Hubbry Logo
Cumulative votingCumulative votingMain
Open search
Cumulative voting
Community hub
Cumulative voting
logo
8 pages, 0 posts
0 subscribers
Be the first to start a discussion here.
Be the first to start a discussion here.
Cumulative voting
Cumulative voting
Cumulative voting
View on Wikipedia
from Wikipedia
A joint Politics and Economics series
Social choice and electoral systems
Single-winner methods
Single vote – plurality methods

Condorcet methods

Positional voting

Cardinal voting

Proportional representation
Party-list

Quota-remainder methods

Approval-based committees

Fractional social choice

Semi-proportional representation

Mixed systems
By results of combination
By mechanism of combination

By ballot type

Paradoxes and pathologies
Spoiler effects

Pathological response

Strategic voting

Paradoxes of majority rule

Social and collective choice
Impossibility theorems

Positive results

icon Mathematics portal

Cumulative voting (sometimes called the single divisible vote) is an election system where a voter casts multiple votes but can lump votes on a specific candidate or can split their votes across multiple candidates. The candidates elected are those receiving the largest number of votes cast in the election, up to the number of representatives to be elected.

Cumulative voting 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.

It may be thought of as a variant of block voting. Under both cumulative voting and block voting, a voter casts multiple votes but in the case of cumulative voting, can lump them all on one candidate (the equivalent of engaging in plumping). When voters do this, the result is similar to SNTV. When supporters of a minority candidate do this, they may be of sufficient strength to elect that minority representative, not a likely occurrence under either first past the post voting or block voting. Thus, cumulative voting generally produces similar results to SNTV (especially if voters are informed and rational, in which case they will tend to engage in plumping. Plumping though reduces cumulative voting's effectiveness at reducing need for strategic voting by allowing the voter to cast a split vote.).

Cumulative voting can also be thought of as a form of cardinal voting: 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.[1][2]

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.[3]

The method can also be used in participatory budgeting.[4]

History

[edit]

Cumulative voting was used to elect the Illinois House of Representatives[5] from 1870 until its repeal in 1980[6][7][8] 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.[9] 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[10][11] which had its first cumulative voting elections for its board of trustees in 2010.[12]

Voting options

Cumulative voting was also used to elect city boards in Toronto, Canada starting in 1904. 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 allows for minority representation.[13][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.[14]

Voting

[edit]
In equal and even voting, points are equally divided between all supported candidates.
In equal and even voting, points are equally divided between all supported candidates.

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.

Fractional vote ballot
Fractional vote ballot
Sticker dot voting

Permissible splits

[edit]

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.

Equal-and-even

[edit]

Possibly the simplest ballot is called satisfaction approval voting or the equal-and-even method. On this ballot, a voter simply marks all candidates they approve of, as in approval voting, and their vote is 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 but simplifying ballot completion.

Dot voting

[edit]

A more common and slightly more complex cumulative voting system is called dot voting[15] or multi-voting.[16] Under this method, voters are given an explicit number of points, which they can distribute among one or more candidates on the ballot. Typically, this is done by having a voter make one mark for each point they wish to assign to the desired candidate. In dot-voting participants vote on their chosen options using a limited number of stickers or marks with pens — dot stickers being the most common. This sticker voting approach is a form of cumulative voting. Dot-voting is now widely used for making quick collaborative decisions by teams adopting agile and lean methodologies. For example, it is one of the methods endorsed by the 18F digital services agency of the United States' General Services Administration, and is part of the Design Sprint methodology.

Generally, the number of points given to each voter is equal to the number of winning candidates (seats to be filled), which is typically a holdover after a transition from block plurality voting.

Fractional voting

[edit]

A similar method is to have the voter write in a desired number of points next to each candidate. Then, the scores on the ballot are divided by the total number of points the voter has assigned, to make sure the allocation adds up to 100%. The need to normalize votes complicates counting by hand, but simplifies the process of voting and gives each voter maximum flexibility.

Properties

[edit]

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.[17]

Robert's Rules of Order Newly Revised states that groups may adopt cumulative voting in its by-laws, and notes 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."[18]

Use

[edit]

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.[5][6] 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. Generally, this has been in an attempt to resolve lawsuits brought against bloc voting methods.[19]

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.

Some Bugzilla installations allow the use of cumulative voting to decide which software bugs most urgently need correcting.[20]

Tactical voting

[edit]

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

Plumping

[edit]

Plump voting occurs when a voter assigns all their points to the same candidate.[21] The issue of "Plumper Votes" was heavily discussed in the early 18th century, when Sir Richard Child was returned for Essex in 1710 with 90% of his votes having been "Plumpers".[22]

Quota

[edit]

The formula to determine the number of votes needed to elect one seat is called the Droop quota and has value:

See also

[edit]

Notes

[edit]
[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Cumulative voting

View on Grokipedia
from Grokipedia

Cumulative voting is a multi-winner in which each voter receives a number of votes equal to the seats available and may distribute them among candidates in any manner, including allocating multiple votes to a single candidate to concentrate support. This mechanism contrasts with standard by enabling voters to strategically amplify the chances of their preferred candidates, particularly benefiting minority groups seeking representation. In , cumulative voting is frequently applied to elections, where shareholders multiply their shares by the number of open seats and allocate votes accordingly, thereby enhancing the ability of minority shareholders to secure at least one board seat. This approach originated in 19th-century practices to counter majority dominance and has been mandated or permitted under various state corporation laws, though its use has declined with the rise of alternative governance structures. Politically, it has been implemented in select U.S. jurisdictions, such as Illinois's state house elections from 1870 until 1980, where it demonstrably increased representation for underrepresented groups like racial minorities by allowing coordinated vote pooling without district boundaries. While proponents highlight its role in fostering proportionality and reducing wasted votes, empirical observations from implementations reveal potential drawbacks, including heightened incentives for tactical alliances and vote-buying due to the lump-sum nature of vote allocation. In Illinois, for instance, the system protected minority interests but also facilitated gerrymandering-like strategies and inter-party deals, contributing to its eventual repeal in favor of single-member districts amid voter preference for clearer accountability. Despite these challenges, cumulative voting persists in niche applications, such as certain school boards and professional associations, underscoring its utility in contexts prioritizing inclusivity over simplicity.

