Cumulative voting
Cumulative voting (accumulation voting or weighted voting) is a (usually) multiple-winner voting system intended to promote proportional representation. It 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 1980. It was used in England in the late 19th century to elect school boards.
In the most common implementation of this system, a voter facing multiple choices is given X number of points. The voter can then assign his points to one or more of the choices, thus enabling one to weight one's vote if desired. This could be achieved through a normalized ratings ballot, or through multiple plurality ballots, one per each point allocated. Typically, each voter will have as many votes as there are winners to be selected. If there was only one winner to be selected and voters were given one vote, this is equivalent to the First Past the Post electoral system voting.
A more generalized implementation would simply be to allow the voter to split their vote in whatever proportions they like i.e. a voter might give 67.3% of their vote to one candidate, and the remainder to another.
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. In general, one should put all of their points behind a single candidate to maximize that candidate's chances of winning i.e. they should use FPTP-like strategy to boost their favorite frontrunner.
 Traditional ballot |
 Variation |
 Generalized ballot |
 For corporate boards |
Quadratic voting
A variant of cumulative voting which gained popularity in 2018 is Quadratic voting. Quadratic voting was conducted in an experiment by the Democratic caucus of the Colorado House of Representatives in April 2019. It differs from Cumulative voting by altering "the cost" and "the vote" relation from linear to quadratic.
Criticism
Quadratic voting has all the major flaws of cumulative voting such as vote splitting and complexity.
Notes
Cumulative voting can be thought of as a generalization of FPTP and SNTV; specifically, when every voter puts all of their points into one candidate, they are all equivalent. Because of this, cumulative voting passes the same weak form of PSC that SNTV does.
In addition, the fractional way of implementing equal-ranking in IRV is a form of equal&even cumulative voting.