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Score voting or range voting is an
electoral system An electoral system or voting system is a set of rules that determine how elections and Referendum, referendums are conducted and how their results are determined. Electoral systems are used in politics to elect governments, while non-political ...
for single-seat elections, in which voters give each candidate a score, the scores are added (or averaged), and the candidate with the highest total is elected. It has been described by various other names including evaluative voting, utilitarian voting, interval measure voting, the point system, ratings summation, 0-99 voting, average voting and utility voting. It is a type of
cardinal voting Cardinal voting refers to any electoral system which allows the voter to give each candidate an independent evaluation, typically a rating or grade. These are also referred to as "rated" (ratings ballot), "evaluative", "graded", or "absolute" ...
electoral system, and aims to implement the
utilitarian social choice rule In social choice and operations research, the utilitarian rule (also called the max-sum rule) is a rule saying that, among all possible alternatives, society should pick the alternative which maximizes the ''sum of the utilities'' of all individual ...
. Score voting should be distinguished from
positional voting Positional voting is a ranked voting electoral system in which the options or candidates receive points based on their rank position on each ballot and the one with the most points overall wins. The lower-ranked preference in any adjacent pair i ...
systems, such as the
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 ...
: in score voting, each voter is free to give any score to any candidate; in positional voting, the score that each voter gives to each candidate is uniquely determined by the candidate's rank in the voter's ballot.


Usage


Political use

Combined approval voting, a 3-rank form of score voting, is used to determine which candidates represent the parties in
Latvia Latvia ( or ; lv, Latvija ; ltg, Latveja; liv, Leţmō), officially the Republic of Latvia ( lv, Latvijas Republika, links=no, ltg, Latvejas Republika, links=no, liv, Leţmō Vabāmō, links=no), is a country in the Baltic region of ...
's
Saeima The Saeima () is the parliament of the Latvia, Republic of Latvia. It is a unicameral parliament consisting of 100 members who are elected by proportional representation, with seats allocated to political parties which gain at least 5% of the po ...
(parliament). The number of seats for each party is determined by the
Webster/Sainte-Laguë method The Webster method, also called the Sainte-Laguë method () or the major fractions method, is a method for allocating seats in a parliament among federal states, or among parties in a party-list proportional representation system. The method ...
of
proportional representation Proportional representation (PR) refers to a type of electoral system under which subgroups of an electorate are reflected proportionately in the elected body. The concept applies mainly to geographical (e.g. states, regions) and political divis ...
. A crude form of score voting was used in some elections in ancient
Sparta Sparta ( Doric Greek: Σπάρτα, ''Spártā''; Attic Greek: Σπάρτη, ''Spártē'') was a prominent city-state in Laconia, in ancient Greece. In antiquity, the city-state was known as Lacedaemon (, ), while the name Sparta referre ...
, by measuring how loudly the crowd shouted for different candidates. This has a modern-day analog of using clapometers in some television shows and the judging processes of some athletic competitions. The
Republic of Venice The Republic of Venice ( vec, Repùblega de Venèsia) or Venetian Republic ( vec, Repùblega Vèneta, links=no), traditionally known as La Serenissima ( en, Most Serene Republic of Venice, italics=yes; vec, Serenìsima Repùblega de Venèsia, ...
elected the
Doge A doge ( , ; plural dogi or doges) was an elected lord and head of state in several Italian city-states, notably Venice and Genoa, during the medieval and renaissance periods. Such states are referred to as " crowned republics". Etymology The ...
in a multi-round system, with the round that actually named the Doge being a three point score election (For, Neutral, Against). This process was used continually, with only minor changes, for over 500 years, until the republic was conquered by Napoleon. A modern governmental example is the selection process for the
Secretary-General of the United Nations The secretary-general of the United Nations (UNSG or SG) is the chief administrative officer of the United Nations and head of the United Nations Secretariat, one of the six principal organs of the United Nations. The role of the secretary-g ...
, which also has a three-point scale ("Encourage," "Discourage," and "No Opinion"). Score voting is used by the Green Party of Utah to elect officers, on a 0–9 scale.