Overview

Definition and Core Mechanism


Cumulative voting is a multi-winner designed for electing multiple representatives from a single district, where each voter is allocated a number of votes equal to the number of seats to be filled. Voters may distribute these votes across in any manner, including concentrating all votes on one or splitting them proportionally. This mechanism enables minority groups to achieve representation by pooling votes behind preferred , rather than diluting support across multiple contenders. The core operational principle involves tallying total votes received by each candidate, with the top vote-getters—equal to the number of available seats—declared winners, regardless of vote concentration. For instance, in an for three seats, a voter with three votes could assign all to one candidate, thereby amplifying that candidate's chances against majority-preferred options. This differs from straight voting, where voters cast one vote per seat but are restricted to one vote per candidate, limiting strategic concentration. Courts have endorsed cumulative voting as a remedial tool under the Voting Rights Act to ensure fair minority representation in jurisdictions with systems prone to diluting minority votes. Mathematically, if S seats are contested and a voter holds S votes, the system guarantees that a cohesive minority comprising at least 1/(S+1) of the electorate can secure one seat by uniformly concentrating votes on a single candidate, assuming maximal opposition efficiency. This threshold derives from the adapted for cumulative allocation, providing a formal basis for proportional minority inclusion absent in systems. Empirical applications, such as in certain U.S. local elections prior to reforms, demonstrated its efficacy in electing minority representatives where plurality methods failed.

Distinction from Straight and Limited Voting

In straight voting, also known as statutory or block voting, each voter in a multi-seat election receives one vote per available seat and must allocate those votes to distinct candidates, with the top vote recipients filling the seats. This system favors majority blocs, as a shareholder or voter group controlling slightly more than half the votes can secure all seats by evenly distributing their support across candidates. Limited voting modifies straight voting by restricting each voter to fewer votes than seats available—typically one fewer or a fixed number less—while still requiring single votes per chosen candidate. This forces voters to forgo supporting a full slate, promoting partial proportionality by enabling cohesive minorities to capture remaining seats if they concentrate votes effectively, though the effect is weaker than in other systems. Cumulative voting diverges fundamentally by granting each voter a total number of votes equal to the product of their shares (or base votes) and the number of seats, which can be freely distributed across candidates, including multiple votes on a single one. Unlike straight or , this concentration mechanism mathematically ensures minority representation; for instance, a group holding one-fifth of votes can guarantee at least one seat by pooling all support on their preferred candidate, countering the winner-take-all dynamic of straight voting.
AspectStraight VotingLimited VotingCumulative Voting
Votes per VoterOne per seat, distinct candidatesFewer than seats, distinct candidatesShares × seats, distributable as desired
Minority EmpowermentMinimal; majority sweeps all seatsModerate; minorities win residual seatsStrong; guarantees seats via concentration
ProportionalityLow; plurality-at-large favors majoritiesSemi-proportional; limits full slatesHigher; enables targeted representation
This table illustrates the core mechanics, where cumulative voting's flexibility addresses the representational deficits in straight and limited systems, particularly in corporate director elections or at-large political contests.

Historical Origins and Evolution

Early Development in Corporate Contexts

Cumulative voting for the election of corporate directors originated in the United States amid concerns over shareholder dominance and corporate abuses in the mid-19th century. Prior to its formal adoption, common law practices generally allowed shareholders one vote per share under straight voting rules, enabling controlling shareholders to monopolize board seats regardless of minority interests. This system exacerbated issues highlighted by scandals such as those involving the , where insiders manipulated governance to the detriment of smaller investors. The mechanism gained constitutional footing through the Illinois Constitution of 1870, which explicitly mandated cumulative voting in Article XI, Section 3 for corporate director elections. Under this provision, each could multiply their votes by the number of shares held and the number of directors to be elected, then allocate them freely across candidates, thereby enabling minority groups to concentrate votes and secure on the board. The Illinois Constitutional Convention debates emphasized this as a safeguard against tyranny, allowing even small shareholders—such as one holding 100 shares in a electing nine directors—to elect at least one representative by pooling votes. Adoption followed public in July 1870, marking the first statewide requirement for cumulative voting in private corporations. Early implementation in corporations addressed practical needs, particularly in railroads and firms where dispersed was common. By the 1880s, the system had demonstrated its utility in electing directors, as evidenced by legal commentaries noting its role in preventing board capture by pluralities as low as 51% under straight voting. This prompted gradual spread to other states; for instance, special corporate charters in places like New York incorporated similar provisions by the late , though not universally mandated until later statutes. Proponents argued it aligned incentives with stakes, fostering without diluting majority control entirely.

Adoption and Use in Political Elections

Cumulative voting was first adopted for political elections in the United States, specifically in , through a ratified on July 1, 1870. This system applied to the election of the House of Representatives, where three representatives were chosen from each of 59 legislative districts, allowing voters to allocate up to three votes per candidate to promote across partisan lines in a politically divided state. The mechanism persisted for over a century, enabling minority parties to secure seats by concentrating votes on preferred candidates, until its abolition via the 1980 Cutback Amendment, which reduced House seats from 177 to 118 and shifted to single-member districts. In the late , cumulative voting gained adoption in numerous U.S. local jurisdictions, often as a remedial measure under Section 2 of the to address vote dilution in elections affecting minority groups. Courts and consent decrees mandated its implementation in places like school boards and city councils, such as the Amarillo Independent School District in , where it was introduced following litigation to enhance minority electoral success without drawing majority-minority districts. By the , over 100 communities, primarily in the and Midwest, had adopted it for municipal or educational elections, including examples in and , though many later reverted to other systems amid administrative complexities or political shifts. Contemporary uses remain limited but include , where cumulative voting for city council elections has facilitated diverse representation, as seen in the 2023 cycle with multiple candidates from varied demographics securing seats through vote pooling. Outside the U.S., adoption in national political elections is rare, with no widespread examples in sovereign legislatures; isolated applications occur in subnational or hybrid contexts, but empirical data indicates it has not achieved broad international traction for parliamentary contests.

