Cumulative voting (also
accumulation voting or
weighted voting) is a multiple-winner
voting systemA voting system or voting theory, allows voters to choose between options, often in an election where candidates are selected for public office. Voting can be also used to award prizes, to select between different plans of action, or by a computer program to find a solution to a problem...
intended to promote
proportional representationProportional representation , sometimes referred to as full representation, is a category of electoral formula aimed at securing a close match between the percentage of votes that groups of candidates obtain in elections and the percentage of seats they receive...
while also being simple to understand.
History
Cumulative voting is used frequently in corporate governance, where it is mandated by many U.S. states, and it was used to elect the
Illinois House of RepresentativesThe Illinois House of is the lower house of the Illinois General Assembly, the state legislature of the U.S. state of Illinois. The body was created by the first Illinois Constitution adopted in 1818. The state House of Representatives is made of 118 representatives elected from individual...
from 1870 until its repeal in 1980. It was used in England in the late 19th century to elect school boards. Currently, some communities in the United States use cumulative voting, all resulting from consent decrees in cases brought under the federal Voting Rights Act. Among them are
Peoria, IllinoisPeoria is the largest city on the Illinois River and the county seat of Peoria County, Illinois, in the United States. As of the 2000 census, the city was the fifth-largest in Illinois, with a population of 112,936; by 2007 it was the sixth-largest city and had population of 113,546...
for half of its city council, Chilton County, Alabama for its county council and school board, and
Amarillo, TexasAmarillo is the 14th-largest city in the U.S. state of Texas, the largest in the Texas Panhandle, and the seat of Potter County. A portion of the city extends into Randall County. The population was 173,627 at the 2000 census. The Amarillo metropolitan area has an estimated population of...
for its school board and College Board of Regents . Courts sometimes mandate its use when they deem it necessary to provide fair representation; an example of this occurred in
Worcester CountyWorcester County is the easternmost county located in the U.S. state of Maryland. The county contains the entire length of the state's Atlantic coast line. It is home to the popular vacation resort area of Ocean City. It was named for an Earl of Worcester. Its county seat is Snow Hill...
, although no court-ordered ruling has ultimately resulted in a jurisdiction adopting cumulative voting.
Voting
A cumulative voting election elects the top vote-getters, just as with a simple
pluralityThe plurality voting system is a single-winner voting system often used to elect executive officers or to elect members of a legislative assembly which is based on single-member constituencies....
election. However, voters are allowed to concentrate their full share of votes on fewer candidates than seats -- unlike
bloc votingPlurality-at-large voting, commonly referred to as block voting or bloc voting, is a voting system for electing several representatives from a single multimember electoral district using a series of check boxes and tallying votes similar to a plurality election...
, where a voter can only award one vote per candidate, up to the number of candidates as seats. With cumulative voting, voters are permitted to not split their votes and instead concentrate them on a single candidate at full value.
Ballots used for cumulative voting differ both in the ways voters mark their selections and in the degree to which voters are permitted to split their own vote. Possibly the simplest ballot uses the
equal and even cumulative voting method, where a voter simply checks off preferred candidates, as in bloc voting, and votes are then automatically divided evenly among those preferred candidates. Voters are unable to specify a differing level of support for a more preferred candidate, giving them less flexibility although making it tactically easier to support a slate of candidates.
A more common and slightly more complex cumulative ballot uses a
points method. Under this system, voters are given an explicit number of points (often referred to as "votes" because in all known cases those number of points equals the number of seats to be elected) to distribute amongst candidates on a single ballot. Typically, this is done with a voter making a mark for each point beside the desired candidate. A similar method is to have the voter write in the desired number of points next to each candidate. This approach is commonly used for corporate elections involving a large number of points on a given ballot, where the voter is given one set of points for each votable share of stock he has in the company. Unless an appropriately programmed electronic voting system is used, however, this write-in ballot type burdens the voter with ensuring that his point allocations add up to his allotted sum.
In typical cumulative elections using the points system, the number of points allotted to a voter is equal to the number of winning candidates. This allows a voter to potentially express some support for all winning candidates, however this need not be required to achieve proportional representation; with only one point the system becomes equivalent to a
single non-transferable voteThe single non-transferable vote or SNTV is an electoral system used in multi-member constituency elections.- Voting :In any election, each voter casts one vote for one candidate in a multi-candidate race for multiple offices. Posts are filled by the candidates with the most votes...