Non-political use

Members of Wikipedia's Arbitration Committee are elected using a three-point scale ("Support", "Neutral", "Oppose"). Ballots are tallied equivalently to averaged
approval voting Approval voting is an electoral system in which voters can select many candidates instead of selecting only one candidate. Description Approval voting ballots show a list of the options of candidates running. Approval voting lets each voter i ...
, with "Neutral" treated as abstention, sometimes called "Explicit approval voting". Non-governmental uses of score voting are common, such as in
Likert scale A Likert scale ( , commonly mispronounced as ) is a psychometric scale commonly involved in research that employs questionnaires. It is the most widely used approach to scaling responses in survey research, such that the term (or more fully the ...
customer satisfaction Customer satisfaction (often abbreviated as CSAT) is a term frequently used in marketing. It is a measure of how products and services supplied by a company meet or surpass customer expectation. Customer satisfaction is defined as "the number of c ...
surveys (such as for a restaurant), automated telephone surveys (where one is asked to press or say a number to indicate their level of satisfaction or likelihood), and any mechanism that involves users rating a product or service in terms of "stars" (such as rating movies on
IMDb IMDb (an abbreviation of Internet Movie Database) is an online database of information related to films, television series, home videos, video games, and streaming content online – including cast, production crew and personal biographies, ...
, products at
Amazon Amazon most often refers to: * Amazons, a tribe of female warriors in Greek mythology * Amazon rainforest, a rainforest covering most of the Amazon basin * Amazon River, in South America * Amazon (company), an American multinational technology c ...
, apps in the iOS or
Google Play Google Play, also known as the Google Play Store and formerly the Android Market, is a digital distribution service operated and developed by Google. It serves as the official app store for certified devices running on the Android (operating sys ...
stores, etc.). Score voting is common for processes with no single winner: for instance, some websites allow users to rate items such as movies (
Internet Movie Database IMDb (an abbreviation of Internet Movie Database) is an online database of information related to films, television series, home videos, video games, and streaming content online – including cast, production crew and personal biographies, ...
), comments, and recipes. The result is a ranked list of items rather than one winning item. Sports such as
gymnastics Gymnastics is a type of sport that includes physical exercises requiring balance, strength, flexibility, agility, coordination, dedication and endurance. The movements involved in gymnastics contribute to the development of the arms, legs, shou ...
rate competitors on a numeric scale. The fact that judges' ratings are public makes them less likely to engage in blatant
tactical voting Strategic voting, also called tactical voting, sophisticated voting or insincere voting, occurs in voting systems when a voter votes for another candidate or party than their ''sincere preference'' to prevent an undesirable outcome. For example, ...
. A multi-winner variant, re-weighted score voting, is used to select five nominees for the
Academy Award for Best Visual Effects The Academy Award for Best Visual Effects is an Academy Award given for the best achievement in visual effects. History of the award The Academy of Motion Picture Arts and Sciences first recognized the technical contributions of special effects ...
using a 0–10 scale. The traditional "highest
grade point average Grading in education is the process of applying standardized measurements for varying levels of achievements in a course. Grades can be assigned as letters (usually A through F), as a range (for example, 1 to 6), as a percentage, or as a numbe ...
" method of selecting a
Valedictorian Valedictorian is an academic title for the highest-performing student of a graduating class of an academic institution. The valedictorian is commonly determined by a numerical formula, generally an academic institution's grade point average (GPA ...
can be seen as a type of score election, wherein instructors "vote" on the student "candidates," with grades as their score-based votes.


