The U.S. Electoral College: Origins and Transformation,

Problems and Prospects

Constitution DaySeptember 17, 2008

Nicholas R. MillerDepartment of Political Science

UMBC

http://userpages.umbc.edu/~nmiller/ELECTCOL.html

September 17, 1787• On this day, the Constitutional Convention completed its

four month’s work and transmited its proposed Constitution to the [Confederal] Congress.– 39 out of 42 delegates present sign the letter of transmittal.

• The Convention had spent much of the preceding two weeks resolving problems concerning the new “national executive,”– and particularly its “manner of appointment.”

• The advocates of the new Constitution (who came to be know as Federalists) knew they would have a hard time getting it ratified by states.– Many opponents (Antifederalists) had strong objection to many

parts of the proposed Constitution.• The Federalist Papers attempted to rebut these objections

Evaluating the “Electoral College”

• Alexander Hamilton, Federalist 68: – The mode of appointment of the Chief Magistrate of the United States is

almost the only part of the system, of any consequence, which has escaped without severe censure, or which has received the slightest mark of approbation from its opponents. . . . I venture somewhat further, and hesitate not to affirm that if the manner of it be not perfect, it is at least excellent.

• Many subsequent evaluations (and the many proposed constitutional amendments) suggest a less favorable assessment of the “mode of appointment of the Chief Magistrate,” i.e., the “Electoral College”:– part of a generally elitist and anti-democratic constitution; or– a last-minute jerry-built compromise; or perhaps– a well designed compromise among diverse considerations, or possibly– the embodiment of well-thought selection criteria.

Evaluating the Electoral College (cont.)

• My own take on the Electoral College:– The original EC was a compromise among diverse considerations

that was cleverly designed but had a fatal flaw that had to be (and was) corrected by constitutional amendment.

– The original EC established a selection system • that was designed to operate in a non-partisan environment, but• did not operate satisfactorily once political parties formed to contest

Presidential selection.– The EC was rapidly transformed into an institution quite different

from its designers had intended.• So, even if you like the existing EC, you can’t really give credit to “the

wisdom of the framers [of the Constitution].”• Likewise, even if you dislike the existing EC, you can’t really blame the

framers.– The transformed EC has proved to be a serviceable institution but

is problematic in a number of ways.

How the Electoral College Works in Practice

• Instead of electing a President (and Vice President) in a single national election,– there are 51 separate state (+ DC) elections,– the winner in each state wins a number of electoral votes equal

in number to the state’s total representation in Congress (total EV = 538), and

– electoral votes are added up to determine the winner of the election, with 270 required for election.

• The result of adding up electoral votes across the states may be different from adding up popular votes across the states (“election reversal”, “wrong winner”, “reversal of winners”), as was true in 2000.

Some Esoteric EC Details• At the present time, ME and NE do not award electoral votes on a

winner-take-all basis (but rather on the basis of a Modified District Plan), so their electoral votes may be split (though in fact this has never happened).

• Lurking beneath electoral votes are real people (elected officials) called Presidential electors.– Candidates may be deprived of electoral votes by “faithless

electors.”• Other methods of selecting Presidential electoral have been used in

the past, sometimes resulting in split electoral votes.• If no candidate wins 270 electoral votes, because either

– a third candidate wins some electoral voter or – there is a 269-269 tie,

the election is “thrown into the House of Representatives” (which last happened in 1824).

• “Unpledged electors” are sometimes elected (AL and MS in 1960).• There is “no constitutional right to vote for President.”

Designing The Original Electoral College

• The menu of options for Presidential selection:– selection by states,

• which would be too much like the Article Confederation;– selection by the Congress,

• which would make the President too dependent on Congress, but

• which was the “default option” found in both VA and NJ plans;

– selection by some kind of popular election• which presented many practical difficulties; or

– some kind of mixed system, which might distinguish between

• a first round of selection (“nomination”) and• a second round of selection (“election” or “runoff”), and • might use “intermediate electors.”

Designing The Original EC (cont.)

• The perceived advantages of an Electoral College of intermediate electors: – unlike Congress, the EC would perform a single task – i.e., cast

votes for President -- and would then disband, so• the President would be subservient to neither Congress nor the

Electoral College; and– unlike popular election, the EC

• avoided difficult questions about the extent of suffrage, and • allowed a compromise between the large vs. small states through its

fine details, and • and public opinion could be refined through representation.