Decline in Political Applications and Modern Persistence

Cumulative voting experienced its broadest political adoption in the United States during the late 19th and early 20th centuries, particularly in state legislatures seeking to enhance minority representation without full proportional systems. By the mid-20th century, however, most jurisdictions abandoned it in favor of single-member , which were viewed as providing clearer geographic and simpler voter mechanics. This shift reflected a broader preference for systems minimizing strategic complexities, such as vote concentration by organized minorities that could distort outcomes beyond proportional intent. Illinois maintained cumulative voting for its longer than any other state, from until its repeal via the Cutback Amendment approved by voters on December 12, 1980. The amendment reduced House seats from 177 to 118 and replaced multi-member districts with 59 pairs of single-member districts, driven by arguments for fiscal savings—estimated at $3 million annually—and enhanced legislator responsiveness to specific constituencies. Opponents, including some Democrats, warned of diminished minority representation, as cumulative voting had elected independent or third-party members in up to 20% of seats in prior decades, but proponents prioritized streamlined elections over such guarantees. Post-repeal analyses noted a subsequent decline in legislative diversity, with fewer non-major-party voices. Internationally, cumulative voting never achieved widespread political use, overshadowed by list-based or systems that better align with party-centric parliaments. In the U.S., its political footprint contracted further after 1980, with abolitions in locales like (pre-1980s switch to at-large) and various cities mirroring state trends. Modern political applications persist in isolated U.S. contexts, such as select school boards, water districts, and small municipal elections where multi-seat races require minority protections under voting rights laws. For instance, some counties employed it under federal oversight until the , though most transitioned post-Voting Rights Act preclearance changes. No state legislatures or national elections currently utilize it, reflecting its marginalization amid preferences for verifiable, low-complexity systems; advocacy groups like FairVote promote revival for equity, but empirical adoption remains negligible.

Operational Mechanics

Vote Allocation Rules

In cumulative voting, each voter receives a total number of votes equal to the product of their base voting entitlement and the number of seats or positions to be filled. For shareholders in corporate , the base entitlement is the number of shares held, multiplied by the number of directors to be elected; for example, a holder of 100 shares facing an for 3 directors receives 300 votes. In political , individual voters typically receive votes equal to the number of seats available in the multi-member district, such as 5 votes for 5 seats. Voters allocate these votes among candidates at their discretion, with no restriction on distributing multiple votes to a single candidate, enabling strategies like where all votes concentrate on one preferred option to maximize its chances. Votes may also be split evenly or unevenly across multiple candidates, such as dividing 300 votes as 150 to one, 100 to another, and 50 to a third. This allocation occurs via ballots where voters specify vote counts per candidate, ensuring the total does not exceed their allotment. The system prohibits fractional votes unless explicitly allowed by rules, requiring whole-number assignments that sum precisely to the voter's total. Winners are determined by ranking candidates by total votes received, with the top vote-getters filling the seats, irrespective of vote concentration effects. This mechanic contrasts with straight voting, where voters cast only one vote per seat, limiting influence to the number of positions.

Variations in Implementation

In , cumulative voting is implemented by multiplying a shareholder's number of shares by the number of director positions available, granting proportional voting power based on ownership stake, with full flexibility to allocate all votes to a single candidate or distribute them unevenly across multiple candidates. This contrasts with straight voting, where shareholders cast one vote per share for each position separately, limiting concentration. State laws vary, with some mandating cumulative voting for public companies while others permit bylaws to opt for straight voting instead. In political elections, implementation typically assigns each voter a fixed number of votes equal to the seats to be filled, enabling concentration or distribution without regard to individual "ownership" equivalents, as seen in at-large contests like ' city council elections where voters receive five votes for five seats and may allocate them freely among candidates. Winners are determined by the highest vote totals, without explicit quotas, though the system mathematically favors minority representation when coordinated. A key variation is equal-and-even cumulative voting, where voters select multiple candidates without specifying vote amounts, resulting in votes being divided equally (often fractionally) among those chosen; for instance, marking two candidates for three seats awards 1.5 votes to each. This simplifies ballot design compared to free-form allocation but reduces strategic flexibility, as voters cannot emphasize preferences unevenly, and has been applied in U.S. local elections like aspects of the Peoria model to promote proportionality while easing voter burden. Fractional outcomes arise naturally in such systems when the number of selected candidates does not evenly divide the total votes.

Formal Properties

Mathematical Guarantees for Representation

Cumulative voting provides a formal mathematical that a cohesive minority holding more than 1S+1\frac{1}{S+1} of the total votes can secure at least one in an for SS positions, provided the group concentrates all its votes on a single . This threshold derives from the of vote pooling: with total votes TVTV distributed across SS seats, the minority's pooled votes exceed TVS+1\frac{TV}{S+1}, ensuring their candidate receives more votes than at least one of the majority's candidates, as the majority cannot distribute its remaining SS+1TV\frac{S}{S+1} TV votes evenly enough to exceed this amount on all SS candidates. The precise for the minimum votes vv required to the of one seat is v>TVS+1v > \frac{TV}{S+1}, or in practice, the smallest greater than this value to account for discrete votes. For corporate , where votes equal shares times seats, this translates to shares r>tS+1r > \frac{t}{S+1} for total shares tt. Extending to kk seats, the holds if the minority controls more than kS+1\frac{k}{S+1} of total votes, allowing concentration on kk candidates. This monotonic property ensures that larger minority shares yield proportionally more guaranteed seats up to the threshold limit. While this mechanism prevents the complete exclusion of minorities above the quota, it does not enforce full proportionality, as uncoordinated voting or strategies like vote spreading can dilute minority gains beyond the guaranteed minimum. The guarantee assumes perfect cohesion and full turnout; deviations reduce effectiveness, though the threshold remains a worst-case assurance under optimal minority strategy. Proofs rely on the : the 's votes, insufficient to surpass the minority's concentrated total on every seat, must leave at least one vulnerable.

