Black's method is an

election method An electoral or voting system is a set of rules used to determine the results of an election. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, nonprofit organizations and inf ...

proposed by

Duncan Black Duncan Black, FBA (23 May 1908 – 14 January 1991) was a Scottish economist who laid the foundations of social choice theory. In particular he was responsible for unearthing the work of many early political scientists, including Charles Lut ...

in 1958 as a compromise between the

Condorcet method A Condorcet method (; ) is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, whenever there is such a candidate. A candidate with this property, the ...

and the

Borda count The Borda method or order of merit is a positional voting rule that gives each candidate a number of points equal to the number of candidates ranked below them: the lowest-ranked candidate gets 0 points, the second-lowest gets 1 point, and so on ...

. This method selects a Condorcet winner. If a Condorcet winner does not exist, then the candidate with the highest Borda score is selected.

Properties

Among methods satisfying the majority criterion, Black's method gives the minimum power to the majority and hence the method is best at protecting minorities.

Satisfied criteria

Black's method satisfies the following criteria: *

Unrestricted domain In social choice theory, unrestricted domain, or universality, is a property of social welfare functions in which all preferences of all voters (but no other considerations) are allowed. Intuitively, unrestricted domain is a common requirement fo ...

* Non-imposition ( a.k.a. citizen sovereignty) *

Non-dictatorship In social choice theory, a dictatorship mechanism is a degenerate voting rule or mechanism where the result depends on one person's. A serial dictatorship is similar, but also designates a series of "backup dictators", who break ties in the origina ...

Homogeneity Homogeneity and heterogeneity are concepts relating to the Uniformity (chemistry), uniformity of a Chemical substance, substance, process or image. A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, ...

Condorcet criterion A Condorcet winner (, ) is a candidate who would receive the support of more than half of the electorate in a one-on-one race against any one of their opponents. Voting systems where a majority winner will always win are said to satisfy the Condo ...

* Majority criterion * Pareto criterion ( a.k.a.

unanimity Unanimity is agreement by all people in a given situation. Groups may consider unanimous decisions as a sign of social, political or procedural agreement, solidarity, and unity. Unanimity may be assumed explicitly after a unanimous vote or imp ...

) *

Monotonicity criterion Electoral system criteria In social choice, the negative response, perversity, or additional support paradox is a pathological behavior of some voting rules where a candidate loses as a result of having too much support (or wins because of in ...

Majority loser criterion The majority loser criterion is a criterion to evaluate single-winner voting systems. The criterion states that if a majority of voters give a candidate no support, i.e. do not list that candidate on their ballot, that candidate must lose (unles ...

Condorcet loser criterion In single-winner voting system theory, the Condorcet loser criterion (CLC) is a measure for differentiating voting systems. It implies the majority loser criterion but does not imply the Condorcet winner criterion. A voting system complying wi ...

Reversal symmetry The reversal symmetry criterion is a voting system criterion which says that if every voter's opinions on each of the candidates is perfectly reversed (i.e. they rank candidates in order from worst to best), the outcome of the election should b ...

Resolvability criterion A voting system is called decisive, resolvable, or resolute if it ensures a low probability of tied elections. There are two different criterion that formalize this. * In Nicolaus Tideman's version of the criterion, adding one extra vote (with no ...

Polynomial time In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations p ...

Failed criteria

Black's method does not satisfy the following criteria: *

Mutual majority criterion The mutual majority criterion is a criterion for evaluating electoral systems. It is also known as the majority criterion for solid coalitions and the generalized majority criterion. This criterion requires that whenever a majority of voters prefe ...

Smith criterion The Smith set, sometimes called the top-cycle or Condorcet winning set, generalizes the idea of a Condorcet winner to cases where no such winner exists. It does so by allowing cycles of candidates to be treated jointly, as if they were a single ...

* Participation *

Consistency In deductive logic, a consistent theory is one that does not lead to a logical contradiction. A theory T is consistent if there is no formula \varphi such that both \varphi and its negation \lnot\varphi are elements of the set of consequences ...

Independence of Smith-dominated alternatives Independence of Smith-dominated alternatives (ISDA, also known as Smith- IIA) is a voting system criterion which says that the winner of an election should not be affected by candidates who are not in the Smith set. Another way of defining ISDA i ...

* Independence of clones *

Independence of irrelevant alternatives Independence of irrelevant alternatives (IIA) is an axiom of decision theory which codifies the intuition that a choice between A and B (which are both related) should not depend on the quality of a third, unrelated outcome C. There are several dif ...

Local independence of irrelevant alternatives In social choice theory and politics, a spoiler effect happens when a losing candidate affects the results of an election simply by participating. Voting rules that are not affected by spoilers are said to be spoilerproof. The frequency and se ...

Sincere favorite criterion The sincere favorite or no favorite-betrayal criterion is a voting system criterion, property of some voting systems that says voters should have no incentive to vote for someone else over their favorite.Alex Small, “Geometric construction of vo ...

References

{{ voting systems Single-winner electoral systems Monotonic Condorcet methods Electoral systems Preferential electoral systems