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. A voting system is a means of choosing between a number of options, based on the input of a number of voters. ... For other uses, see Politics (disambiguation). ... This article is about the political process. ... Single-winner voting systems are voting systems in which a predetermined constituency elects a single person to some office; they contrast generally with proportional representation, in which constituencies are combined to elect several representatives at once. ... An example of a plurality ballot. ... An example of runoff voting. ... The exhaustive ballot is a voting system used to elect a single winner. ... Preferential voting (or preference voting) is a type of ballot structure used in several electoral systems in which voters rank a list or group of candidates in order of preference. ... The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate. ... A Condorcet method is a single winner election method in which voters rank candidates in order of preference. ... Copelands method is a Condorcet method in which the winner is determined by finding the candidate with the most pairwise victories. ... The Kemeny-Young method is a voting system that uses preferential ballots, a tally table, and sequence scores to identify the most popular choice, and also identify the second-most popular choice, the third-most popular choice, and so on down to the least-popular choice. ... Minimax is often considered to be the simplest of the Condorcet methods. ... The Borda count can be combined with an Instant Runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method. ... It has been suggested that Maximize Affirmed Majorities be merged into this article or section. ... The Schulze method is a voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. ... Bucklin is a voting system that can be used for single-member districts and also multi-member districts. ... The Coombs method, created by Clyde Coombs, is a voting system used for single-winner elections in which each voter rank-orders the candidates. ... Example Instant-runoff voting ballot Instant-runoff voting (IRV) is a voting system most commonly used for single member elections in which voters have one vote, but can rank candidates in order of preference. ... The Borda count is a single winner election method in which voters rank candidates in order of preference. ... On an approval ballot, the voter can vote for any number of candidates. ... Range voting (also called ratings summation, average voting, cardinal ratings, 0–99 voting, or the score system or point system) is a voting system for one-seat elections under which voters score each candidate, the scores are added up, and the candidate with the highest score wins. ... Voters at the voting booths in the US in 1945 Voting systems are methods (algorithms) for groups of people to select one or more options from many, taking into account the individual preferences of the group members. ... Proportional representation (sometimes referred to as full representation, or PR), is a category of electoral formula aiming at a close match between the percentage of votes that groups of candidates (grouped by a certain measure) obtain in elections and the percentage of seats they receive (usually in legislative assemblies). ... Mixed member proportional representation, also termed mixed-member proportional voting and commonly abbreviated to MMP, is a voting system used to elect representatives to numerous legislatures around the world. ... Party-list proportional representation systems are a family of voting systems used in multiple-winner elections (e. ... Open list describes any variant of party-list proportional representation where voters have at least some influence on the (by the political party itself supplied) order in which party candidates are elected. ... Closed list describes the variant of party_list proportional representation where voters can (effectively) only vote for political parties as a whole and thus have no influence on the (party-supplied) order in which party candidates are elected. ... The DHondt method (mathematically but not operationally equivalent to Jeffersons method, and Budder-Ofer method) is a highest averages method for allocating seats in party-list proportional representation. ... The highest averages method is one way of allocating seats proportionally for representative assemblies with party list voting systems. ... The largest remainder method is one way of allocating seats proportionally for representative assemblies with party list voting systems. ... The Sainte-Laguë method of the highest average (equivalent to Websters method or divisor method with standard rounding) is one way of allocating seats proportionally for representative assemblies with party list voting systems. ... This STV ballot for the Australian Senate illustrates group voting tickets. ... The Quota Borda System or Quota Preference Score was devised by the british philosopher Michael Dummett and first published in 1984 in his book, Voting Procedures, and again in his Principles of Electoral Reform in 1997. ... The matrix vote can be used when one group of people wishes to elect a smaller number of persons, each of whom is to have a different assignment. ... The Additional Member System (AMS) is a voting system in which some representatives are elected from geographic constituencies and others are elected under proportional representation from party lists. ... Parallel voting describes a mixed voting system where voters in effect participate in two separate elections using different systems, and where the results in one election have little or no impact on the results of the other. ... The Single Non-Transferable Vote or SNTV is an electoral system used in multi-member constituency elections. ... Bloc voting (or block voting) refers to a class of voting systems which can be used to elect several representatives from a single multimember constituency. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Sortition, also known as allotment, is a fair method of selection by some form of lottery such as drawing coloured pebbles from a bag. ... Cumulative Voting example ballot Created for Wikipedia, by Tom Ruen, May 2004 with MSPaint File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Cumulative Voting example ballot Created for Wikipedia, by Tom Ruen, May 2004 with MSPaint File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... A voting system is a means of choosing between a number of options, based on the input of a number of voters. ... Proportional representation (sometimes referred to as full representation, or PR), is a category of electoral formula aiming at a close match between the percentage of votes that groups of candidates (grouped by a certain measure) obtain in elections and the percentage of seats they receive (usually in legislative assemblies). ...