Quota Calculations and Thresholds

In cumulative voting systems, the threshold of exclusion represents the minimum proportion of total votes required to guarantee the election of at least one , assuming optimal vote concentration by the and even distribution by opponents. This threshold is derived from the worst-case scenario where opponents allocate votes evenly across the maximum number of candidates needed to fill the remaining seats. For S seats, the formula yields a proportion exceeding 1S+1\frac{1}{S+1} of the total valid votes (or shares in corporate contexts). The precise number of votes needed to assure one seat is ⌊VS+1⌋+1\left\lfloor \frac{V}{S+1} \right\rfloor + 1, where VV is the total number of votes cast. In corporate elections, where each share entitles the holder to S votes (total V=V = total shares ×S\times S), a minority holding shares XX can secure one board seat by concentrating all X×SX \times S votes on a single candidate, provided X>total sharesS+1X > \frac{\text{total shares}}{S+1}. For instance, with 100 shares and 3 seats, a group needs more than 25 shares (25% + epsilon) to exceed the even split of the remaining 75 shares across 3 candidates. This threshold aligns with the principle adapted to cumulative voting's plurality mechanics, lowering the effective barrier for minority representation compared to straight voting (which requires over 50% for any seat). In political applications, such as the 2010 Port Chester, New York, elections under the Voting Rights Act, the 1/7 threshold (for 6 seats) was approximately 14.29%, enabling Hispanic voters (46.2% of the population) to exceed it and secure seats by concentrating votes. Failure to surpass this level risks exclusion, even with plurality wins possible below it if opponents coordinate. Variations may incorporate turnout adjustments or constraints, but the core 1S+1\frac{1}{S+1} proportion holds across implementations, providing a mathematical of representation without requiring proportional outcomes. Empirical analyses confirm this lowers exclusion risks in multi-seat contests, though strategic remains essential for realization.

Applications and Contexts

Corporate Governance Uses

Cumulative voting enables shareholders in corporations to allocate the product of their shares and the number of director positions to one or more candidates, facilitating minority shareholders' ability to secure board representation proportional to their ownership stake. This contrasts with straight voting, where each share receives one vote per director slot, often allowing majority shareholders to dominate the entire board. By concentrating votes, a minority bloc holding at least 1/(n+1) of shares—where n is the number of directors—can guarantee electing one director, calculated via the adapted for multi-winner contests. Historically, emerged in U.S. in the late to mitigate majority shareholder entrenchment, with pioneering its mandate in corporate charters around 1870 before embedding it in state statutes. By 1900, at least a dozen states had incorporated cumulative voting rights into their constitutions or general laws, reflecting concerns over industrial monopolies and shareholder disenfranchisement. This system proliferated as a statutory default in states like and New York, empowering dissident shareholders—such as family factions in closely held firms or institutional investors—to challenge incumbent boards without full ownership control. In practice, corporations adopt cumulative voting through bylaws or charter provisions, often in jurisdictions where statutes permit but do not require it, such as under its General Corporation Law, which defaults to straight voting unless opted into. Major U.S. firms like and historically utilized it to balance interests among diverse shareholder bases, while today it persists in regulated utilities, cooperatives, and some non-profits to foster board diversity without proxy fights. Internationally, China's 2005 Company Law reforms mandating cumulative voting for listed firms aimed to dilute controlling shareholder power, enabling minority nominees in elections for up to one-third of seats. Empirical analyses of pre- and post-reform data indicate it increased appointments by 5-10% in affected firms, though coordination challenges limited broader contestability. Shareholder activism leverages cumulative voting for tactical gains, such as "plumping" votes on a single insurgent to force concessions or monitor . Studies of U.S. firms retaining the system post-1980s show minority-elected directors correlate with higher firm valuation premiums (up to 2-3% ) in concentrated ownership settings, attributing this to reduced agency costs via diversified oversight. However, opt-outs via shareholder votes—prevalent since the 1980s amid dispersed ownership—have diminished its use, with fewer than 20% of firms employing it by 2000, as majority coalitions prioritize streamlined elections.

Political and Electoral Implementations

Cumulative voting has been implemented in political elections mainly at the state and local levels, often in multi-member districts to improve representation for racial, ethnic, or ideological minorities without fully adopting . Voters in such systems receive votes equal to the number of seats available and may allocate them disproportionately to favored candidates, enabling coordinated minority blocs to secure at least one seat by concentrating votes—a mechanism known as or . This approach contrasts with equal and even distribution rules in some other systems and has been praised for lowering for smaller groups but criticized for encouraging intra-party competition and vote-buying risks. The longest and most extensive application occurred in the Illinois , where cumulative voting was adopted via a ratified on July 2, 1870, establishing three-member districts statewide with each voter receiving three votes to cast for one, two, or three candidates. This persisted for 110 years, electing all 177 House members (59 districts × 3 seats) biennially until its replacement in 1980 by a voter initiative that reduced the House to 118 single-member districts via , passing with 1,906,605 yes votes against 1,319,322 no votes on November 4, 1980. During its tenure, the method facilitated the election of independent and third-party candidates, including socialists in the early and African American representatives from districts with small Black populations, as a minority holding about one-third of votes could guarantee a seat through coordination. However, it also fostered intense intra-party primaries and perceptions of gerrymandering-like districting to manipulate outcomes, contributing to its abolition amid broader electoral reforms.)) At the local level, cumulative voting has seen sporadic adoption in city councils and school boards, particularly in and , to address vote dilution under the Voting Rights Act of 1965. For example, , implemented it for its at-large city council elections starting in the 1990s, with a 2023 election yielding a council of seven members where coordinated voting among Latino and progressive blocs secured diverse representation, including the election of candidates with 15-20% district support. Similarly, the Amarillo Independent School District in adopted cumulative voting in 1994 for its seven board seats following a federal court ruling on minority vote dilution, allowing voters to pool votes for preferred candidates and resulting in increased representation from zero to two seats by 2000 through strategies. These implementations often require voter education to counter low turnout and coordination failures, with empirical data showing seat gains for minorities proportional to their population share when mobilization occurs. Internationally, pure cumulative voting remains rare in national elections, with no major sovereign states currently employing it for parliamentary seats as of 2025; historical experiments, such as limited uses in 19th-century local assemblies in , have largely shifted to or list proportional systems that achieve similar minority protections without multiple vote allocation. Proposals for its adoption persist in advocacy for hybrid systems, but empirical adoption lags due to administrative complexity and preferences for simpler plurality or proportional methods.

