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Cumulative voting (also accumulation voting, weighted voting or multi-voting) is a multiple-winner method intended to promote more proportional representation than winner-take-all elections such as block voting or first past the post. Cumulative voting is used frequently in corporate governance, where it is mandated by some (7) U.S. states [1] (see, e.g., Minn. Stat. Sec. 302A.111 subd. 2(d)).
Cumulative voting was used to elect the Illinois House of Representatives [2] from 1870 until its repeal in 1980 [3] [4] [5] and used in England and Scotland in the late 19th century to elect some school boards. As of March 2012, more than fifty communities in the United States use cumulative voting, all resulting from cases brought under the National Voting Rights Act of 1965. Among them are Peoria, Illinois for half of its city council, Chilton County, Alabama for its county council and school board, and Amarillo, Texas, for its school board and College Board of Regents. [6] Courts sometimes mandate its use as a remedy in lawsuits brought under the Voting Rights Act in the United States; an example of this occurred in 2009 in Port Chester, New York, [7] [8] which had its first cumulative voting elections for its board of trustees in 2010. [9]
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| A points method ballot design like this one is the most common for governmental elections using cumulative voting. Voters are typically instructed to make only one mark per column. | ||
Cumulative voting was also used to elect city boards in Toronto, Canada starting in 1903. The Proportional Representation Review (September 1903) described it like this:
Cumulative voting as applied to the Board of Control, means that each elector will have four votes but that he need not give each of them to a different candidate. He may do so if he wishes; but he has also the power to give all his four votes to one candidate. This makes "plumping" four times as powerful as it was by the old "block" vote system, when if you "plumped" for one candidate, you threw away three out of your four votes. Now you have the benefit of your full voting power, whether you plump or not. And plumping is the correct thing; in fact proportional representation is simply effective representation with the addition in the best systems of a provision for transfer of votes, so as to prevent wasting too many on one candidate...
Besides permitting an elector to give all four votes to one candidate, the cumulative plan enables him to give two of his votes to one candidate and two to another, or he may give three votes to one candidate and his fourth to another candidate. In fact he may distribute or cumulate his four votes as he pleases....
If one-fourth of the voters give all their votes to one candidate, they can elect him, no matter what the other three-fourths choose to do.... (Thus Cumulative Voting if used carefully allowed for minority representation.) [10] [ unreliable source? ]
A form of cumulative voting has been used by group facilitators as a method to collectively prioritize options, for example ideas generated from a brainstorming session within a workshop. This approach is described as "multi-voting" and was likely derived from the nominal group technique and is one of many tools suggested within the Six Sigma business management strategy. [11]
Cumulative voting is used in elections where more than one seat is filled. It permits voters to cast multiple votes, as many as the number of seats to be filled, allows each voter to put more than one vote on a preferred candidate. When voters in the minority concentrate their votes in this way for just one candidate, it increases their chances of obtaining representation in a legislative body. This is different from bloc voting, where a voter may not vote more than once for any candidate and the largest single block, even if less than 50 percent, can control all the representation elected in the district.
Cumulative voting systems differ both in the ways voters mark their selections and in the degree to which voters are permitted to split their votes. Possibly the simplest ballot uses the equal and even cumulative voting method, where a voter simply marks preferred candidates, as in bloc voting, and votes are then automatically distributed 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 voting system uses a points method. Under this method, voters are given an explicit number of points, often referred to as "votes." (In most governmental elections held today, the number of points (votes) that each voter can cast equals the number of seats to be elected, although this is not a hard and fast rule historically; under Limited Voting voters cast fewer votes than the number of seats to fill.) Voters then distribute their points amongst one or more candidates on the 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 latter 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. However, it should not be necessary that a voter use up all his allotment. It is more important that voting systems not allow the voter's allotted sum to be exceeded.
When used as a facilitation technique for group decision-making this process is often called “multi-voting”. [12] Participants are given stickers or points which they can apply among a list of options; often these are ideas that were generated by the group. Because dot stickers are commonly used for multi-voting, the process is also often called dot voting. [13]
In typical cumulative elections using the points method, the number of points allotted to a voter is equal to the number of winning candidates (seats to be filled). This allows a voter potentially to express some support for all winning candidates; however, this need not be required to achieve proportional representation. If many voters each lump their votes just on one candidate, the method becomes equivalent to a single non-transferable vote system where a voter has just one vote in a multi-member district.