• Since legislative election was the default choice, it is more accurate to say the framers settled on the EC– as an alternative to legislative election, rather than– as an alternative to popular election.

The Original Electoral College Rules

• Each state selects a number of “electors” equal in number to its total (House + Senate) representation in Congress (H + 2).

• The legislature of each state determines the mode of selection of the electors from its state, the most likely options being – election by the legislature itself,– popular election from districts, and– popular election on a state-wide general ticket.

• Congress has the power to determine – when electors are selected, and– when electors cast their votes (which must be the

same day for all states).– Originally, Congress gave the states a window of

about 30 days within which to select electors.

The Original Electoral College (cont.)• The “Electoral College” never meets as a group in one

place.– Rather electors meet and vote in their own state capitals

• Electors were originally required to– cast two votes for two different candidates, – at least one of whom had to be a resident of another state,– In effect, electors could vote for one “favorite son” but we required also

vote for at least one “national candidate.”• Once cast, the electoral votes are each are transmitted

to Congress,– to be counted before a joint session presided over by the President of

the Senate (Vice President of U.S.).• To be elected by the Electoral College, a candidate was

originally required to receive – votes from a majority of electors and – more votes than any other candidate.– Given the double vote system, these requirements were logically

distinct.• In particular, more that one candidate could receive the required

majority.

The Original Electoral College (cont.)• If no candidate meets both requirements, the election is

“thrown into the House of Representatives.”– The House chooses

• between the two (or more) tied candidates, in the event both (or all) received votes from a majority of electors, or

• (in the original EC) among the top five candidates, in the event no candidate received votes from a majority of electors.

– Voting in the House is by state delegation, with each delegation casting one vote.

– Balloting continues until some candidate is supported by a majority of state delegations.

• In any event, in the original EC, the runner-up Presidential candidate would become Vice President (an office that had never been previously discussed).– The framers evidently believed that a second prize was necessary

to induce electors to take their second votes seriously.

Expectations Concerning the Original EC

• This original Electoral College system was designed to operate in a non-partisan environment. – It therefore was expected that

• typically there would be many potential Presidential candidates, • who would not declare themselves as such, let alone actively

campaign for the office, and• electors would choose among these candidates on the basis of

their character and connections, not party affiliation or policy promises.

– Therefore, it was also expected that electoral votes would be widely scattered and the “House contingent procedure” would be used “19 times out of 20,” so

• big states would have the dominant role in “screening/nominating” candidates (in the EC), while

• small states would have equal role in most final/runoff elections (in the House).

Expectations Concerning the EC (cont.)

• It was generally hoped and expected that electors would typically be – popularly elected – from single-member districts (like most state

legislators, delegates to the state ratifying conventions, members of the British House of Commons, and as was expected also for members of the new U.S. House); and

– that they would be well-informed local notables who would act as representative trustees of their states and districts.

The Hazardous Game: President Selection under the Original Electoral College

• There were problems from the very start• In the very first election of 1789, it was generally agreed

that – George Washington should be the first President and– John Adams should be the first Vice President.

• Most or all electors were expected to cast one vote for Washington and one vote for Adams.

• Alexander Hamilton (who disliked Adams) was afraid that some New England electors would withhold votes from Washington, thereby making Adams president.– In anticipation of this, he urged some other electors to withhold

votes from Adams.• In fact, all electors voted for Washington but quite a few

did not vote for Adams,– so in fact the agreed upon “ticket” was elected.

Duverger’s Law and the Hazardous Game

• The framers’ expectations did not anticipate the development of a national two-party system.

• Duverger’s Law: Given politically ambitious candidates, single-winner elections produce (in equilibrium) two-candidate contests and sustain a two-party system.

• Given the early development of a two-party [Federalist vs. Republican] system, the combination of the double-vote and runner-up-is-VP provisions of the original Electoral College proved to be a fatal flaw.

The Hazardous Game:1796• The first contested Presidential election:

• Federalists: John Adams (MA) & Thomas Pickney (SC)• Republicans: Thomas Jefferson (VA) & Aaron Burr (NY)• They were “nominated” by their respective Congressional Caucuses. • Note the regionally balanced tickets.