Other Specialized Uses

Cumulative voting finds application in labor unions for electing officers, where members allocate multiple votes to prioritize candidates representing specific factions or interests, thereby mitigating dominance by groups. For instance, platforms designed for union elections highlight its use in multi-candidate races to distribute votes flexibly across nominees for positions like stewards or executives, promoting broader participation among rank-and-file members. In homeowners' associations (HOAs), cumulative voting serves as an alternative to straight voting for board elections, enabling owners to pool votes for preferred directors and achieve proportional outcomes in multi-seat contests. Under law, HOAs may adopt this method via bylaws or amendments, particularly when conventional one-vote-per-candidate systems risk entrenching majorities; it requires candidates to secure a quota based on total votes divided by seats plus one. This approach has been implemented in community associations to balance representation among diverse homeowner interests, though it demands clear instructions to avoid voter confusion. Cooperative organizations, including and agricultural co-ops, utilize cumulative voting for director elections to empower minority members, who multiply their shares by open seats and distribute votes strategically. In such entities, each member's votes equal their ownership units times the number of board positions, allowing concentration on aligned candidates to secure at least one seat via the formula where votes needed exceed (total shares × seats) / (seats + 1). This mechanism, outlined in guidelines, contrasts with statutory voting by reducing free-rider incentives and fostering coalition-building among smaller stakeholders. Limited adoption occurs in other private associations, such as certain non-profit boards or trade groups, where bylaws permit it to ensure diverse without statutory mandates; however, empirical on prevalence remains sparse, with usage often tied to jurisdictions allowing opt-in provisions for enhanced minority leverage.

Strategic and Tactical Considerations

Voter Strategies Including

In cumulative voting, voters receive a number of votes equal to the number of seats to be filled and may distribute them freely among , enabling strategies that range from even allocation across multiple preferences to concentrated support on fewer options. Plumping, the practice of assigning all or most votes to a single , serves to amplify the electoral prospects of that individual, particularly when voters hold intense preferences or seek to overcome dominance. This tactic derives from the system's allowance for vote , allowing a voter with S votes in an S-seat to propel one candidate toward the effective quota, typically around V/(S+1) + 1 where V is total votes cast. Plumping proves strategically advantageous for minority factions aiming to secure at least one seat, as uncoordinated spreading of votes risks falling below thresholds for any candidate. Empirical analysis from U.S. jurisdictions implementing cumulative voting under Voting Rights Act remedies, such as , in 2006–2015, demonstrates that voter education campaigns emphasized to enhance minority representation, with Hispanic voters increasing turnout and achieving proportional outcomes by concentrating votes on aligned candidates. In contrast, majority groups often opt for balanced distribution across a slate to maximize total seats, as uneven by opponents can disrupt proportionality if not anticipated. Coordination within groups—such as through party directives or —mitigates free-riding, where individual dilutes collective strength, though it introduces gamesmanship risks like vote wastage from miscoordination. Historical precedents, including Illinois's state legislative elections from 1870 to 1980, illustrate 's tactical role in multi-member , where minority parties instructed supporters to allocate all three votes to one , ensuring a against plurality majorities that spread votes evenly. Corporate applications similarly incentivize minority shareholders to plump shares toward dissident directors, countering entrenched boards, though success hinges on accurate quota calculations and bloc cohesion. While plumping fosters targeted representation, its efficacy depends on voter information and turnout; studies indicate lower comprehension in uneducated electorates leads to suboptimal even splits, underscoring the need for transparent rules to realize strategic intent.

Potential for Coordination and Free-Riding

In cumulative voting systems, achieving for minority groups hinges on voters coordinating to concentrate their multiple votes—often through —on a limited number of preferred candidates to surpass the electoral quota, typically calculated as votes divided by seats plus one. Without such coordination, dispersed vote allocation can prevent minorities from securing seats, even when their total support exceeds the threshold, as individual strategic choices may prioritize personal favorites over group-optimal concentration. This coordination challenge is exacerbated in large electorates, where information asymmetries and lack of communication channels hinder consensus on vote targets. Free-riding emerges as a principal-agent within these dynamics: voters aware of the need for concentrated support may withhold full participation, anticipating that others will bear the effort of aligning on candidates, thereby diluting overall efficacy and risking seat forfeiture for the group. Empirical analyses of cumulative voting in school board elections, such as those in districts from the 1980s to 1990s, reveal that fragmented minority coalitions often failed to coordinate sufficiently, resulting in underrepresentation despite aggregate vote shares sufficient for one or more seats, attributable in part to free-rider incentives where individuals conserved votes for less viable alternatives. In experiments simulating multi-seat elections, coordination failures under cumulative rules led to equilibria where free-riding reduced collective payoffs by 15-20% compared to fully scenarios, underscoring the tension between individual rationality and group success. In applications, cumulative voting amplifies these issues among dispersed shareholders, who must coordinate to cumulate shares toward electing dissident directors against entrenched . The intensifies here due to high monitoring costs: activist shareholders investing in nomination and proxy solicitation enable passive ones to benefit from improved board representation without contributing, often leading to coordination breakdowns and reliance on institutional investors for . Jeffrey Gordon argues that while cumulative voting theoretically mitigates free-riding by enabling vote concentration, practical barriers like proxy advisory silos and short-term horizons perpetuate under-coordination, with from U.S. firms showing minority slates succeeding in under 10% of cumulative voting contests from 1990-2000 absent institutional backing. Reforms like relational investing frameworks have been proposed to internalize these costs, yet persistent free-riding contributes to entrenchment in over 70% of applicable cases.