Types

Score voting uses a
ratings ballot A rating is an evaluation or assessment of something, in terms of quality, quantity, or some combination of both. Rating or ratings may also refer to: Business and economics * Credit rating, estimating the credit worthiness of an individual, ...
; that is, each voter rates each candidate with a number within a specified score, such as 0 to 9 or 1 to 5. In the simplest system, all candidates must be rated. The scores for each candidate are then summed, and the candidate with the highest sum is the winner. (This is simpler for voters than
cumulative voting Cumulative voting (also accumulation voting, weighted voting or multi-voting) is a multiple-winner method intended to promote more proportional representation than winner-take-all elections such as block voting or first past the post. Cumulative ...
, where they are not permitted to provide scores for more than some number of candidates.) Some systems allow voters to explicitly ''abstain'' from rating certain candidates, as opposed to implicitly giving the lowest number of points to unrated candidates. In this case, a candidate's score would be the ''average'' rating from voters who did rate this candidate. However, some method must then be used to exclude candidates who received too few votes, to provide a meaningful average. In some competitions subject to judges' scores, a
truncated mean A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median. It involves the calculation of the mean after discarding given parts of a probability distribution or sample at the high and low end, an ...
is used to remove extreme scores. For example, score voting with truncated means is used in figure skating competitions to avoid the results of the third skater affecting the relative positions of two skaters who have already finished their performances (the
independence of irrelevant alternatives The independence of irrelevant alternatives (IIA), also known as binary independence or the independence axiom, is an axiom of decision theory and various social sciences. The term is used in different connotation in several contexts. Although it a ...
), using truncation to mitigate biases of some judges who have ulterior motives to score some competitors too high or low. Another method of counting ratings ballots is to find the
median In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic fe ...
score of each candidate, and elect a candidate with the highest median score. This method is also referred to as
Majority Judgment Majority judgment (MJ) is a single-winner voting system proposed in 2007 by Michel Balinski and Rida Laraki. It is a highest median rule, i.e., a cardinal voting system that elects the candidate with the highest median rating. Unlike other vo ...
. It could have the effect of reducing the incentive to exaggerate. A potential disadvantage is that multiway exact ties for winner may become common, although a method exists in Majority Judgment to break such ties. In conventional score voting, these ties would be extremely rare. Another consequence of using medians is that adding an "all-zero ballot" can alter the election winner, which is arguably a disadvantage. Another proposed variant is
STAR voting STAR voting is an electoral system for single-seat elections. Variations also exist for multi-winner and proportional representation elections. The name (an allusion to star ratings) stands for "Score then Automatic Runoff", referring to the f ...
(Score Then Automatic Runoff). Under this system, each voter may assign a score, from 0 to the maximum score, to any number of candidates. Of the two highest-scoring candidates, the winner is the one more voters assigned a higher score. The concept was first proposed publicly in October 2014 by
Center for Election Science The Center for Election Science (CES) is an American 501(c)(3) organization, 501(c)(3) organization that focuses on voter education and promoting election science. The organization promotes electoral systems favored by Social choice theory, soc ...
co-founder Clay Shentrup. The runoff step was introduced in order to correct for strategic distortion in ordinary score voting, such as
Bullet voting Bullet voting, also known as single-shot voting and plump voting, is a voting tactic, usually in multiple-winner elections, where a voter is entitled to vote for more than one candidate, but instead votes for only one candidate. A voter might do th ...
and tactical maximization. Score voting in which only two different votes may be submitted (0 and 1, for example) is equivalent to
approval voting Approval voting is an electoral system in which voters can select many candidates instead of selecting only one candidate. Description Approval voting ballots show a list of the options of candidates running. Approval voting lets each voter i ...
. As with approval voting, score voters must weigh the adverse impact on their favorite candidate of ranking other candidates highly. The term "range voting" is used to describe a more theoretical system in which voters can express any
real number In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every real ...
within the
range Range may refer to: Geography * Range (geographic), a chain of hills or mountains; a somewhat linear, complex mountainous or hilly area (cordillera, sierra) ** Mountain range, a group of mountains bordered by lowlands * Range, a term used to i ...
, 1 The comma is a punctuation mark that appears in several variants in different languages. It has the same shape as an apostrophe or single closing quotation mark () in many typefaces, but it differs from them in being placed on the baseline (t ...
While convenient for mathematical analysis, this scale is not practical for real-world elections, and is typically approximated as a score voting system with many possible grades, such as a
slider Slider or Sliders may refer to: Arts * K.K. Slider, a fictional character within the ''Animal Crossing'' franchise * '' The Slider'', a 1972 album by T. Rex * ''Sliders'' (TV series), an American science fiction and fantasy television series * ...
in a computer interface.


