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Duggan–Schwartz Theorem
The Duggan–Schwartz theorem (named after John Duggan and Thomas Schwartz) is a result about voting systems designed to choose a nonempty set of winners from the preferences of certain individuals, where each individual ranks all candidates in order of preference. It states that for three or more candidates, at least one of the following must hold: #The system is not anonymous (some voters are treated differently from others). #The system is imposed (some candidates can never win). #Every voter's top preference is in the set of winners. #The system can be manipulated by either an optimistic voter, one who can cast a ballot that would elect some candidate to a higher rank than all of those candidates who would have been elected if that voter had voted honestly; or by a pessimistic voter, one who can cast a ballot that would exclude some candidate to a lower rank than all of those candidates who were elected due that voter voting strategically. The first two conditions are consider ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Duggan (political Scientist)
John Duggan may refer to: * John Duggan (rugby, born 1929) (1929–2022), English former rugby union and rugby league footballer * John Duggan (rugby union, born 1948), Irish former Leicester Tigers winger * John Duggan (bishop) (1918–2000), Bishop of Tuam, Killala, and Achonry, 1970–1985 * Jack Duggan (politician) (1910–1993), Australian politician for Electoral district of Toowoomba West * Johnny Duggan (jockey), on racehorse Gold and Black * John Duggan, main character in the TV series '' Duggan'' * John Duggan, character in the TV series ''The Thick of It'' * Jack Duggan (ice hockey) (1897–1977), ice hockey player * Jack Duggan (politician) John Edmund Duggan (30 December 1910 – 19 June 1993) was a member of the Queensland Legislative Assembly. He was the Deputy Premier of Queensland from 1953 until 1957 and Leader of the Opposition of Queensland from 1958 until 1966. Early li ... (1910–1993), member of the Queensland Legislative Assembly * John Duggan (poli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas Schwartz (political Scientist)
Thomas Allen Schwartz (born 7 March 1945) is a retired United States Army four-star general who commanded the United States Army Forces Command from 1998 to 1999 and United States Forces Korea from 1999 to 2002. Early life and education Schwartz was born on 7 March 1945, in St. Paul, Minnesota. He attended Cretin High School (now Cretin-Derham Hall High School) in Saint Paul, Minnesota. While there, Schwartz was in the school’s Junior Reserve Officers' Training Corps and was the school’s 46th cadet colonel in 1963. Military career Schwartz was commissioned in the infantry following graduation from the United States Military Academy in 1967. He served as a platoon leader and company commander with the 2nd Battalion, 505th Infantry in Vietnam from August 1968 to October 1969, earning both a Silver Star and a Purple Heart. In addition to Forces Command and United States Forces Korea, Schwartz also commanded III Corps and the 4th Infantry Division from October 1993 to November ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voting System
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 informal organisations. These rules govern all aspects of the voting process: when elections occur, who is allowed to vote, who can stand as a candidate, how ballots are marked and cast, how the ballots are counted, how votes translate into the election outcome, limits on campaign spending, and other factors that can affect the result. Political electoral systems are defined by constitutions and electoral laws, are typically conducted by election commissions, and can use multiple types of elections for different offices. Some electoral systems elect a single winner to a unique position, such as prime minister, president or governor, while others elect multiple winners, such as members of parliament or boards of directors. When electing a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gibbard–Satterthwaite Theorem
The Gibbard–Satterthwaite theorem is a theorem in social choice theory. It was first conjectured by the philosopher Michael Dummett and the mathematician Robin Farquharson in 1961 and then proved independently by the philosopher Allan Gibbard in 1973 and economist Mark Satterthwaite in 1975. It deals with deterministic ordinal electoral systems that choose a single winner, and shows that for every voting rule of this form, at least one of the following three things must hold: # The rule is dictatorial, i.e. there exists a distinguished voter who can choose the winner; or # The rule limits the possible outcomes to two alternatives only; or # The rule is not straightforward, i.e. there is no single always-best strategy (one that does not depend on other voters' preferences or behavior). Gibbard's proof of the theorem is more general and covers processes of collective decision that may not be ordinal, such as cardinal voting. Gibbard's 1978 theorem and Hylland's theorem are e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strategic Voting
Strategic or tactical voting is voting in consideration of possible ballots cast by other voters in order to maximize one's satisfaction with the election's results. Gibbard's theorem shows that no voting system has a single "always-best" strategy, i.e. one that always maximizes a voter's satisfaction with the result, regardless of other voters' ballots. This implies all voting systems can sometimes encourage voters to strategize. However, weaker guarantees can be shown under stronger conditions. Examples include one-dimensional preferences (where the median rule is strategyproof) and dichotomous preferences (where approval or score voting are strategyproof). With large electoral districts, party list methods tend to be difficult to manipulate in the absence of an electoral threshold. However, biased apportionment methods can create opportunities for strategic voting, as can small electoral districts (e.g. those used most often with the single transferable vote). Proportio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arrow's Impossibility Theorem
Arrow's impossibility theorem is a key result in social choice theory showing that no ranked-choice procedure for group decision-making can satisfy the requirements of rational choice. Specifically, Arrow showed no such rule can satisfy the independence of irrelevant alternatives axiom. This is the principle that a choice between two alternatives and should not depend on the quality of some third, unrelated option, . The result is often cited in discussions of voting rules, where it shows no ranked voting rule to eliminate the spoiler effect. This result was first shown by the Marquis de Condorcet, whose voting paradox showed the impossibility of logically-consistent majority rule; Arrow's theorem generalizes Condorcet's findings to include non-majoritarian rules like collective leadership or consensus decision-making. While the impossibility theorem shows all ranked voting rules must have spoilers, the frequency of spoilers differs dramatically by rule. Plurality-rule me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voting Theory
Social choice theory is a branch of welfare economics that extends the theory of rational choice to collective decision-making. Social choice studies the behavior of different mathematical procedures ( social welfare functions) used to combine individual preferences into a coherent whole.Amartya Sen (2008). "Social Choice". ''The New Palgrave Dictionary of Economics'', 2nd EditionAbstract & TOC./ref> It contrasts with political science in that it is a normative field that studies how a society can make good decisions, whereas political science is a descriptive field that observes how societies actually do make decisions. While social choice began as a branch of economics and decision theory, it has since received substantial contributions from mathematics, philosophy, political science, and game theory. Real-world examples of social choice rules include constitutions and parliamentary procedures for voting on laws, as well as electoral systems; as such, the field is occasionall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