Advantages and Empirical Support

Enhancements to Minority Representation

Cumulative voting improves minority representation in multi-seat elections by allowing voters to allocate multiple votes to fewer candidates, enabling cohesive minority groups to secure at least one even if they hold less than a of total votes. This mechanism contrasts with straight voting systems, where majorities can monopolize all s, as minorities can "plump" votes—concentrating all their votes on a single candidate—to surpass the threshold needed for election. The required vote share to guarantee a approximates 1s+1\frac{1}{s+1} of total votes, where ss is the number of s, providing a mathematical floor for minority influence absent in single-vote plurality systems. In , cumulative voting empowers minority by multiplying their shares by the number of director positions, permitting them to pool votes for a preferred and elect a representative to the board despite lacking overall control. This protects against entrenchment by majority owners, as evidenced in statutes authorizing the practice, which aim to align board composition more closely with diverse ownership interests. For instance, a with 10% of shares in a nine-director can direct all 90 votes (10 shares × 9) to one , potentially securing a seat if coordinated with like-minded holders. Electorally, cumulative voting has demonstrably boosted descriptive representation for ethnic and ideological minorities. Illinois employed it for its House of Representatives from 1870 to 1980 in three-member districts, yielding seats for Black candidates and third-party voices that single-member districts often excluded, with minority election shares aligning more proportionally to population demographics than under subsequent plurality rules. A 2021 laboratory experiment confirmed theoretical predictions: under costly voting conditions mimicking real turnout barriers, cumulative voting raised minority participation rates relative to majorities and increased their seat shares by up to 20-30% compared to one-vote systems. Similarly, Peoria, Illinois, adopted cumulative voting for city council in 2019, resulting in more diverse outcomes, including representation for underrepresented districts in its 2023 elections. These enhancements stem from the system's for minorities to coordinate without requiring party-list structures, though depends on voter cohesion and awareness of strategies. Empirical reviews of cumulative and implementations in U.S. jurisdictions found African American representation levels comparable to those in larger single-member districts, attributing gains to vote concentration rather than district .

Evidence from Case Studies and Data

A experiment conducted in 2021 tested (CV) in multi-member districts with costly turnout, finding that it significantly increased minority turnout relative to the majority and boosted the minority's share of elected representatives compared to . In the experiment, subjects representing a (20-40% of the ) achieved representation rates 15-25% higher under CV when coordinating votes, aligning with theoretical predictions that CV incentivizes minority bloc voting without requiring turnout from all group members. Field implementations in U.S. jurisdictions under the Voting Rights Act provide empirical support for CV's role in enhancing minority representation. In , where the population was approximately 16% and 6% , elections prior to 1989 yielded no minority school board members since the 1970s despite a 22% minority share; after adopting CV for the Amarillo Independent School District board in 1989, the first election elected one trustee out of seven seats, and subsequent elections (1990s-2000) consistently produced minority winners proportional to or exceeding population shares in coordinated efforts, such as votes on preferred candidates. Analyses of CV in over 200 U.S. localities during the , including counties like Chilton, revealed that Black representation under CV exceeded expectations from at-large plurality systems once Black population reached 10-20%, with regression models showing CV reduced the vote threshold for minority success by allowing vote concentration—e.g., a cohesive 18% minority bloc could secure one seat in a five-member , compared to near-impossibility under dispersed voting. Aggregate data from these cases indicated CV elected minorities at rates 1.5-2 times higher than unmodified at-large systems in similar demographics, though outcomes depended on voter coordination.

Criticisms and Empirical Challenges

Risks of Strategic Manipulation and Instability

Cumulative voting is vulnerable to strategic manipulation by both and minority groups, as participants can concentrate votes () or adjust nominations to alter outcomes beyond . In multi-seat elections, a holding just over 50% of votes can secure all seats by nominating exactly the number of candidates equal to available seats and directing supporters to distribute votes evenly among them, preventing any single minority candidate from reaching the threshold of votes/(seats+1) needed for election. This tactic exploits the system's , where uncoordinated minorities risk vote wastage by spreading support thinly, while coordinated majorities minimize opposition gains. Empirical analysis of Illinois's state legislative elections under cumulative voting from to revealed frequent party strategies, such as nominating fewer candidates than seats to enable , which often resulted in major-party sweeps despite minority vote shares exceeding the theoretical guarantee. Such manipulation extends to voter behavior, where tactical or from certain candidates can invert intended proportionality. For instance, game-theoretic models applied to districts showed that rational , anticipating opponents' strategies, could deviate from sincere voting to block rivals, increasing the incentive for pre-election or campaigns. This susceptibility undermines the system's goal of fair minority inclusion, as outcomes hinge on superior organization rather than raw vote shares, with documented cases in corporate elections where controlling shareholders neutralized cumulative rules through slate nominations and proxy solicitation. Instability arises from the system's reliance on voter coordination and information, leading to volatile results sensitive to turnout fluctuations or miscalculations. In uncoordinated settings, small shifts—such as a 5-10% change in participation—can cause disproportionate seat losses for the if votes fragment across too many candidates, or for minorities if fails due to dispersed support. Illinois's experience highlighted this, with legislative compositions swinging erratically between parties due to strategic errors or voter over optimal vote allocation, contributing to fragmentation and the system's eventual repeal in 1980 amid complaints of unpredictability. Critics argue this dynamic fosters short-term over stable representation, as elected bodies may reflect tactical maneuvers rather than enduring voter preferences, exacerbating deadlock in divided districts.

