|
Summability Criterion
In election science, a voting method satisfies the summability criterion if it is possible to tally election results locally by precinct, then calculate the results by adding up all the votes. More formally, the compilation or summation complexity of a voting system measures the difficulty of vote counting for individual precincts, and is equal to the smallest number of bits needed to summarize all the votes. A voting method is called summable if the number of bits grows as a polynomial function of the number of candidates. Often, a group has to accept a decision, but not all the votes can be gathered together in a single location. In such a situation, we need to take the votes of the present voters and summarize them such that, when the other votes arrive, we can determine the winner. The compilation complexity of a voting-rule is the smallest number of bits required for the summary. A key advantage of low compilation complexity is it makes it easier to verify voting outcomes. L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Election Science
Election science is a field that deals with the conduct and administration of Election, elections. It is distinct from the study of public opinion and election forecasting (which fall under political science and psephology). Election science combines the theoretical study of social choice theory (a branch of math and welfare economics) with empirical research dealing with the administration of elections (a branch of political science). The study of election science can be traced back to early scientific studies of electoral systems and particularly the development of the field of social choice theory, including the Marquis de Condorcet's analysis of Electoral system, electoral systems in the 18th century. The field came into being following the 2000 United States presidential election, where several administrative and technical failures may have affected the outcome of the election. Examples of subjects where election science methods are applied include gerrymandering, electoral ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tournament (graph Theory)
In graph theory, a tournament is a directed graph with exactly one edge between each two vertices, in one of the two possible directions. Equivalently, a tournament is an orientation of an undirected complete graph. (However, as directed graphs, tournaments are not complete: complete directed graphs have two edges, in both directions, between each two vertices.) Equivalently, a tournament is a complete asymmetric relation. The name ''tournament'' comes from interpreting the graph as the outcome of a round-robin tournament, a game where each player is paired against every other exactly once. In a tournament, the vertices represent the players, and the edges between players point from the winner to the loser. Many of the important properties of tournaments were investigated by H. G. Landau in 1953 to model dominance relations in flocks of chickens. Tournaments are also heavily studied in voting theory, where they can represent partial information about voter preferences am ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Communication Complexity
In theoretical computer science, communication complexity studies the amount of communication required to solve a problem when the input to the problem is distributed among two or more parties. The study of communication complexity was first introduced by Andrew Yao in 1979, while studying the problem of computation distributed among several machines. The problem is usually stated as follows: two parties (traditionally called Alice and Bob) each receive a (potentially different) n- bit string x and y. The goal is for Alice to compute the value of a certain function, f(x, y), that depends on both x and y, with the least amount of communication between them. While Alice and Bob can always succeed by having Bob send his whole n-bit string to Alice (who then computes the function f), the idea here is to find clever ways of calculating ''f'' with fewer than n bits of communication. Note that, unlike in computational complexity theory, communication complexity is not concerned with the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partially Ordered Set
In mathematics, especially order theory, a partial order on a Set (mathematics), set is an arrangement such that, for certain pairs of elements, one precedes the other. The word ''partial'' is used to indicate that not every pair of elements needs to be comparable; that is, there may be pairs for which neither element precedes the other. Partial orders thus generalize total orders, in which every pair is comparable. Formally, a partial order is a homogeneous binary relation that is Reflexive relation, reflexive, antisymmetric relation, antisymmetric, and Transitive relation, transitive. A partially ordered set (poset for short) is an ordered pair P=(X,\leq) consisting of a set X (called the ''ground set'' of P) and a partial order \leq on X. When the meaning is clear from context and there is no ambiguity about the partial order, the set X itself is sometimes called a poset. Partial order relations The term ''partial order'' usually refers to the reflexive partial order relatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knowledge Compilation
Knowledge compilation is a family of approaches for addressing the intractability of a number of artificial intelligence problems. A propositional model is compiled in an off-line phase in order to support some queries in polynomial time. Many ways of compiling a propositional model exist.Adnan Darwiche, Pierre Marquis,A Knowledge Compilation Map, Journal of Artificial Intelligence Research 17 (2002) 229-264 Different compiled representations have different properties. The three main properties are: * The compactness of the representation * The queries that are supported in polynomial time * The transformations of the representations that can be performed in polynomial time Classes of representations Some examples of diagram classes include OBDDs, FBDDs, and non-deterministic OBDDs, as well as MDD. Some examples of formula In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Single Non-transferable Vote
Single non-transferable vote or SNTV is a multi-winner electoral system in which each voter casts a single vote. Being a semi-proportional variant of first-past-the-post voting, under SNTV small parties, as well as large parties, have a chance to be represented. Under SNTV, a single party seldom will take all seats in a city or district, as generally happens with winner-take-all systems. Under certain conditions, such as perfect tactical voting, SNTV is equivalent to proportional representation by the D'Hondt method. SNTV is a combination of multi-member districts and each voter casting just one vote. SNTV can be considered a variant of dot voting where each voter has only one point to assign. It can also be seen as a variant of limited voting where each elector has one vote, or as a simple version of Single Transferable Voting where votes are not transferred. Unlike block voting or limited voting, where voters can cast multiple votes, under SNTV each voter casts just on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Approval Ballot
