Borda count

The Borda count is a family of positional voting rules which gives each candidate, for each ballot, a number of points corresponding to the number of candidates ranked lower. In the original variant, the lowest-ranked candidate gets 0 points, the next-lowest gets 1 point, etc., and the highest-ranked candidate gets n − 1 points, where n is the number of candidates. Once all votes have been counted, the option or candidate with the most points is the winner. The Borda count is intended to elect broadly acceptable options or candidates, rather than those preferred by a majority, and so is often described as a consensus-based voting system rather than a majoritarian one.^[1]

The Borda count was developed independently several times, being first proposed in 1435 by Nicholas of Cusa (see History below),^[2]^[3]^{[note 1]} but is named for the 18th-century French mathematician and naval engineer Jean-Charles de Borda, who devised the system in 1770.^[4] It is currently used to elect two ethnic minority members of the National Assembly of Slovenia,^[5] in modified forms to determine which candidates are elected to the party list seats in Icelandic parliamentary elections, and for selecting presidential election candidates in Kiribati. A variant known as the Dowdall system is used to elect members of the Parliament of Nauru.^[6] Until the early 1970s, another variant was used in Finland to select individual candidates within party lists. It is also used throughout the world by various private organizations and competitions.

In the Modified Borda count, any unranked options receive 0 points, the lowest ranked receives 1, the next-lowest receives 2, etc., up to a possible maximum of n points for the highest ranked option if all options are ranked. The Quota Borda system is another variant used to attain proportional representation in multiwinner voting.

^ Lippman, David. "Voting Theory" (PDF). Math in Society. Borda count is sometimes described as a consensus-based voting system, since it can sometimes choose a more broadly acceptable option over the one with majority support.
^ Emerson, Peter (16 January 2016). From Majority Rule to Inclusive Politics. Springer. ISBN 978-3-319-23500-4.
^ Emerson, Peter (1 February 2013). "The original Borda count and partial voting". Social Choice and Welfare. 40 (2): 353–358. doi:10.1007/s00355-011-0603-9. ISSN 0176-1714. S2CID 29826994.
^ McLean, Urken & Hewitt 1995, p. 81.
^ "Slovenia's electoral law". www.minelres.lv. Archived from the original on 4 March 2016. Retrieved 15 June 2009.
^ Cite error: The named reference Fraenkel_Grofman_2014 was invoked but never defined (see the help page).

Cite error: There are <ref group=note> tags on this page, but the references will not show without a {{reflist|group=note}} template (see the help page).

[Lippman-1] Lippman, David. "Voting Theory" (PDF). Math in Society. Borda count is sometimes described as a consensus-based voting system, since it can sometimes choose a more broadly acceptable option over the one with majority support.

[Emerson_2016-2] Emerson, Peter (16 January 2016). From Majority Rule to Inclusive Politics. Springer. ISBN 978-3-319-23500-4.

[:2-3] Emerson, Peter (1 February 2013). "The original Borda count and partial voting". Social Choice and Welfare. 40 (2): 353–358. doi:10.1007/s00355-011-0603-9. ISSN 0176-1714. S2CID 29826994.

[FOOTNOTEMcLeanUrkenHewitt199581-5] McLean, Urken & Hewitt 1995, p. 81.

[6] "Slovenia's electoral law". www.minelres.lv. Archived from the original on 4 March 2016. Retrieved 15 June 2009.

[Fraenkel_Grofman_2014-7] Cite error: The named reference Fraenkel_Grofman_2014 was invoked but never defined (see the help page).

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