Evidence of Drawbacks in Practice

In the state of , cumulative voting was employed for electing the from 1870 until its abolition in 1980, but empirical observations revealed significant drawbacks including heightened gamesmanship and reinforcement of entrenched political machines. Political groups risked losing seats entirely if they fielded multiple candidates whose vote pools fragmented under the system's requirement for concentrated , pressuring parties to limit candidacies and avoid intra-bloc competition. This dynamic favored highly disciplined organizations, such as Chicago's Democratic machine, which leveraged superior coordination to secure disproportionate influence through informal seat-sharing pacts, thereby entrenching one-party dominance in multi-member districts rather than fostering broader accountability. The system's tendency toward further diminished voter choice, as parties routinely agreed on preordained vote splits—often 2-1 in three-member districts—or left slots vacant to prevent from exploiting them, resulting in uncontested races that insulated incumbents from electoral pressure. These practices contributed to public disillusionment, culminating in the 1980 Cutback Amendment, a voter-approved constitutional change that eliminated cumulative voting alongside multi-member districts, slashing seats from 177 to 118 amid scandals over legislative pay hikes and perceived unresponsiveness. Beyond , cumulative voting has been critiqued for exacerbating polarization in jurisdictions where it incentivizes bloc-style voting along ethnic or ideological lines, as minorities concentrate votes to secure representation at the expense of cross-group alliances. For instance, in remedial applications under the Voting Rights Act, such as , where it replaced elections in 2010 following a federal dilution finding, turnout remained chronically low at around 10% in subsequent cycles, potentially reflecting voter confusion or disengagement from the complex ballot mechanics despite achieving minority seat gains. In corporate settings, empirical analyses indicate that cumulative voting can elect directors backed by minority shareholders, leading to boards where key members lack broad ownership support and contribute to friction or stalled initiatives. A difference-in-differences study of Taiwan's 2015 mandate for cumulative voting in listed firms found it reduced controlling shareholders' expropriation but also correlated with heightened board-minority tensions, as minority-elected directors pursued agendas misaligned with majority interests, potentially impairing firm-level efficiency. Similarly, strategic vote concentration has enabled minority blocs to block value-enhancing actions like mergers, entrenching suboptimal in U.S. corporations opting for the system.

Ongoing Relevance and Reforms

Current Global Usage

In political elections, cumulative voting is employed in a limited number of local jurisdictions, primarily in the United States, to promote minority representation in multi-member districts. For instance, , continues to use cumulative voting for its city council elections, as demonstrated in the 2023 cycle where it facilitated diverse outcomes by allowing voters to concentrate multiple votes on preferred candidates. Similar applications persist in select U.S. municipalities and school boards, often as remedies under the Voting Rights Act to address voting dilution, though adoption remains sporadic and confined to subnational levels without widespread national or international use in sovereign legislatures as of 2025. In , cumulative voting maintains broader application worldwide, enabling minority shareholders to pool votes for board director elections. In the United States, it is authorized in over 30 states for electing corporate directors, with shareholders multiplying shares by open seats to favor specific candidates, though many firms opt for straight voting via charters. India permits it under Section 163 of the , allowing in director appointments to safeguard smaller investors, particularly in public companies. mandates cumulative voting for large-cap listed firms to enhance board diversity, alongside separate elections for members, as part of ongoing reforms. Other jurisdictions, including and , incorporate it optionally or in hybrid forms to balance control with minority influence, though empirical studies indicate mixed effects on firm and entrenchment risks.

Proposals for Modification or Alternatives

Limited voting has been proposed as a simpler alternative to cumulative voting, particularly for elections aimed at securing minority representation without the coordination challenges of . In , each voter receives a fixed number of votes—typically fewer than the number of seats available—but cannot concentrate them on fewer candidates, which curbs majority dominance while still allowing some proportionality. This system was implemented in over 100 U.S. jurisdictions under the Voting Rights Act to remedy vote dilution, often yielding minority seat shares roughly proportional to population without requiring voters to strategize vote allocation across multiple candidates. Choice voting, also known as single transferable vote (STV), represents another reform proposal favored by electoral analysts for surpassing cumulative voting's proportionality while eliminating the need for minority groups to pre-coordinate vote dumping. Voters rank candidates in multi-seat districts, with initial counts followed by transfers of surplus votes or eliminations based on preferences until seats are filled, ensuring seats reflect voter support more evenly across factions. FairVote, a nonpartisan advocacy group for ranked-choice systems, argues STV mitigates cumulative voting's risks of uneven representation—such as electing isolated minority candidates at the expense of broader group gains—and has demonstrated higher minority inclusion in simulations and trials compared to cumulative methods. Empirical cases, including Cambridge, Massachusetts's long-term STV use, show consistent descriptive representation exceeding that in cumulative systems without heightened instability. Modifications to cumulative voting itself are less common in electoral contexts but include variants promoting even vote distribution to temper plumping's extremes, such as equal and even allocation where multiple votes are divided fractionally among supported candidates rather than lumped. This adjustment, akin to satisfaction approval voting, seeks to enhance voter expressiveness and proportionality by discouraging single-candidate focus, though it remains experimental and primarily discussed in voting theory rather than widespread adoption. In , reforms like authorizing charters to of cumulative voting for straight voting have gained traction to streamline director elections and boost , as evidenced by Delaware's model influencing over 80% of U.S. public companies by 2020 to abandon it.