An approval ballot, also called an unordered ballot, is a ballot in which a voter may vote for any number of candidates simultaneously, rather than for just one candidate. Candidates that are selected in a voter's ballot are said to be ''approved'' by the voter; the other candidates are said to be ''disapproved'' or ''rejected''. Approval ballots do not let the voters specify a preference-order among the candidates they approve; hence the name ''unordered''. This is in contrast to ranked ballots, which are ordered. There are several electoral systems that use approval balloting; they differ in the way in which the election outcome is determined: * In approval voting, there is a single winner, and he/she is the candidate with the largest number of votes. * In multiple non-transferable vote (also called block voting) there is a fixed number (say ''k'') of winners, and they are the ''k'' candidates with the largest number of votes. * In other multiwinner approval voting systems, there i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ranked Ballot
A ranking is a relationship between a set of items, often recorded in a list, such that, for any two items, the first is either "ranked higher than", "ranked lower than", or "ranked equal to" the second. In mathematics, this is known as a weak order or total preorder of objects. It is not necessarily a total order of objects because two different objects can have the same ranking. The rankings themselves are totally ordered. For example, materials are totally preordered by hardness, while degrees of hardness are totally ordered. If two items are the same in rank it is considered a tie. By reducing detailed measures to a sequence of ordinal numbers, rankings make it possible to evaluate complex information according to certain criteria. Thus, for example, an Internet search engine may rank the pages it finds according to an estimation of their relevance, making it possible for the user quickly to select the pages they are likely to want to see. Analysis of data obtained by ranki ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiwinner Voting
Multiwinner or committee voting refers to electoral systems that elect several candidates at once. Such methods can be used to elect parliaments or committees. Goals There are many scenarios in which multiwinner voting is useful. They can be broadly classified into three classes, based on the main objective in electing the committee: # Excellence. Here, voters judge the quality of each candidate individually. The goal is to find the "objectively" best candidates. An example application is shortlisting: selecting, from a list of candidate employees, a small set of finalists, who will proceed to the final stage of evaluation (e.g. using an interview). Here, each candidate is evaluated independently of the others. If two candidates are similar, then probably both will be elected or both will be rejected. # Diversity. Here, the elected candidates should be as ''different'' as possible. For example, suppose the contest is about choosing locations for two fire stations or other fac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Highest Median Voting Rules
The highest median voting rules are a class of graded voting rules where the candidate with the highest median rating is elected. The various highest median rules differ in their treatment of ties, i.e., the method of ranking the candidates with the same median rating. Proponents of highest median rules argue that they provide the most faithful reflection of the voters' opinion. They note that as with other cardinal voting rules, highest medians are not subject to Arrow's impossibility theorem. However, critics note that highest median rules violate participation and the Archimedean property; highest median rules can fail to elect a candidate almost-unanimously preferred over all other candidates. Example As in score voting, voters rate candidates along a common scale, e.g.: An elector can give the same appreciation to several different candidates. A candidate not evaluated automatically receives the mention "Bad". Then, for each candidate, we calculate what percentage o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bucklin Voting
Bucklin voting is a class of voting methods that can be used for single-member and multi-member districts. As in highest median rules like the majority judgment, the Bucklin winner will be one of the candidates with the highest median ranking or rating. It is named after its original promoter, the Georgist politician James W. Bucklin of Grand Junction, Colorado, and is also known as the Grand Junction system. Voting process Bucklin rules varied, but here is a typical example: Voters are allowed rank preference ballots (first, second, third, etc.). First choice votes are first counted. If one candidate has a majority, that candidate wins. Otherwise the second choices are added to the first choices. Again, if a candidate with a majority vote is found, the winner is the candidate with the most votes accumulated. Lower rankings are added as needed. A majority is determined based on the number of valid ballots. Since, after the first round, there may be more votes cast than vot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
STAR Voting
STAR voting is an electoral system for single-seat elections. The name (an allusion to Star (classification), star ratings) stands for "Score Then Automatic Runoff", referring to the fact that this system is a combination of score voting, to pick two finalists with the highest total scores, followed by an "automatic runoff" in which the finalist who is preferred on more ballots wins. It is a type of cardinal voting electoral system. Method In STAR, voters are given a score ballot (or ratings ballot) on which each voter scores candidates with a number from 0 up to 5, with 0 representing "worst" and 5 representing "best". The scores for each candidate are then summed, and the two highest-scored candidates are selected as finalists. In the automatic runoff round, the finalist who was given a higher score on a greater number of ballots is selected as the winner. Usage The concept was first proposed in October 2014 by Mark Frohnmayer, and was initially called score runoff voting ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