Other than general egalitarian concerns of electoral equality, there is nothing in the CV method 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 advocated for governmental elections outside 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 ranked voting where the numbers represent the order of a voter's ranking of candidates (i.e. they are ordinal numbers), in cumulative voting the numbers represent quantities (i.e. they are cardinal numbers). Under Cumulative voting, votes are not transferrable and if placed on different candidates may actually work against each other.
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. All forms of cumulative voting achieve this objective (although if two or more candidates of that minority run in the same election, vote splitting may deny the group its possible representation).
In a corporate setting, challengers of cumulative voting argue that the board of directors gets divided and this hurts the company's long term profit. Using a staggered board of directors can diminish the ability of minority factions to obtain representation by reducing the number of seats up for election at any given time. [14]
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 member of the board. However, this method of voting, which permits a member to cast multiple votes for a single candidate, must be viewed with reservation since it violates a fundamental principle of [US] parliamentary law that each member is entitled to one and only one vote on a question." [15]
Comparative academic analysis of voting methods usually centers on certain voting method criteria.
Cumulative voting satisfies the monotonicity criterion, the participation criterion, the consistency criterion, and reversal symmetry. Cumulative voting does not satisfy independence of irrelevant alternatives, later-no-harm criterion nor the Condorcet criterion. It does not satisfy the plurality criterion. The 11th edition of Robert's Rules of Order Newly Revised states, [16] "If it is desired to elect by mail, by plurality vote, by preferential voting, or by cumulative voting, this must be expressly stated, and necessary details of the procedure should be prescribed (see 45)." (Emphasis added). Robert's Rules describes the cumulative voting process. [17] It provides that, "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 member of the board." (Emphasis added). Thus, cumulative voting, when permitted, is a right to accumulate or stack votes but not a guarantee that this stacking will meet or override other election criteria such as a majority vote or majority present.
The Norfolk Island Legislative Assembly on Norfolk Island was elected using a form of cumulative voting where voters cannot give all their votes to one candidate. It is also used heavily in corporate governance, where it is mandated by seven U.S. states, and it was used to elect the Illinois House of Representatives from 1870 until 1980. [2] [3] It was used in England between 1870 and 1902, under the Elementary Education Act 1870, to elect school boards. Starting in the late 1980s, 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 methods. [18]
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
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. This inequality is correct under all circumstances. Under most reasonable circumstances, however, an approximation may be used to the value for N, by reducing the number of shares by 1:
This approximation addresses the case where the right side of the inequality is an integer. By reducing the number of shares by one, the number of directors is reduced in the equation compared to the inequality. Under reasonable circumstances, the number of directors is reduced by one, yielding the correct answer. This approximation fails however under certain circumstances, such as when the number of shares is 1.
This is equivalent to the Droop quota for each seat desired.
However this is not a hard and fast rule. In Illinois State House of Representative elections, in the 1st District, conducted using CV, the proportion of voters taken by successful candidates varied from 31 percent to 20 percent in the 1956-1966 period. [19]
Some Bugzilla installations allow the use of cumulative voting to decide which software bugs most urgently need correcting. [20]
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Voters in a cumulative election can employ different strategies for allocating their vote.
Limiting the spread of your votes (plumping) can by done under CV by allotting multiple votes to the same candidate. This will help to make that individual more likely to win. The issue of "Plumper Votes" was much to the fore in the early 18th century, when a candidate such as Sir Richard Child was returned for Essex in 1710 with 90% of his votes having been "Plumpers". [21] This was therefore a sign of his high popularity with those voters. The term is defined by the Oxford English Dictionary as: (verb) "to vote plump, to vote straight or without any qualification", (attrib.noun) "plumper vote, a vote given solely to one candidate at an election (when one has the right to vote for 2 or more)". [22]
Voters typically award most, if not all, of their votes to their most preferred candidate[ citation needed ].