.
Other than general
egalitarianEgalitarianism has two distinct definitions in modern English. It is defined either as a political doctrine that holds that all people should be treated as equals and have the same political, economic, social, and civil rights or as a social philosophy advocating the removal of economic...
concerns of electoral equality, there is nothing in this system that requires each voter to be given the same number of points. If certain voters are seen as more deserving of influence, for example because they own more shares of stock in the company, they can be directly assigned more points per voter. Rarely, this explicit method of granting particular voters more influence is sometimes advocated for governmental elections outside of corporate management, perhaps because the voters are members of an oppressed group; currently, all governmental elections with cumulative voting award equal numbers of points for all voters.
Unlike choice voting where the numbers represent the order of a voter's ranking of candidates (i.e. they are
ordinal numberIn set theory, an ordinal number, or just ordinal, is the order type of a well-ordered set. They are usually identified with hereditarily transitive sets. Ordinals are an extension of the natural numbers different from integers and from cardinals...
s), in cumulative votes the numbers represent quantities (i.e. they are
cardinal numberIn mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number – the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite...
s).
If each voter has the same number of points then typically the number of votes would be equal to the number of winners, although there is no reason why this should be required. If each voter is given just one point then the system becomes identical to a
single non-transferable voteThe single non-transferable vote or SNTV is an electoral system used in multi-member constituency elections.- Voting :In any election, each voter casts one vote for one candidate in a multi-candidate race for multiple offices. Posts are filled by the candidates with the most votes...
; with one point and one winner it is first past the post.
While giving voters more points may appear to give them a greater ability to graduate their support for individual candidates, it is not obvious that it changes the democratic structure of the method.
The most flexible ballot (not the easiest to use) allows a full vote to be divided in any fraction among all candidates, so long as the fractions add to less than or equal to 1. (The value of this flexibility is questionable since voters don't know where their vote is most needed.)
Advocates of cumulative voting often argue that political and racial minorities deserve better representation. By concentrating their votes on a small number of candidates of their choice, voters in the minority can win some representation -- for example, a like-minded grouping of voters that is 20% of a city would be well-positioned to elect one out of five seats. Both forms of cumulative voting achieve this objective.
In a corporate setting, challengers of cumulative voting argue that the board of directors get divided and this hurts the company's long term profit.
Robert's Rules of Order Newly Revised, which asserts a principle that the majority should have the right to make all decisions, states, "A minority group, by coordinating its effort in voting for only one candidate who is a member of the group, may be able to secure the election of that candidate as a minority of the board. However, this method of voting, which permits a member to transfer votes, must be viewed with reservation since it violates a fundamental principle of parliamentary law."
Voting systems criteria
Comparative academic analysis of voting systems usually centers on certain voting system criteria.
Cumulative voting satisfies the
monotonicity criterionThe monotonicity criterion is a voting system criterion used to analyze both single and multiple winner voting systems. A voting system is monotonic if it satisfies one of the definitions of the monotonicity criterion, given below.Douglas R...
, the
participation criterionThe participation criterion is a voting system criterion for evaluating voting systems and is also known as the No show paradox. It has been defined as follows:...
, the
consistency criterionA voting system is consistent if, when the electorate is divided arbitrarily into two parts and separate elections in each part result in the same choice being selected, an election of the entire electorate also selects that alternative...
, the
plurality criterionPlurality criterion is a voting system criterion devised by Douglas R. Woodall for ranked voting methods with incomplete ballots. It is stated as follows:...
, and
reversal symmetryReversal symmetry is a voting system criterion that is stated as follows: If a candidate A is the unique winner, and the individual preferences of each voter are inverted, then candidate A must not be elected. Methods that satisfy reversal symmetry include Borda count, the Kemeny-Young method, and...
. Cumulative voting does not satisfy
independence of irrelevant alternativesIndependence of irrelevant alternatives is a term for an axiom of decision theory and various social sciences. Although exact formulations of IIA differ, intentions of the usages are similar in attempting to provide a rational account of individual behavior or aggregation of individual...
