each bar is proportional to the
  winning partys percent of the popular vote in
  that state.
• Note this isnt yet a proper Sterling diagram.
• Carleton W. Sterling, Electoral College
  Misrepresentation A Geometric Analysis, Polity,
  Spring 1981.

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Sterling Diagrams (cont.)

• It is tempting to think that the shaded and
  unshaded areas of the diagram represent the
  proportions of the popular vote won by the
  winning and losing parties respectively.
• But this isnt true until we make one adjustment
  and thereby create a Sterling diagram.
• Rescale the width of each bar so it is
  proportional, not to the states share of
  electoral votes, but to the states share of the
  popular national popular vote.
• Draw a vertical line at the point on the
  horizontal axis where a cumulative electoral vote
  majority is achieved.
• In a perfectly apportioned system, this would be
  at or just above the 50 mark.
• If there is no systematic apportionment bias in
  the particular election, this will also be just
  about at the 50 mark.

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