– Intra-Federalist maneuvering:• Hamilton (continuing to feud with Adams) unsuccessfully urged some

Southern electors to vote for Pickney & anybody but Adams• However, some Northern electors learned about this and withheld

votes from Pickney.– The electoral vote outcome was very close:

• Federalists won 71 electors, all of whom voted for Adams, giving Adams the required majority of 70 for election as President.

• Republicans won 68 electors, all of whom voted for Jefferson.– But the withholding of second votes from Pickney lowered his vote total to

59, dropping him to third place behind Jefferson,• So the defeated Republican Presidential candidate became Vice

President.• Burr had only 30 votes

Lessons from the Hazardous Game

• Electors are expected to be party men,– i.e., “pledged electors.”– However, Samuel Miles (Fed. PA) violated his pledge.

• An angry Federalist supporter complained: “What, do I chuse Samuel Miles to determine for me whether John Adams or Thomas shall be President? No! I chuse him to act, not to think.”

• State legislative elections (perhaps coming a year or more in advance of Presidential elections), become very important for politicians with national ambitions, because– legislatures chose how to select electors and may

change the method from election to election; and– legislatures may choose to appoint the electors

themselves.

Lessons from the Hazardous Game (cont.)• A party that controls a state legislature may not want to

risk a popular election for electors.– States using legislative election increased to 10 in

1800.• And if a controlling party is confident it can win popular

election, the particular mode of popular election can be manipulated to short-term party advantage.

• Madison to Monroe (1800):– “All agree that an election by districts would be best if

it could be general, but while ten states choose either by their legislatures or by a general ticket, it is folly or worse for the other six not to follow.”

The Hazardous Game: 1800• Largely a repeat of 1796:

– same candidates; and– same battle lines.

• However, the strategic implications of the EC rules were better understood:– manipulation of elector selection; and– danger of withholding too many votes.

• The election of 1800 was as close as 1796 but tipped the other way.– Republicans won 73 electors vs. 65 for Federalists.– The Republicans (unlike the Federalists) failed to

withhold one “Vice Presidential” electoral vote.• Jefferson: 73 Pickney: 64• Burr: 73 Jay: 1• Adams: 65

The Hazardous Game: 1800 (cont.)• But the original EC rules did not distinguish between

“Presidential” vs. “Vice-Presidential” electoral votes.• So the election was “thrown into House,” under the

contingent procedure,– choosing between the tied candidates Jefferson and Burr only.– Burr did not chose to withdraw.

• Four electoral votes from GA had been improperly certified but the “intent of the voters” was clear (four votes for each of Jefferson and Burr).– Had they been disqualified as invalid, no candidate would have received the

required 70 electoral votes, in which case – the House could have chosen any of the five candidates as President.– But Jefferson, presiding over the counting of electoral votes, “counted

himself [and Burr] in.”• Note that the single Federalist elector who voted for Adams

and Jay could have voted for Adams and Burr,– in which case Burr would have immediately been elected President on the

basis of electoral votes (with no House election) and – Jefferson would have remained Vice President.

The Hazardous Game: 1800 (cont.)• Until 20th Amendment (1933), a newly elected Congress did not convene until

late in the year following Congressional elections. • So the 1800 Presidential election was thrown into the “lame duck” House

elected in 1798, which was still controlled by the Federalists (55-50), though Republicans would control the House elected in 1800.– There were 18 state delegations, so 10 votes were required for election.– Each delegation would decide how to vote by majority vote within the

delegation.• Republicans controlled 8 state delegations.• Federalists controlled 6 state delegations.• Two state delegation were equally split.

– Evidently, virtually all Republican representatives supported Jefferson as the intended Presidential candidate.

– Likewise, virtually all Federalist representatives supported Burr, in order to deny the presidency to more formidable Jefferson.

– The two internally tied delegations had to abstain.– For 35 ballots, the House deadlocked: Jefferson 8 and Burr 6 with 2

abstentions. – Ultimately, the four Federalists within in the tied delegations abstained,

resulting in Jefferson’s election on the 36th ballot.

The 12th Amendment• After the 1800 fiasco, Congress proposed, and the

states quickly ratified (in time for 1804 election), the 12th Amendment to the Constitution. – Electors now cast separate (single) votes for President and Vice

President.– The required electoral vote majority for President (and for Vice

President) is a simple majority of votes cast (= number of electors), which at most one candidate can achieve.

