Below are lexical items in the Leipzig–Jakarta list as ranked by semantic stability, i.e. words least likely to be replaced by other words as a language evolves.
A ranked society in anthropology is one that ranks individuals in terms of their genealogical distance from the chief. Closer relatives of the chief have higher rank or social status than more distant ones. Societies who follow this kind of structure associate rank with power, where other societies associate wealth with power. When individuals and groups rank about equally, competition for positions of leadership may occur. In some cases rank is assigned to entire villages rather than individuals or families. The idea of a ranked society was criticized by Max Weber and Karl Marx. Ranks in ranked society are the different levels, platforms, or classes that determine someone’s influence on political aspects, votes, decision making, etc. A person’s ranking also gives them societal power (power within their civilisation).
Ranked voting, also called ranked-choice voting, is an election voting system in which voters rank choices in a hierarchy on the ordinal scale (ordinal voting systems): 1st, 2nd, 3rd, etc. In some areas, ranked-choice voting is called preferential voting, but in other places this term has various more-specialized meanings. The other major branch of voting systems is cardinal voting, where candidates are independently rated rather than ranked relative to each other.
Of the formal voting criteria, the ranked pairs method passes the majority criterion, the monotonicity criterion, the Smith criterion (which implies the Condorcet criterion), the Condorcet loser criterion, and the independence of clones criterion. Ranked pairs fails the consistency criterion and the participation criterion. While ranked pairs is not fully independent of irrelevant alternatives, it still satisfies local independence of irrelevant alternatives.
Positional voting is a ranked voting electoral system in which the options receive points based on their rank position on each ballot and the option with the most points overall wins.
The following table compares Ranked Pairs with other preferential single-winner election methods:
Ranked pairs (RP) or the Tideman method is an electoral system developed in 1987 by Nicolaus Tideman that selects a single winner using votes that express preferences. RP can also be used to create a sorted list of winners.
Used in national elections in Australia, this system is said to simulate a series of runoff elections. If no candidate is the first choice of more than half of the voters, then all votes cast for the candidate with the lowest number of first choices are redistributed to the remaining candidates based on who is ranked next on each ballot. If this does not result in any candidate receiving a majority, further rounds of redistribution occur.
Selection of the Condorcet winner is generally considered by psephologists as the ideal election outcome for a ranked system, so "Condorcet efficiency" is important when evaluating different methods of preferential voting. The Condorcet winner is the one that would win every two-way contest against every other alternative.
In mathematics, a ranked partially ordered set - or poset - may be either:
In theoretical computer science and formal language theory, a ranked alphabet is a pair of an ordinary alphabet F and a function Arity: F→ℕ. Each letter in F has its arity so it can be used to build terms. Nullary elements (of zero arity) are also called constants. Terms built with unary symbols and constants can be considered as strings. Higher arities lead to proper trees.
Ranked pairs fails independence of irrelevant alternatives. However, the method adheres to a less strict property, sometimes called independence of Smith-dominated alternatives (ISDA). It says that if one candidate (X) wins an election, and a new alternative (Y) is added, X will win the election if Y is not in the Smith set. ISDA implies the Condorcet criterion.
There are many types of preferential voting, with several used in governmental elections. Instant-runoff voting is employed in Australian state and federal elections, in Ireland for its presidential elections, and by some jurisdictions in the United States, United Kingdom, and New Zealand. A type and classification of ranked voting is called the single transferable vote, which is used for national elections in Ireland and Malta, the Australian Senate, for regional and local elections in Northern Ireland, for all local elections in Scotland, and for some local elections in New Zealand and the United States. Borda count is used in Slovenia and Nauru. Contingent vote and Supplementary vote are also used in a few locations. Condorcet methods have found more use among private organizations and minor parties.
An equivalent definition is to find the order of finish that minimizes the size of the largest reversed majority. (In the 'lexicographical order' sense. If the largest majority reversed in two orders of finish is the same, the two orders of finish are compared by their second largest reversed majorities, etc. See the discussion of MinMax, MinLexMax and Ranked Pairs in the 'Motivation and uses' section of the Lexicographical Order article). (In the example, the order of finish "A, B, C" reverses the 60% who rank C over A. Any other order of finish would reverse a larger majority.) This definition is useful for simplifying some of the proofs of Ranked Pairs' properties, but the "constructive" definition executes much faster (small polynomial time).
The ranked battle system is a ranking ladder which organizes players using RP (reputation points), which are rewarded or lost at the end of a completed battle. These points place players within a certain league, depending on how much RP they have. From lowest to highest, there are 5 leagues: Training, Bronze, Silver, Gold, and Masters. Upon entering a league for the first time, the game will grant players with the paint and 5 containers for the corresponding league. Every 2 months, the league system enters a new season. At that time, the game will award players with crystals, x crystals, and league containers for the league they ended the season in. The game also reduces each player's RP by a certain amount, depending on where they are at.
For example, in an election conducted using the Condorcet compliant method Ranked pairs the following votes are cast:
B is the Condorcet winner and therefore the Ranked pairs winner.
Following the 2014 provincial election, the Minister of Municipal Affairs and Housing, Ted McMeekin, announced the province would be reexamining the Municipal Elections Act, 1996 to determine if the length and voting systems of Ontario's municipal elections needed alterations. Part of the reexamination was a proposal that would have allowed municipalities to adopt a ranked ballot system for the 2018 municipal elections.
In 2016, the provincial government passed Bill 181, the Municipal Elections Modernization Act, which permitted municipalities to adopt ranked ballots for municipal elections.
This example shows that the Ranked pairs method violates the IIA criterion. Assume three candidates A, B and C and 7 voters with the following preferences: