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

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
  • and a House runoff in the event no candidate
    receives the required majority.

The EC as a Vote Counting Mechanism (cont.)
  • We ignore constitutional details, e.g.,
  • states might revert to legislative election of
  • 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.

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.

Districted Electoral Systems (cont.)
  • Districted electoral system are extremely
  • 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
  • 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.

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,

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

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

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

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.

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
  • The claim that such systems have exagger-ation
    effects is simply to say that the swing ratio is
    greater than one.

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
  • Such outcomes are actually more common in many
    parliamentary systems than in U.S. Presidential

Historical Overview of EC as a Vote Counting
  • 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
Evidently EC has no systematic tendency to
produce wrong winners
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
  • We can get as many data points from a single
    election using a cross-sectional approach.

The Cross-sectional or Uniform National Swing
  • 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
  • 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.

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
  • The second (D2PC) column shows the Democratic
    percent of the two-party presidential vote (i.e.,
    excluding votes casts for minor parties) in each
  • 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
  • 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.

1988 List (cont.)
  • The fourth column (DPOP) is equal to 46.10
  • 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.

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

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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.

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

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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
  • Because the PVEV step function is monotonic, it
    can pass through only one of the two wrong winner
  • So for a given electoral landscape, only one
    candidate can be a potential wrong winner.

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).

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
  • 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.

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
  • It occupies 0.000333 of the maximum wrong winner
  • 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.

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
  • 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
  • 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.

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
  • 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
  • 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
  • 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

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
  • 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

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).

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).

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.

Perfect Apportionment (cont.)
  • With perfect apportionment, the PVEV function
    looks essentially the same as a typical PVEV
  • 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.

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
  • 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).

Apportionment vs. Distribution Effects in 1860
  • The 1860 election was based on highly imper-fect
  • The southern states (for the last time) benefited
    from the 3/5 compromise pertaining to
  • 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.

Apportionment vs. Distribution Effects in 1860
  • 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.

Apportionment vs. Distribution Effects in 1860
  • 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

Apportionment vs. Distribution Effects in 1860
  • 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.

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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