– If no candidate receives the required simple majority for President, the House (still voting by state delegations) chooses from among the top three [vs. top five] candidates.

– If no candidate receives the required majority for Vice President, the Senate (voting individually) chooses from among the top two candidates.

– Early drafts of the amendment included a requirement that electors be popularly elected from districts, but this provision was later dropped.

• The 12th Amendment remains the constitutional language governing Presidential elections.

The Transformation of the Electoral College

• By the 1830s, the Electoral College, already formally modified by the 12th Amendment, had been further transformed into the kind of (essentially) automatic popular vote counting system that exists today.

• This transformation – was driven largely by the development of a two-party

system, and– was brought about without any further constitutional

amendments or (with one minor exception) change in federal law,

– but rather by changes in state laws and party practice.

Elements of the Transformation (cont.)• In early elections, the mode of selecting Presidential

electors was regularly manipulated by party politicians in each state, on the basis of partisan calculations.

• By 1832, Presidential electors were almost universally selected by popular (vs. legislative) vote (and by much expanded electorates).– South Carolina was the lone hold out.

• By 1836, the mode of popular election in every state was (following Madison’s strategic advice) the general ticket (or party slate), rather than election from districts (or by some kind of proportional representation).– This induced the almost universal “winner-take-all” rule for the

casting electoral votes at the state level.– However, at the present time two small states (ME and NE) use

the “Modified District Plan.”

Mode of Elector Selection

Mode of Elector Selection (cont.)• Why were state legislatures willing to give up the power to select

Presidential electors?– The intensity of party competition declined after 1800.– Legislative appointment of electors was disrupting state legislative

elections.• cf. the willingness of state legislatures to ratify the 17th Amendment

(popular election of U.S. Senators)• Why did election of electors by districts give way to election of electors

at-large (usually on a slate or “general ticket”)?– Partisan strategic considerations,

• as expressed by Madison to Monroe in 1800.– More important: state strategic considerations.

• No matter what other states may do, each state could enhance its influence in Presidential politics by casting electoral votes on a winner-take-all basis.

• There is no “equilibrium” until all states use the winner-take-all method.• It turns out that this “equilibrium” results in a new balance of Electoral

College voting power that is much more favorable to the large states, much more than counterbalancing the small-state advantage in apportionment of electoral votes.

Bypassing the House Runoff

• Given the 12th Amendment and a two-party system, it is virtually assured that one or other Presidential (and Vice Presidential) candidate will receive the required majority of electoral votes.

• Thus the Electoral College system was transformed into something in two ways more favorable to large states than the Framers expected, i.e.,– not only do large states gain more power in the first

(electoral vote) stage (due to winner-take-all electoral votes), but also

– the second (House contingent election stage) stage (where small states have equal power) is almost always bypassed.

The Election 1824 and the Problem of Multi-Candidate Elections

• On this point, the election of 1824 (the second and last time an election was thrown into the House) is the “exception that proved the rule.”– The Federalist Party had collapsed and the Democratic-

Republican Party was unchallenged.– Consequently there was no longer pressure for D-Rs to unite

behind a single Presidential-Vice Presidential ticket.– Four candidates, all nominally belonging to the same D-R party,

sought the Presidency.– Unsurprisingly, no candidate received a majority of the electoral

votes and the election was thrown into the House.

The Election 1824 (cont.)

Presidential election results (“first round”): Electoral Votes Popular Votes*

Jackson 99 41% Adams 84 31% Crawford 41 11% Clay 37 13% Others 0 4%*Bear in mind that six states still appointed electors and that states that used

popular election varied considerably with respect to the extent of franchise.

• The compromise candidate Clay (most everyone’s second choice) was squeezed out of third place in the electoral vote ranking by Crawford.

• Under the 12th Amendment, the House could chose only from among top three candidates.

The Election of 1824 (cont.)• Clay probably would have been elected president

– if the House could still chose among the top five candidates; or– if Crawford had not been a candidate (Crawford was a spoiler to

Clay).• Even if Adams or Jackson had won all the electoral votes cast for

Crawford, Clay would have been among top three candidates.• However, if Jackson had won at least 32 of Crawford’s electoral

votes, Jackson would have been elected without a House runoff.• Clay had great influence in the House.