Conversely, spreading out votes can increase the number of like-minded candidates who are elected.
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 number of votes needed to win. Consequently, it is beneficial for voters to have good information about the relative support levels of various candidates, such as through opinion polling.
Some supporters of the single transferable vote (STV) method describe STV as a form of cumulative voting with fractional votes[ citation needed ]. 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[ citation needed ]. (The whole-vote form of STV does not use fractional votes.)
Under cumulative voting, a voter may split his or her votes in such a way as to hurt their strongest preferred choice. The ranked choice format of the STV ballot makes it impossible for voters to split their votes among candidates in a manner that hurts their strongest preferred choice. This is because in most systems of STV, no second choice is considered until the first choice candidate has been elected or eliminated.
With cumulative voting, it is possible to "waste" votes by giving some candidates more votes than necessary to win and by splitting the vote among multiple candidates such that none of them win. Under STV, as circumstances permit, surplus votes are transferred away from successful candidates and votes can be concentrated behind a lesser number of candidates to ensure some representation is elected by a particular voting group.
CV is harder to count on some voting equipment, but is easier for voters on strategic grounds if they are unsure about which of their favored candidates needs more of their votes. It also makes it nearly impossible to cast an invalid ballot, although in practice a jurisdiction still may want to limit the number of marks to the number of seats being contested.
Proportional representation (PR) refers to any type of electoral system under which subgroups of an electorate are reflected proportionately in the elected body. The concept applies mainly to political divisions among voters. The essence of such systems is that all votes cast – or almost all votes cast – contribute to the result and are effectively used to help elect someone – not just a bare plurality or (exclusively) the majority – and that the system produces mixed, balanced representation reflecting how votes are cast.
The single transferable vote (STV), sometimes known as proportional ranked choice voting (P-RCV), is a multi-winner electoral system in which each voter casts a single vote in the form of a ranked-choice ballot. Voters have the option to rank candidates, and their vote may be transferred according to alternate preferences if their preferred candidate is eliminated or elected with surplus votes, so that their vote is used to elect someone they prefer over others in the running. STV aims to approach proportional representation based on votes cast in the district where it is used, so that each vote is worth about the same as another.
Single non-transferable vote or SNTV is an electoral system used to elect multiple winners. It is a generalization of first-past-the-post, applied to multi-member districts with each voter casting just one vote. Unlike FPTP, which is a single-winner system, in SNTV multiple winners are elected, typically in electoral districts; additionally, unlike FPTP, SNTV produces mixed representation and makes it unlikely for a single party to take all the seats in a city or a set area, which can happen under FPTP.
A Condorcet method is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, whenever there is such a candidate. A candidate with this property, the pairwise champion or beats-all winner, is formally called the Condorcet winner. The head-to-head elections need not be done separately; a voter's choice within any given pair can be determined from the ranking.
Voting is a method by which a group, such as a meeting or an electorate, convenes together for the purpose of making a collective decision or expressing an opinion usually following discussions, debates or election campaigns. Democracies elect holders of high office by voting. Residents of a jurisdiction represented by an elected official are called "constituents", and the constituents who choose to cast a ballot for their chosen candidate are called "voters." There are different systems for collecting votes, but while many of the systems used in decision-making can also be used as electoral systems, any which cater to proportional representation can only be used in elections.
Block voting, also known as bloc voting, refers to certain electoral systems where multiple candidates are elected simultaneously. They do not guarantee minority representation and allow a group of voters to ensure that only their preferred candidates are elected. In these systems, a voter can select as many candidates as there are open seats. That is, the voter has as many votes to cast as the number of seats to fill. The block voting systems are among various election systems available for use in multi-member districts where the voting system allows for the selection of multiple winners at once.
An electoral district, also known as an election district, legislative district, voting district, constituency, riding, ward, division, electorate, or (election) precinct, is a subdivision of a larger state created to provide its population with representation in the larger state's constituency. That body, or the state's constitution or a body established for that purpose, determines each district's boundaries and whether each will be represented by a single member or multiple members. Generally, only voters (constituents) who reside within the district are permitted to vote in an election held there. District representatives may be elected by a first-past-the-post system, a proportional representative system, or another voting method. They may be selected by a direct election under universal suffrage, an indirect election, or another form of suffrage.