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 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, Chilton County, Alabama for its county council and Amarillo, Texas for its school board. The Illinois House of Representatives convenes at the Illinois State Capitol in Springfield. ... : See how it plays in Peoria United States Illinois Peoria 46. ... Amarillo redirects here. ...

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 not to split their votes and instead concentrate them on a single candidate at full value. Cumulative Equal&Even Voting example ballot Created for Wikipedia, by Tom Ruen, May 2004 with MSPaint File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Cumulative Equal&Even Voting example ballot Created for Wikipedia, by Tom Ruen, May 2004 with MSPaint File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... For the use of the term in political theory, see Pluralism (political theory). ... Bloc voting (or block voting) refers to a class of voting systems which can be used to elect several representatives from a single multimember constituency. ...

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. Bloc voting (or block voting) refers to a class of voting systems which can be used to elect several representatives from a single multimember constituency. ...

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 finance a share is a unit of account for various financial instruments including stocks, mutual funds, limited partnerships, and REITs. ...

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. The Single Non-Transferable Vote or SNTV is an electoral system used in multi-member constituency elections. ...

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. Egalitarianism (derived from the French word égal, meaning equal or level) is a political doctrine that holds that all people should be treated as equals from birth. ...

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). Term preferential voting (also known as the preference voting) has several different meanings: (1) A ranked ballot or preferential voting system is a type of voting system in which each voter casts their vote by ranking candidates in order of preference. ... In set theory, ordinal, ordinal number, and transfinite ordinal number refer to a type of number introduced by Georg Cantor in 1897, to accommodate infinite sequences and to classify sets with certain kinds of order structures on them. ... Aleph-0, the smallest infinite cardinal In mathematics, cardinal numbers, or cardinals for short, are a generalized kind of number used to denote the size of a set, known as its cardinality. ...

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. The Single Non-Transferable Vote or SNTV is an electoral system used in multi-member constituency elections. ... The First Past the Post electoral system, is a voting system for single-member districts. ...

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.) Fractional Cumulative Voting ballot sample Created for Wikipedia, by Tom Ruen, May 2004 with MSPaint File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...

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.

Robert's Rules of Order states, "this method of voting, which permits a member to transfer votes, must be viewed with reservation since it violates a fundamental principles of parliamentary law."^[1] 1876 edition Roberts Rules of Order is the informal short title of a book containing rules of order intended to be adopted for use by a deliberative assembly. ...

Voting systems criteria

Comparative academic analysis of voting systems usually centers on certain voting system criteria. Wikipedia does not yet have an article with this exact name. ...

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. A voting system is monotonic if it satisfies the monotonicity criterion, given below. ... Statement of Criterion Adding one or more ballots that vote X over Y should never change the winner from X to Y. Complying Methods Plurality voting, Approval voting, Cardinal Ratings, Borda count, and Woodalls DAC method all pass the Participation Criterion. ... A voting system is consistent if, when the electorate is divided arbitrarily into two parts and separate elections in each part result in the same alternative being selected, an election of the entire electorate also selects that alternative. ... Plurality criterion is a voting system criterion devised by Douglas Woodall. ... Reversal symmetry is a voting method 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. ... Independence of irrelevant alternatives (IIA) is an axiom often adopted by social scientists as a basic condition of rationality. ... The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate. ...

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. Weighted Cumulative Voting Ballot example Created for Wikipedia, by Tom Ruen, May 2004 with MSPaint File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Weighted Cumulative Voting Ballot example Created for Wikipedia, by Tom Ruen, May 2004 with MSPaint File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... The Norfolk Legislative Assembly has 9 members, elected for a three year term. ... Corporate governance is the set of processes, customs, policies, laws and institutions affecting the way in which a corporation is directed, administered or controlled. ... Official language(s) English[1] Capital Springfield Largest city Chicago Largest metro area Chicago Metropolitan Area Area  Ranked 25th  - Total 57,918 sq mi (140,998 km²)  - Width 210 miles (340 km)  - Length 390 miles (629 km)  - % water 4. ... For other uses, see England (disambiguation). ...

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. The Droop quota is the quota most commonly used in elections held under the Single Transferable Vote (STV) system. ...

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 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. In voting systems, tactical voting (or strategic voting) occurs when a voter supports a candidate other than his or her sincere preference in order to prevent an undesirable outcome. ...

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. This STV ballot for the Australian Senate illustrates group voting tickets. ...

See also

• List of democracy and elections-related topics

Politics is the process and method of gaining or maintaining support for public or common action: the conduct of decision-making for groups. ...

External links

• 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

References