– He detested Jackson and endorsed Adams.• Adams (just) won on the first ballot (24 state

delegations):• Adams 13• Jackson 7• Crawford 4

– Adams subsequently appointed Clay Secretary of State.– Jackson and his supporters denounced the “corrupt bargain” between

Adams and Clay.

House Runoff (cont.)• Whenever there is a “serious” third-party ticket (especially

one with a geographical base of support such that it may win electoral votes), the possibility arises that the election may be thrown into the House arises.

• Moreover, since the 23rd Amendment (giving the District of Columbia three electoral votes) was ratified in 1961, the total number of electoral votes has been an even number (538), – so a 269-269 electoral vote tie is possible, and– an election might be thrown into the House even in the absence of

a third-party candidate winning election votes.

• Prior to the 1825 House election, the House adopted special rules for its conduct.– These rules remain in effect and would (presumably) by used in

any future House election.

The EC as a Vote-Counting Mechanism

• In 1845 Congress established a uniform nationwide Presidential election day (i.e., day for selecting Presidential electors), namely– the Tuesday after the first Monday in November.

• On November 4, 2008, voters in each state will go to the polls and vote for either the Democratic or Republican (or possibly some other) slate of elector candidates, who are pledged to their party’s (Pres. + VP) nominees. – With popular election of slates of pledged electors, American

voters may be forgiven for thinking they are actually voting directly for a Presidential-Vice Presidential ticket.

• Often only fine print on the ballot indicates otherwise– and in some states not even that.

Vote-Counting Mechanism (cont.)• In each state, the elector slate receiving the most votes is elected

(with the possible exceptions noted for ME and NE).• The electors will meet in their state capitals in mid-December and

cast their electoral votes as pledged.• Electoral vote tallies will be transmitted from each state capital to

Congress and will be counted before a joint session on January 5, 2009.

• The President of the Senate [Vice President Cheney] will announce the votes for President and Vice President and proclaim that ?? and ?? are the President-elect and Vice President-elect.

• So (almost certainly) everything will be determined on election night in November, and the remaining steps are merely ceremonial; that is, TV prognosticators can– report the popular vote winner in each state,– add up the corresponding electoral votes, and– declare a President-elect.

SupplementarySlides

(Alleged) Problems with the EC

• The Voting Power Problem. Does the EC give voters in different states [member nations] unequal voting power?– If so, the EC [EU] violates the criterion of “One Person, One Vote” (OPOV).– Which voters are favored and which disfavored and by how much?

• The Election Reversal Problem. The candidate who wins the most popular votes nationwide may fail to be elected.– The election 2000 provides an example (provided we take the official

popular vote in FL at face value).• The Partisan Bias Problem. Does the EC as a vote counting system

favor one party over the other (at the present time or in times past)?– This is closely connected with the Election Reversal Problem.

• The Battleground States Problem. The Electoral College focuses the Presidential election contest on a few “battleground states,” which get very disproportionate attention from the candidates and parties.– This is loosely connected with the Voting Power Problem.

• Other Problems -- mere vote-counting may fail.– What if electors violate their pledges?– What about the House contingent procedure?– Americans have “no constitutional right to vote for President.”

The Apportionment of Electoral Votes

• The apportionment of electoral votes produces a systematic and substantial small-state advantage in the apportionment of electoral votes relative to the apportionment population.– This is the basis of the argument that the Electoral College

advantages voters in smaller (rural, more conservative, etc.) states.

• The magnitude of this small-state apportionment advantage is not fixed in the Constitution.– It varies (inversely) with the size of the House (relative to the

Senate), which is determined by Congress.– If the House had been sufficiently larger than 435, Gore would

have won the 2000 election (even while losing Florida).

The Small-State Apportionment Advantage

EC Variants: The Apportionment of Electoral Votes

• Keep the winner-take all practice [in 2000, Bush 271, Gore 267; in 2004, Bush 286, Kerry, 252] but use a different formula to apportioning electoral votes among states (All require a constitutional amendment.)

– Apportion electoral votes [in whole numbers] on basis of House seats only] [Bush 211, Gore 225; Bush 224, Kerry 212]

• Apportion electoral votes [fractionally] precisely proportional to population [Bush 268.96092, Gore 269.03908; Bush 275.67188, Kerry 262.32812]

Translated outcomes take account of Duverger’s “mechanical effects” only (vs. “psychological/strategic effects”)

EC Variants: The Apportionment of Electoral Votes (cont.)