References

  1. https://archive.fairvote.org/?page=563
  2. https://www.investopedia.com/terms/c/cumulativevoting.asp
  3. https://www.cato.org/blog/cumulative-voting-drastic-remedy-election-ills
  4. https://www.investor.gov/introduction-investing/investing-basics/glossary/cumulative-voting
  5. https://corporatefinanceinstitute.com/resources/management/cumulative-voting/
  6. https://www.jstor.org/stable/725580
  7. https://core.ac.uk/download/pdf/234121362.pdf
  8. https://archive.fairvote.org/?page=226
  9. https://www.law.cornell.edu/wex/cumulative_voting
  10. https://academiccommons.columbia.edu/doi/10.7916/d8-dkca-2w41/download
  11. https://blogs.cuit.columbia.edu/ac186/files/2021/04/NBERw28674.pdf
  12. https://electionbuddy.com/features/voting-systems/cumulative-voting/
  13. https://corporatefinanceinstitute.com/resources/equities/straight-voting/
  14. https://opencasebook.org/casebooks/9289-business-associations/resources/9.1.2.2-straight-voting-vs-cumulative-voting/
  15. https://archive.fairvote.org/factshts/comparis.htm
  16. https://www.nonprofitvote.org/fair-vote-methods-for-multi-seat-elections/
  17. https://www.canr.msu.edu/news/alternatives_to_plurality_voting_cumulative_voting
  18. https://aaronhall.com/cumulative-voting-vs-straight-voting-in-shareholder-elections/
  19. https://repository.law.uic.edu/cgi/viewcontent.cgi?article=2548&context=lawreview
  20. https://repository.law.umich.edu/cgi/viewcontent.cgi?article=7232&context=mlr
  21. https://heinonline.org/hol-cgi-bin/get_pdf.cgi?handle=hein.journals/busl10&section=19
  22. https://scholarship.law.nd.edu/cgi/viewcontent.cgi?article=3619&context=ndlr
  23. https://dc.law.utah.edu/cgi/viewcontent.cgi?article=1006&context=ulr
  24. https://ballotpedia.org/Illinois_Cumulative_Voting_Amendment_%28July_1870%29
  25. https://www.jstor.org/stable/40189408
  26. https://www.lib.niu.edu/1991/ii910713.html
  27. https://www.mtas.tennessee.edu/librarycatalog/cumulative-voting-remedy-voting-rights-cases
  28. https://www.wtamu.edu/~jrausch/southernpaper.pdf
  29. https://archive.fairvote.org/?page=418
  30. https://fairvote.org/cumulative-voting-a-step-towards-proportional-representation/
  31. https://www.lib.niu.edu/1980/ii800104.html
  32. https://digitalcommons.iwu.edu/cgi/viewcontent.cgi?article=1289&context=parkplace
  33. https://fairvote.org/archives/fair_voting_in_the_united_states/
  34. https://www.dictionary.com/browse/cumulative-voting
  35. https://www.corporatefinanceinstitute.com/resources/management/cumulative-voting/
  36. https://www.upcounsel.com/cumulative-voting
  37. https://www.thecorporategovernanceinstitute.com/insights/lexicon/what-is-cumulative-voting/
  38. https://www.formpl.us/blog/cumulative-voting-in-corporate-elections-the-complete-guide
  39. https://www.stimmel-law.com/en/articles/basics-cumulative-voting
  40. https://archive.fairvote.org/factshts/cumulati.htm
  41. https://pages.nist.gov/ElectionGlossary/
  42. https://scholarship.law.duke.edu/cgi/viewcontent.cgi?article=2147&context=dlj
  43. https://egrove.olemiss.edu/cgi/viewcontent.cgi?article=5203&context=jofa
  44. https://brooklynworks.brooklaw.edu/cgi/viewcontent.cgi?article=1185&context=blr
  45. https://scholarcommons.sc.edu/cgi/viewcontent.cgi?article=2693&context=sclr
  46. https://corpgov.law.harvard.edu/2023/01/31/voting-rights-in-corporate-governance-history-and-political-economy/
  47. https://archive.fairvote.org/?page=2524
  48. https://www.sciencedirect.com/science/article/abs/pii/S0929119920300997
  49. https://scholarship.law.columbia.edu/context/faculty_scholarship/article/1071/viewcontent/Gordon_Institutions_as_Relational_Investors.pdf
  50. https://www.lib.niu.edu/1976/ii761113.html
  51. https://votem.com/10-cumulative-voting-examples-to-enhance-union-decision-making/
  52. https://votem.com/statutory-vs-cumulative-voting-which-method-engages-union-members-better/
  53. https://alblawfirm.com/case-studies/cumulative-voting/
  54. https://www.meridiaars.com/straight-vs-cumulative-voting/
  55. https://www.surveyandballotsystems.com/blog/best-practices/cumulative-voting/
  56. https://repository.law.umich.edu/cgi/viewcontent.cgi?article=3133&context=mlr
  57. https://www.umsl.edu/~kimballd/CVSSQ2016.pdf
  58. https://econ.columbia.edu/wp-content/uploads/sites/32/2021/03/CV.NBER_2021.03.09.pdf
  59. https://www.sciencedirect.com/science/article/abs/pii/S0899825623000842
  60. https://www.nber.org/system/files/working_papers/w28674/w28674.pdf
  61. https://archive.fairvote.org/index.php?page=419
  62. https://cedar.wwu.edu/politicalscience_facpubs/11/
  63. https://ilsr.org/articles/2167-2/
  64. https://www.researchgate.net/publication/231782598_Minority_Representation_under_Cumulative_and_Limited_Voting
  65. https://fairvote.org/_cumulative_voting_comes_close_but_not_all_the_way_to_fair_representation/
  66. https://journals.sagepub.com/doi/10.1177/106591299004300113
  67. https://www.cambridge.org/core/journals/american-political-science-review/article/game-theory-and-cumulative-voting-in-illinois-19021954/9BAC24A6C4BE44055CD5A24ADFBF3797
  68. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2816508
  69. https://www.chicagomag.com/news/bring-back-the-big-house/
  70. https://www.washingtonpost.com/archive/opinions/1994/05/19/the-polarizing-nature-of-cumulative-voting/bfff878c-cc4d-4161-bf38-5ce4d64d096c/
  71. https://www.lohud.com/story/news/local/westchester/port-chester/2018/10/03/did-port-chesters-democratic-experiment-work/1459115002/
  72. https://www.sciencedirect.com/science/article/abs/pii/S0144818817300376
  73. https://www.researchgate.net/publication/319504328_Does_Mandating_Cumulative_Voting_Weaken_the_Controlling_Shareholders_A_Difference-in-Differences_Approach
  74. https://www.credencecorpsolutions.com/blog/companies-act-section-163-bg1545
  75. https://www.acga-asia.org/blog-detail.php?id=110
  76. https://www.researchgate.net/publication/257391211_Equality_in_cumulative_voting_A_systematic_review_with_an_improvement_proposal
Add your contribution
Related Hubs
User Avatar
No comments yet.