Example

Suppose that 100 voters each decided to grant from 0 to 10 points to each city such that their most liked choice got 10 points, and least liked choice got 0 points, with the intermediate choices getting an amount proportional to their relative distance. Nashville, the capital in real life, likewise wins in the example. However, if voters from Knoxville and Chattanooga were to rate Nashville as 0 (so too for Memphis) and both sets of voters were to rate Chattanooga as 10, the winner would be Chattanooga over Nashville by 508 to 428 (and 484 for Memphis). This would be a better outcome for the voters in those cities than what they would get if they were to reflect their true preferences, and is considered to be an instance of tactical voting. Such tactical voting would be less effective if the ballots were counted using median scores (the principle behind
Majority Judgment Majority judgment (MJ) is a single-winner voting system proposed in 2007 by Michel Balinski and Rida Laraki. It is a highest median rule, i.e., a cardinal voting system that elects the candidate with the highest median rating. Unlike other vo ...
). For comparison, note that traditional first-past-the-post would elect Memphis, even though most citizens consider it the worst choice, because 42% is larger than any other single city.
Instant-runoff voting Instant-runoff voting (IRV) is a type of ranked preferential voting method. It uses a majority voting rule in single-winner elections where there are more than two candidates. It is commonly referred to as ranked-choice voting (RCV) in the Un ...
would elect the 2nd-worst choice (Knoxville), because the central candidates would be eliminated early (and Chattanooga voters preferring Knoxville above Nashville). In
Approval voting Approval voting is an electoral system in which voters can select many candidates instead of selecting only one candidate. Description Approval voting ballots show a list of the options of candidates running. Approval voting lets each voter i ...
, with each voter selecting their top two cities, Nashville would win because of the significant boost from Memphis residents. A
two-round system The two-round system (TRS), also known as runoff voting, second ballot, or ballotage, is a voting method used to elect a single candidate, where voters cast a single vote for their preferred candidate. It generally ensures a majoritarian resul ...
would have a runoff between Memphis and Nashville where Nashville would win.


Properties

Score voting allows voters to express preferences of varying strengths. Score voting satisfies the
monotonicity criterion The monotonicity criterion is a voting system criterion used to evaluate both single and multiple winner ranked voting systems. A ranked voting system is monotonic if it is neither possible to prevent the election of a candidate by ranking them h ...
, i.e. raising your vote's score for a candidate can never hurt their chances of winning, and lowering it can never help their chances. Also, score voting satisfies the
participation criterion The participation criterion is a voting system criterion. Voting systems that fail the participation criterion are said to exhibit the no show paradox and allow a particularly unusual strategy of tactical voting: abstaining from an election can he ...
, i.e. casting a sincere vote can never result in a worse election winner (from your point of view) than if you had simply abstained from voting. Score voting is independent of clones in the sense that if there is a set of candidates such that every voter gives the same rating to every candidate in this set, then the probability that the winner is in this set is independent of how many candidates are in the set. In summary, score voting satisfies the
monotonicity criterion The monotonicity criterion is a voting system criterion used to evaluate both single and multiple winner ranked voting systems. A ranked voting system is monotonic if it is neither possible to prevent the election of a candidate by ranking them h ...
, the
participation criterion The participation criterion is a voting system criterion. Voting systems that fail the participation criterion are said to exhibit the no show paradox and allow a particularly unusual strategy of tactical voting: abstaining from an election can he ...
, the
consistency criterion A voting system is consistent if, whenever the electorate is divided (arbitrarily) into several parts and elections in those parts garner the same result, then an election of the entire electorate also garners that result. Smith calls this property ...
,
independence of irrelevant alternatives The independence of irrelevant alternatives (IIA), also known as binary independence or the independence axiom, is an axiom of decision theory and various social sciences. The term is used in different connotation in several contexts. Although it a ...
,
resolvability criterion Resolvability criterion can refer to any voting system criterion that ensures a low possibility of tie votes. * In Nicolaus Tideman's version of the criterion, for every (possibly tied) winner in a result, there must exist a way for one added vot ...
, and
reversal symmetry Reversal symmetry is a voting system criterion which requires that if candidate A is the unique winner, and each voter's individual preferences are inverted, then A must not be elected. Methods that satisfy reversal symmetry include Borda count, r ...
, provided voters do not have perfect information (see below; if they do have perfect information, it becomes a Condorcet method, which means it fails participation, consistency, and independence of irrelevant alternatives). It is immune to cloning, except for the obvious specific case in which a candidate with clones ties, instead of achieving a unique win. It does not satisfy either the
Condorcet criterion An electoral system satisfies the Condorcet winner criterion () if it always chooses the Condorcet winner when one exists. The candidate who wins a majority of the vote in every head-to-head election against each of the other candidatesthat is, a ...
(therefore is not a
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, that is, a candidate preferred by more voters than any others, whenever ...
) or the
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 ...
, although with all-strategic voters and perfect information the Condorcet winner is a
Nash equilibrium In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equili ...
. It does not satisfy the
later-no-harm criterion The later-no-harm criterion is a voting system criterion formulated by Douglas Woodall. Woodall defined the criterion as " ding a later preference to a ballot should not harm any candidate already listed." For example, a ranked voting method in w ...
, meaning that giving a positive rating to a less preferred candidate can cause a more preferred candidate to lose. It does not satisfy the
majority criterion The majority criterion is a single-winner voting system criterion, used to compare such systems. The criterion states that "if one candidate is ranked first by a majority (more than 50%) of voters, then that candidate must win". Some methods that ...
, but it satisfies a weakened form of it: a majority ''can'' force their choice to win, although they might not exercise that capability. To address this point, some proponents of score voting argue for the inclusion of an extra instant-runoff round in which a majority preference is established between the two top-rated candidates. As it satisfies the criteria of a deterministic voting method, with non-imposition, non-dictatorship, monotonicity, and independence of irrelevant alternatives, it may appear that it violates
Arrow's impossibility theorem Arrow's impossibility theorem, the general possibility theorem or Arrow's paradox is an impossibility theorem in social choice theory that states that when voters have three or more distinct alternatives (options), no ranked voting electoral syste ...
. The reason that score voting is not a counter-example to Arrow's theorem is that it is a cardinal voting method, while the "universality" criterion of Arrow's theorem effectively restricts that result to ordinal voting methods.