• Apportion electoral votes [fractionally] to be precisely proportional to population but then add back the “constant two” [Bush 277.968, Gore 260.032; Bush 285.407, Kerry 252.593]

• Apportion electoral votes equally among the states [in the manner of the House contingent procedure] [Bush 30, Gore 21; Bush 31, Kerry 20]

– National Bonus Plan: 538 electoral votes are apportioned and cast as at present but an additional bloc of electoral votes [e.g., 100] are awarded on a winner-take-all basis to the national popular vote winner. [Bush 271, Gore 367; Bush 386, Kerry 252]

EC Variants: The Casting of Electoral Votes

• Apportion electoral votes as at present but use something other than winner-take-all for casting state electoral votes. (Some can be adopted on a state-by-state basis.) All are likely to produce splits in state electoral votes.

– Pure District Plan: select electors from single-member districts (as originally expected), so each electoral vote is cast for the district winner.

– Modified District Plan: select the two “Senate electors” statewide and the “House electors” by district [probably CDs -- present NE and ME practice]. [Bush 289, Gore 249; I don’t have good data for 2004]

EC Variants: The Casting of Electoral Votes (cont.)

– Pure Proportional Plan: electoral votes are cast [fractionally] in precise proportion to state popular vote. [Bush 259.2868, Gore 258.3364, Nader 14.8100, Buchanan 2.4563, Other 3.1105; Bush 277.857, Kerry 260.143 (excluding minor candidates)] (implies doing away with electors as individuals)

– Whole Number Proportional Plan [e.g., Colorado Prop. 36]: electoral votes are cast in whole numbers on the basis of some (PR-style) apportionment formula applied to each state’s popular vote. [Bush 263, Gore 269, Nader 6, or Bush 269, Gore 269; Bush 280, Kerry 258]

The Popular Vote Alternative to the EC• Elect the President and Vice President on the basis the popular vote

of the nation as a whole.– Requires national election administration, voter qualifications and

registration, ballot access rules, etc.?– Runoff requirement? With what threshold?

• Supplementary vote [like London mayor], IRV etc.?

• To bypass the constitutional amendment process, adopt the National Popular Vote Plan,– to be effected by interstate compact (which requires the consent of

Congress but not a constitutional amendment).– The states in the compact pledge to cast their electoral votes for the

national popular vote winner.– Problems:

• There is no official “national popular vote winner.”• The Plan largely ignores general popular vote problems noted

above.• Would the compact hold in an election like 2000 (i.e., in which there

would be an election reversal if the EC operated in the normal manner)?

Individual Voting Power Under the Existing EC

“House Electoral Votes” Only

Electoral Votes Precisely Proportional to Population

EVs Precisely Proportional to Population, plus Two

Electoral Votes Apportioned Equally Among States(or House Contingent Procedure)

Individual Voting Power under Alternative Rules for Casting Electoral Votes

• Calculations for the Pure District Plan, Pure Proportional Plan, and the Whole-Number Proportional Plan are straightforward.

• Under the Modified District Plan (or National Bonus Plan), each voter casts a single vote that counts two ways:– within the district (or state) and – at-large (i.e., within the state or nation).

• Calculating individual voting power in such systems is far from straightforward.

• I am in the process of working out approximations based on very large samples of Bernoulli elections.

Pure District System

Modified District System (Approximate)

A Unilateral Move From Winner-Take-All to the (Pure) District System

• In the mid-1990s, the Florida state legislature seriously considered switching to the Modified District Plan.

• The effect of such a switch on the individual voting power is shown in the following chart.– However, I assume a switch to the Pure District Plan, because

this can be directly calculated. – Madison’s earlier strategic advice is powerfully confirmed,

• though the voting-power consideration is logically distinct from the party-advantage consideration Madison had in mind.

– Another point also arises: considering “mechanical” effects only, if Florida had made the switch, Gore would have been elected President (regardless of the statewide vote in Florida).

• Even if a district system is universally agreed to be socially superior (as Madison considered it), states will not voluntary choose to move that direction. – States are faced with a “Prisoners’ Dilemma.”