The majority favorite or absolute majority criterion is a voting system criterion. The criterion states that "if only one candidate is ranked first by a majority of voters, then that candidate must win." It is sometimes referred to simply as the majority criterion, but this term is more often used to refer to Condorcet's majority-rule principle.
The Borda count electoral system can be combined with an instant-runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method. Both methods are designed to satisfy the Condorcet criterion, and allow for incomplete ballots and equal rankings.
Bullet, single-shot, or plump voting is when a voter supports only a single candidate, typically to show strong support for a single favorite.
Historically, the single transferable vote (STV) electoral system has seen a series of relatively modest periods of usage and disusage throughout the world; however, today it is seeing increasing popularity and proposed implementation as a method of proportional representation and a goal of electoral reform. STV has been used in many different local, regional and national electoral systems, as well as in various other types of bodies, around the world.
There are a number of complications and issues surrounding the application and use of single transferable vote proportional representation that form the basis of discussions between its advocates and detractors.
The multiple non-transferable vote (MNTV) is a group of voting system, in which voters elect several representatives at once, with each voter having more than one vote. MNTV uses multi-member electoral districts or only one district, which contains all voters, which is used to provide at-large representation.
The Borda count is a family of positional voting rules which gives each candidate, for each ballot, a number of points corresponding to the number of candidates ranked lower. In the original variant, the lowest-ranked candidate gets 0 points, the next-lowest gets 1 point, etc., and the highest-ranked candidate gets n − 1 points, where n is the number of candidates. Once all votes have been counted, the option or candidate with the most points is the winner. The Borda count is intended to elect broadly acceptable options or candidates, rather than those preferred by a majority, and so is often described as a consensus-based voting system rather than a majoritarian one.
Schulze STV is a draft single transferable vote (STV) ranked voting system designed to achieve proportional representation. It was invented by Markus Schulze, who developed the Schulze method for resolving ties using a Condorcet method. Schulze STV is similar to CPO-STV in that it compares possible winning candidate pairs and selects the Condorcet winner. It is not used in parliamentary elections.
Instant-runoff voting (IRV), also known as plurality with elimination or plurality loser, is a ranked-choice voting system that modifies plurality by repeatedly eliminating the last-place finisher until only one candidate is left. In the United Kingdom, it is generally called the alternative vote (AV). In the United States, IRV is often conflated with ranked-choice voting (RCV); however, this conflation is not completely standard, and social choice theorists tend to prefer more explicit terms.
In elections that use the single transferable vote (STV) method, quotas are used (a) for the determination of candidates considered elected; and (b) for the calculation of surplus votes to be redistributed. Two quotas in common use are the Hare quota and the Droop quota. The largest remainder method of party-list proportional representation can also use Hare quotas or Droop quotas.
An electoral system or voting system is a set of rules that determine how elections and referendums are conducted and how their results are determined. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, non-profit organisations and informal organisations. These rules govern all aspects of the voting process: when elections occur, who is allowed to vote, who can stand as a candidate, how ballots are marked and cast, how the ballots are counted, how votes translate into the election outcome, limits on campaign spending, and other factors that can affect the result. Political electoral systems are defined by constitutions and electoral laws, are typically conducted by election commissions, and can use multiple types of elections for different offices.
The term ranked voting, also known as preferential voting or ranked-choice voting, pertains to any voting system where voters indicate a rank to order candidates or options—in a sequence from first, second, third, and onwards—on their ballots. Ranked voting systems vary based on the ballot marking process, how preferences are tabulated and counted, the number of seats available for election, and whether voters are allowed to rank candidates equally.
Sequential proportional approval voting (SPAV) or reweighted approval voting (RAV) is an electoral system that extends the concept of approval voting to a multiple winner election. It is a simplified version of proportional approval voting. It is a special case of Thiele's voting rules, proposed by Danish statistician Thorvald N. Thiele in the early 1900s. It was used in Sweden for a short period from 1909-1921, and was replaced by a cruder "party-list" style system as it was easier to calculate.