,
later-no-harm criterionThe later-no-harm criterion is a voting system criterion formulated by Douglas Woodall. The criterion is satisfied if, in any election, a voter giving an additional ranking or positive rating to a less preferred candidate cannot cause a more preferred candidate to lose.- Complying methods :Single...
nor the
Condorcet criterion.
Usage
The
Norfolk Legislative AssemblyThe Norfolk Legislative Assembly is the prime legislative body of Norfolk Island. Formed after The Norfolk Island Act was passed in the Australian parliament, its first members were elected on the tenth of August, 1979 . The current assembly is the 11th, and was elected on the 20th of October,...
is elected using a form of cumulative voting where voters cannot give all their votes to one candidate. It is also used heavily in
corporate governanceCorporate governance is the set of processes, customs, policies, laws, and institutions affecting the way a corporation is directed, administered or controlled. Corporate governance also includes the relationships among the many stakeholders involved and the goals for which the corporation is...
, where it is mandated by many U.S. states, and it was used to elect the
IllinoisIllinois , the 21st state admitted to the United States of America, is the most populous and demographically diverse Midwestern state and the fifth most populous state in the nation...
House of Representatives from 1870 until 1980. It was used in
EnglandEngland is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west and the North Sea to the east, with the English Channel to the south separating it from continental...
in the late 19th century to elect school boards. Starting in the late 1980s's, it has been adopted in a growing number of jurisdictions in the United States, in each case to resolve a lawsuit brought against bloc voting systems.
With strategic voting, one can calculate how many shares are needed to elect a certain number of candidates, and to determine how many candidates a person holding a certain number of shares can elect.
The formula to determine the number of shares necessary to elect a majority of directors is:
where
- X = number of shares needed to elect a given number of directors
- S = total number of shares at the meeting
- N = number of directors needed
- D = total number of directors to be elected
The formula to determine how many directors can be elected by a faction controlling a certain number of shares is:
with
N becoming the number of directors which can be elected and
X the number of shares controlled. Note that several sources include a variation of this formula using "X" rather than "(X-1)". Such a formulation does not assure you of having enough votes to elect a director if the "-1” is missing. Without the "-1" you will only be able to determine how many shares you must have to tie, not what you need to win. Of course not every shareholder votes perfectly every time, so the flawed formula may work in many practical instances despite it being conceptually flawed and mathematically wrong.
This is equivalent to the
Droop quotaThe Droop Quota is the quota most commonly used in elections held under the Single Transferable Vote system. It is also sometimes used in elections held under the largest remainder method of party-list proportional representation . In an STV election the quota is the minimum number of votes a...
for each seat desired.
A simple cumulative-voting calculator appears at sbbizlaw.com, which eliminates the need for formulas and fractions. The reader can enter the number of shares voting; the readout states the number of directors the reader can elect, and vice versa. By entering the number of directors to be elected, the reader can find the number of shares necessary to elect one or any specified number of directors.
Tactical voting
Tactical votingIn voting systems, tactical voting occurs, in elections with more than two viable candidates, when a voter supports a candidate other than his or her sincere preference in order to prevent an undesirable outcome.It has been shown by the Gibbard-Satterthwaite theorem that any voting method which is...
is the rational response to this system. The strategy of voters should be to balance how strong their preferences for individual candidates are against how close those candidates will be to the critical number of votes needed for election. Voters typically award most, if not all, of their votes to their most preferred candidate. When seeking to help elect more than one candidate, voters may choose to spread their votes evenly between or among those candidates.
Some supporters of the
single transferable voteThe Single transferable vote is a system of preferential voting designed to minimize "wasted" votes and provide proportional representation while ensuring that votes are explicitly expressed for individual candidates rather than for party lists...
method describe STV as a form of Cumulative voting with fractional votes. The difference is that the STV method itself determines the fractions based on a rank preference ballot from voters and interactions with the preferences of other voters. Furthermore, the ranked choice feature of the STV ballot makes it unlikely that voters might split their votes among candidates in a manner that hurts their interests; with cumulative voting, it is possible to "waste" votes by giving some candidates more votes than necessary to win and by dividing votes among multiple candidates such that none of them win.
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