(Pure) Pure Proportional System

The Whole-Number Proportional Plan• This plan divides a state’s electoral votes between (or among) the

candidates in a way that is as close to proportional to the candidates’ state popular vote shares as possible, given that the apportionment must be in whole numbers.– Unlike the (Pure) Proportional Plan, whole-number proportionality

allows for the retention of electors.– Accordingly, it is the only proportional plan that can be

implemented at the state level (as Colorado Prop. 36 proposed).– Colorado Proposition 36 used a distinctly ad hoc apportionment

formula. • But, in the event there are just two candidates (as in Bernoulli

elections), all apportionment formulas work in the same straightforward way:– multiply each candidate’s share of the popular vote by the state’s

number of electoral votes, and then – round off in the normal manner.

• The following chart shows that this plan produces a truly bizarre distribution of voting power.

Whole-Number Proportional Plan

Similar calculations and chart were produced, independently and earlier, by Claus Beisbart and Luc Bovens, “A Power Analysis of the Amend-ment 36 in Colorado,” University of Konstanz, May 2005, and Public Choice, March 2008.

National Bonus Plan(s)

Individual Voting Power: Summary Chart

Election Reversals• Any districted electoral system can produce an election

reversal. – That is, the candidate or party that wins the most

popular votes nationwide may fail to win the most parliamentary seats or electoral votes (and may therefore lose the election).

– Such outcomes are actually more common in some parliamentary systems than in U.S. Presidential elections.

• The U.S. Electoral College has produced three manifest election reversals (though all were very close) outcomes).– But the mother of all EC election reversals is not

usually recognized as such.

EC Election Reversals Election Winner Runner-up Winner’s 2-P PV

2000 271 [Bush (R)] 267 [Gore (D)] 49.73%1888 233 [Harrison (R)] 168 [Cleveland (D) 49.59% 1876 185 [Hayes (R)] 184 [Tilden (D)] 48.47%

• The 1876 election was decided (on inauguration eve) by

a Electoral Commission that, by a bare majority and on a straight party line vote, awarded all of 20 disputed electoral votes to Hayes. – Unlike Gore and Cleveland, Tilden won an absolute majority

(51%) of the total popular vote.• Note that, of the two undoubted “wrong winner”

elections, 1888 was “worse” than 2000 in that, while the (relative) popular vote margins were about the same, Bush won with the smallest electoral vote margin since 1876, while Harrison won quite decisively in the Electoral College.

The 1860 ElectionCandidate Party Pop. Vote % EV

Lincoln Republican 39.82 180Douglas Northern Democrat 29.46 12Breckinridge Southern Democrat 18.09 72Bell Constitutional Union 12.61 39

Total Democratic Popular Vote 47.55Total anti-Lincoln Popular Vote 60.16

• It may appear that Douglas and Breckinridge were spoilers against each other (like the rival Republicans Taft and Roosevelt in 1912).

• Under a direct popular vote system, this would have been true.• But under the Electoral College system, Douglas and Breckinridge

were not spoilers against each other.

A Counterfactual 1860 Election• Suppose the Democrats could have held their Northern

and Southern wings together and won all the votes captured by each wing separately.– Suppose further that it had been a Democratic vs. Republican straight

fight and that the Democrats had also won all the votes that went to Constitutional Union party.

– And for good measure suppose that the Democrats had won all NJ electoral votes (which for peculiar reasons were actually split between Lincoln and Douglas).

• Here is the outcome of the counterfactual 1860 election:

Party Pop. Vote % EV

Republican 39.82 169Democratic 60.16 134

• We will return to the 1860 election.

An Empirical Approach to the Analysis of Election Reversals

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”).

Uniform Swing AnalysisOf all the states that Dukakis carried,

he carried Washington (10 EV) by the smallest margin of 50.81%.If the Dukakis popular vote of

46.10% were (hypothetically) to decline by 0.81% uniformly across all states (to 45.29%), WA would tip out of his column (reducing his EV to 102).

Of all the states that Dukakis failed carry, he came closest to carrying Illinois (24 EV) with 48.95%. If the Dukakis popular vote of

46.10% were (hypothetically) to increase by 1.05% uniformly across all states (to 47.15%), IL would tip into his column (increasing his EV to 136).