Strategy

Ideal score voting strategy for well-informed voters is identical to ideal
approval voting Approval voting is an electoral system in which voters can select many candidates instead of selecting only one candidate. Description Approval voting ballots show a list of the options of candidates running. Approval voting lets each voter i ...
strategy, and a voter would want to give their least and most favorite candidates a minimum and a maximum score, respectively. The game-theoretical analysis shows that this claim is not fully general, even if it holds in most cases. This leaves the tactical concern any voter has for scoring their second-favorite candidate, in the case that there are 3 or more candidates. Score too high (or anything above the minimum) and the voter harms their favorite candidate's chance to win. Score too low and the voter helps the candidate they least desire to beat their second-favorite and perhaps win. Another strategic voting tactic is given by the weighted mean utility theorem, maximum score for all candidates preferred compared to the expected winners weighted with winning probability and minimum score for all others. The validity of this problem is called into question by a 2009 paper which found that "experimental results support the concept of bias toward unselfish outcomes in large elections." The authors observed what they termed ethical considerations dominating voter behavior as pivot probability decreased. This would imply that larger elections, or those perceived as having a wider margin of victory, would result in fewer tactical voters. Exit poll experiments have shown that voters do make use of intermediate grades and tend to vote more sincerely for candidates they perceive have no chance of winning. How voters precisely grade candidates is a topic that is not fully settled, although experiments show that their behavior depends on the grade scale, its length, and the possibility to give negative grades. Advocates of score voting conclude that score voting may thus yield higher support for third party and independent candidates, unless those candidates become viable, than other common voting methods, and they refer to this possibility as the "nursery effect". They point out that score voting methods (including approval voting) give no reason to ever dishonestly rank a less-preferred candidate over a more-preferred one in 3-candidate elections. However, detractors respond that it provides motivation to rank a less-preferred and more-preferred candidate equally or near-equally (i.e., both 0-1 or both 98-99). This could lead to undemocratic results if different segments of the population used strategy at significantly different rates. (Note that traditional first-past-the-post voting forces all candidates except one to be ranked equally, so that all voters are compressing their preferences equally.) Addressing these criticisms, the Equal Vote Coalition, a voting reform advocacy group, proposes a variant of score voting with an extra second round featuring the two top-rated candidates, in which the candidate with the majority of preference wins. It is claimed that the existence of a second round would discourage approval-style strategic ballots and exaggeration of ratings, making it behave like a hybrid of ranked and rated voting systems.


