Cumulative voting

Cumulative voting (sometimes called the single divisible vote) is a variant on the single non-transferable vote (SNTV), which differs in that it allows a voter to split their support across multiple candidates. This can simplify strategic voting, by allowing larger groups of voters to elect multiple representatives by splitting their vote between multiple candidates. This removes the complexity associated with randomized or coordinated strategies. Apart from this, the method is equivalent to single non-transferable voting, and produces identical results if voters are informed and rational.

Cumulative voting can also be thought of as a variant on score voting, where the total scores for each candidate must add up to a fixed value (e.g. 100%). If instead the sum of squares must add up to a fixed value, the method becomes quadratic voting.

Cumulative voting is semi-proportional, allowing for more representative government than winner-take-all elections using block plurality voting or block instant-runoff voting. Cumulative voting is commonly-used in corporate governance, where it is mandated by 7 U.S. states.

History
Cumulative voting was used to elect the Illinois House of Representatives from 1870 until its repeal in 1980 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. 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, which had its first cumulative voting elections for its board of trustees in 2010. 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.)"

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.

Voting


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 among 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”. 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.

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.

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."

Use
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. 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.

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:
 * $$X>{S N \over D+1}$$

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:
 * $$N< {X * (D+1) \over S}$$

with N becoming the number of directors which can be elected and X the number of shares controlled.

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.

Some Bugzilla installations allow the use of cumulative voting to decide which software bugs most urgently need correcting.

Tactical voting
Voters in a cumulative election can employ different strategies for allocating their vote.

Plumper votes
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". 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)".

Voters typically award most, if not all, of their votes to their most preferred candidate.

Spread-out votes
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.