The PVEV Step Function for 1988

PVEV and Election Reversals

Zoom into Critical Region: Reversal Interval from 50.00% to 50.08%

The Election Reversal Interval in 1988

• We see that, given the “electoral landscape” revealed in the actual state-by-state votes in 1988, 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 an election reversal if (under the uniform swing assumption) Dukakis had received between 50.0000% and 50.0765% of the popular vote.

Magnitude and Direction of Election Reversal Intervals

First Source of Possible Election Reversals• This PVEV visualization makes it evident that there are

two distinct ways in which election reversals may occur. • First, an election reversal may occur as a result of the

(non-systematic) “rounding error” (so to speak) necessarily entailed by the fact that the PVEV function moves up and down in discrete steps. – In this event, a particular electoral landscape may allow a wrong

winner of one party only but small perturbations of that landscape would allow a wrong winner of the other party.

• The 1988 chart (and similar charts for all recent elections [including 2000]) provides a clear illustration of a possible election reversal due to “rounding error” only.– So if the election had been much closer (in popular votes) and

the electoral landscape slightly perturbed, Dukakis might have been a wrong winner instead of Bush.

A Sample of 32,000 Simulated Elections Based on the 2004 Electoral Landscape

2000 vs. 1988

• The only real difference between the 2000 and 1988 (or 2004 and other recent) elections is that it was much closer.

– The election reversal interval was (in absolute terms) hardly larger in 2000 than in 1988:

• DPV 50.00% to 50.08% in 1988• DPV 50.00% to 50.27% in 2000

– But the actual DPV was 50.267%, i.e., (just) within the reversal interval.

Second Source of Possible Election Reversals• Second, an election reversal may occur as result of

(systematic) asymmetry or bias in the general character of the PVEV function. – In this event, small perturbations of the electoral

landscape will not change the partisan identity of potential wrong winners.

• In times past (e.g., in the New Deal era and earlier), there was a clear asymmetry in the PVEV function that resulted largely from the electoral peculiarities of the old “Solid South,” in particular,– its overwhelmingly Democratic popular vote

percentages, combined with– its strikingly low voting turnout.

Two Distinct Sources of Bias in the PVEV

• Asymmetry or bias in the PVEV function can results from two distinct phenomena:

• distribution effects.• apportionment effects; and

– Either effect alone can produce a reversal of winners, and they can either reinforce or counterbalance each other.

Apportionment Effects• A perfectly apportioned districted electoral system is one

in which each state’s 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 vote if and only if it wins states with X% of the total popular vote.– Note that this says nothing about the popular vote margin by

which the party/candidate wins (or loses) states.– Therefore this does not say that the party wins X% (or any other

specific %) of the popular vote.

• An electoral system cannot 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 state’s 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 Natapoff’s perfectly apportioned system.

– Natapoff’s 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, for many reasons. – 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.• All these factors vary considerably from state to state (and district to

district).– House seats (and electoral votes) must be apportioned in whole

numbers and therefore can’t be precisely proportional to anything.

– Small states are guaranteed a minimum of three electoral votes.

Imperfect Apportionment (cont.)• Similar imperfections apply (in lesser or greater degree)

in all districted systems.

• Imperfect apportionment may or may not bring about bias in the PVEV function.– This depends on the extent to which states (districts)

having greater or lesser weight than they would have under perfect apportionment is correlated with their support for one or other candidate or party.

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 candidate’s or party’s vote may be more “efficiently” distributed than the other’s, causing an election reversal 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 VotesD 5 1R 4 2

R’s votes are more efficiently distributed, so R wins a majority of electoral votes with a minority of popular 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 (uniform) districts or in non-uniform 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.

• The elections reversal interval is (just short of) 25 percentage points wide.

• If the candidate or party with the favorable vote distribution is also favored by imperfect apportionment, the reversal interval could be winners could be even more extreme.

Distribution Effects (cont.)

• The Pure Proportional Plan for the Electoral College would entirely eliminate distribution effects.

• Election reversal could still occur due to apportionment effects– The reversals would favor candidates 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 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.

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

would have been even greater in the absence of the countervailing apportionment effects.

• If the most salient characteristic of the Electoral College is that it may produce election reversals, one’s evaluation of the EC may depend on whether one thinks Lincoln should have been elected President in 1860.