Advocacy

Albert Heckscher was one of the earliest proponents, advocating for a form of score voting he called the "immanent method" in his 1892 dissertation, in which voters assign any number between -1 and +1 to each alternative, simulating their individual deliberation. This variant is also known as combined approval voting. Currently, score voting is advocated by The Center for Election Science, Center for Range Voting
Citoyens pour le Vote de Valeur
Counted and the website RangeVote.com. Guy Ottewell, who helped develop the method of
approval voting Approval voting is an electoral system in which voters can select many candidates instead of selecting only one candidate. Description Approval voting ballots show a list of the options of candidates running. Approval voting lets each voter i ...
, now endorses score voting.
Kenneth Arrow Kenneth Joseph Arrow (23 August 1921 – 21 February 2017) was an American economist, mathematician, writer, and political theorist. He was the joint winner of the Nobel Memorial Prize in Economic Sciences with John Hicks in 1972. In economics ...
is on record as saying that "score ..is probably the best." No elected official in the United States is known to endorse score voting. Since 2014, the Equal Vote Coalition advocates a variant method (
STAR A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
) with an extra second evaluation step to address some of the criticisms of traditional score voting.


See also

*
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 ...
*
Cardinal voting Cardinal voting refers to any electoral system which allows the voter to give each candidate an independent evaluation, typically a rating or grade. These are also referred to as "rated" (ratings ballot), "evaluative", "graded", or "absolute" ...
*
List of democracy and elections-related topics Types of democracy refers to pluralism of governing structures such as governments ( local through to global) and other constructs like workplaces, families, community associations, and so forth. Types of democracy can cluster around values. F ...
*
Consensus decision-making Consensus decision-making or consensus process (often abbreviated to ''consensus'') are group decision-making processes in which participants develop and decide on proposals with the aim, or requirement, of acceptance by all. The focus on es ...
*
Decision making In psychology, decision-making (also spelled decision making and decisionmaking) is regarded as the cognitive process resulting in the selection of a belief or a course of action among several possible alternative options. It could be either rati ...
*
Democracy Democracy (From grc, δημοκρατία, dēmokratía, ''dēmos'' 'people' and ''kratos'' 'rule') is a form of government in which the people have the authority to deliberate and decide legislation (" direct democracy"), or to choose gov ...
* Implicit utilitarian voting *
Utilitarian social choice rule In social choice and operations research, the utilitarian rule (also called the max-sum rule) is a rule saying that, among all possible alternatives, society should pick the alternative which maximizes the ''sum of the utilities'' of all individual ...
*
Hot or Not Hot or Not, currently rebranded as Chat & Date, is a rating site that allowed users to rate the attractiveness of photos submitted voluntarily by others. The site offered a matchmaking engine called 'Meet Me' and an extended profile feature ca ...
— a real-world example *
Majority judgment Majority judgment (MJ) is a single-winner voting system proposed in 2007 by Michel Balinski and Rida Laraki. It is a highest median rule, i.e., a cardinal voting system that elects the candidate with the highest median rating. Unlike other vo ...
— similar voting method, based on
median In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic fe ...
s instead of
average In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For example, the average of the numbers 2, 3, 4, 7, ...
s


Notes


External links


The Center for Range Voting
and it


The Center for Election Science
includes a
article on Score Voting

Equal Vote Coalition
which promotes a
STAR voting STAR voting is an electoral system for single-seat elections. Variations also exist for multi-winner and proportional representation elections. The name (an allusion to star ratings) stands for "Score then Automatic Runoff", referring to the f ...
, a variant of score voting, in the United States
RangeVote
includes a user-friendly presentation on score voting\

Article by Brian Olson. * {{voting methods Electoral systems Single-winner electoral systems Cardinal electoral systems Monotonic electoral systems Utilitarianism