cumulative voting

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 (also accumulation voting or weighted voting) is a multiple-winner voting system intended to promote proportional representation while also being simple to understand.

History

Cumulative voting is used heavily in corporate governance, where it is mandated by many U.S. states, and it was used to elect the Illinois House of Representatives 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, among them Peoria, Illinois for half of its city council, and Amarillo, Texas for its school board.

Voting

In an equal and even cumulative ballot, as in Peoria, an individual's vote is fractionally divided evenly among all candidates for whom he or she indicates support. As the number of candidates increases, this can result in the need for computing sums of multiple fractions.

A cumulative voting election elects the top vote-getters, just as with a simple plurality election. However, voters are allowed to concentrate their full share of votes on fewer candidates than seats -- unlike bloc voting, 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 vote.

Other than general egalitarian 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 preference voting where the numbers represent ranks of choices or candidates in some order (i.e. they are ordinal numbers), in cumulative votes the numbers represent quantities (i.e. they are cardinal numbers).

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 vote; 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.

Voting systems criteria

Comparative academic analysis of voting systems usually centers on certain voting system criteria.

Cumulative voting satisfies the monotonicity criterion, the participation criterion, the consistency criterion, the plurality criterion, and reversal symmetry. Cumulative voting does not satisfy independence of irrelevant alternatives, nor the Condorcet criterion.

Usage

Corporate ballot

The Norfolk Legislative Assembly 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 governance, where it is mandated by many U.S. states, and it was used to elect the Illinois House of Representatives from 1870 until 1980. It was used in England 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 conceptionally flawed and mathematically wrong.

This is equivalent to the Droop quota 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.

A Corporate Example

Apple Computer's first meeting as a public company, held in January 1981, only a month after its historic IPO. provided a dramatic and surprising example of cumulative voting in action. Apple's bylaws had provided for cumulative voting, but this clause had never been used. Shareholders meetings had been small, exclusive gatherings in small, quiet rooms. Voting proxies were collected by mail and counted before the meeting. There were never any surprises. Product demos were not needed: major investors had already seen anything important.

This meeting was different. The business part of the meeting was planned, as usual, to take 15 minutes. Five seats were open on the Board of Directors; management had chosen suitable candidates for each, which most shareholders would naturally adopt.

Apple founder Steve Jobs started his prepared speech, but was interrupted: a large number of proxies had been delivered at the meeting, more than usual. Rather than a few hundred cards for a few hundred shares each, millions of votes had arrived at the last minute. There were enough votes to elect Randy Wigginton, a young programmer and one of Apple's first employees, to the board. Most of the votes had come from Michael Scott and Steve Wozniak, and each share had become five votes for Wigginton: there had been five vacant seats.

The company's lawyers concluded that two huge blocks of shares, multiplied fivefold, could swing the vote. However, Wigginton, who had no management experience and did not know that he had been nominated, said he was not interested. Eventually, the management slate was elected by default.

Tactical voting

Tactical voting 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 vote 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.

See also

• List of democracy and elections-related topics
• The Midwest Democracy Center
• Cumulative voting page at FairVote - Center for Voting and Democracy
• A Handbook of Electoral System Design from International IDEA
• Electoral Design Reference Materials from the ACE Project

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