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Donald G. Saari
Donald Gene Saari (born March 1940) is an American mathematician, a Distinguished Professor of Mathematics and Economics and former director of the Institute for Mathematical Behavioral Sciences at the University of California, Irvine. His research interests include the -body problem, the Borda count voting system, and application of mathematics to the social sciences. Contributions Saari has been widely quoted as an expert in voting methods and lottery odds. He is opposed to the use of the Condorcet criterion in evaluating voting systems, and among positional voting schemes he favors using the Borda count over plurality voting, because it reduces the frequency of paradoxical outcomes (which however cannot be avoided entirely in ranking systems because of Arrow's impossibility theorem). For instance, as he has pointed out, plurality voting can lead to situations where the election outcome would remain unchanged if all voters' preferences were reversed; this cannot happen with t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Houghton, Michigan
Houghton (; ) is the largest city and seat of government of Houghton County in the U.S. state of Michigan. Located on the Keweenaw Peninsula, Houghton is the largest city in the Copper Country region. It is the fifth-largest city in the Upper Peninsula, with a population of 8,386 at the 2020 census. Houghton is the principal city of the Houghton micropolitan area, which includes all of Houghton and Keweenaw County. The city of Houghton and the county were named after Douglass Houghton, an American geologist and physician, primarily known for his exploration of the Keweenaw Peninsula. Houghton has been listed as one of the "100 Best Small Towns in America" despite it being considered a city. Houghton is home to Michigan Technological University, a public research college founded in 1885. Michigan Tech hosts a yearly Winter Carnival in February, drawing thousands of visitors from around the world. History Native Americans mined copper in and around what would later be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voting Methods
Voting is a method by which a group, such as a meeting or an electorate, can engage for the purpose of making a collective decision or expressing an opinion usually following discussions, debates or election campaigns. Democracies elect holders of high office by voting. Residents of a jurisdiction represented by an elected official are called "constituents," and the constituents who choose to cast a ballot for their chosen candidate are called "voters." There are different systems for collecting votes, but while many of the systems used in decision-making can also be used as electoral systems, any which cater for proportional representation can only be used in elections. In smaller organizations, voting can occur in many different ways. Formally via ballot to elect others for example within a workplace, to elect members of political associations or to choose roles for others. Informally voting could occur as a spoken agreement or as a verbal gesture like a raised hand or ele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Celestial Mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to produce ephemeris data. History Modern analytic celestial mechanics started with Isaac Newton's Principia of 1687. The name "celestial mechanics" is more recent than that. Newton wrote that the field should be called "rational mechanics." The term "dynamics" came in a little later with Gottfried Leibniz, and over a century after Newton, Pierre-Simon Laplace introduced the term "celestial mechanics." Prior to Kepler there was little connection between exact, quantitative prediction of planetary positions, using geometrical or arithmetical techniques, and contemporary discussions of the physical causes of the planets' motion. Johannes Kepler Johannes Kepler (1571–1630) was the first to closely integrate the predictive geom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economic Equilibrium
In economics, economic equilibrium is a situation in which economic forces such as supply and demand are balanced and in the absence of external influences the ( equilibrium) values of economic variables will not change. For example, in the standard text perfect competition, equilibrium occurs at the point at which quantity demanded and quantity supplied are equal. Market equilibrium in this case is a condition where a market price is established through competition such that the amount of goods or services sought by buyers is equal to the amount of goods or services produced by sellers. This price is often called the competitive price or market clearing price and will tend not to change unless demand or supply changes, and quantity is called the "competitive quantity" or market clearing quantity. But the concept of ''equilibrium'' in economics also applies to imperfectly competitive markets, where it takes the form of a Nash equilibrium. Understanding economic equilibriu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chaos Theory
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning that there is sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause a tornado in Texas. Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Price Mechanism
In economics, a price mechanism is the manner in which the profits of goods or services affects the supply and demand of goods and services, principally by the price elasticity of demand. A price mechanism affects both buyer and seller who negotiate prices. A price mechanism, part of a market system, comprises various ways to match up buyers and sellers. The price mechanism is an economic model where price plays a key role in directing the activities of producers, consumers, and resource suppliers. An example of a price mechanism uses announced bid and ask prices. Generally speaking, when two parties wish to engage in trade, the purchaser will announce a price he is willing to pay (the bid price) and the seller will announce a price he is willing to accept (the ask price). The primary advantage of such a method is that conditions are laid out in advance and transactions can proceed with no further permission or authorization from any participant. When any bid and ask pair are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economics
Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interactions of Agent (economics), economic agents and how economy, economies work. Microeconomics analyzes what's viewed as basic elements in the economy, including individual agents and market (economics), markets, their interactions, and the outcomes of interactions. Individual agents may include, for example, households, firms, buyers, and sellers. Macroeconomics analyzes the economy as a system where production, consumption, saving, and investment interact, and factors affecting it: employment of the resources of labour, capital, and land, currency inflation, economic growth, and public policies that have impact on glossary of economics, these elements. Other broad distinctions within economics include those between positive economics, desc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apportionment (politics)
Apportionment is the process by which seats in a legislative body are distributed among administrative divisions, such as states or parties, entitled to representation. This page presents the general principles and issues related to apportionment. The page Apportionment by country describes specific practices used around the world. The page Mathematics of apportionment describes mathematical formulations and properties of apportionment rules. The simplest and most universal principle is that elections should give each voter's intentions equal weight. This is both intuitive and stated in laws such as the Fourteenth Amendment to the United States Constitution (the Equal Protection Clause). However, there are a variety of historical and technical reasons why this principle is not followed absolutely or, in some cases, as a first priority. Common problems Fundamentally, the representation of a population in the thousands or millions by a reasonable size, thus accountable govern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, in a simple plurality election, a voter might gain a better outcome by voting for a less preferred but more generally popular candidate. Gibbard's theorem shows that ''all'' single-winner voting methods are susceptible to strategic voting, unless there are only two options or ''dictatorial'' (i.e., a distinguished agent exists who can impose the outcome). For multi-winner elections no general theorem for strategic voting exists. Strategic voting is observed due to non-proportionality, electoral thresholds and quotas. Types of strategic voting ; (sometimes "useful vote"): A voter insincerely ranks an alternative higher in the hope of getting that candidate elected. For example, in the first-past-the-post election, voters may vote for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steven Brams
Steven J. Brams (born November 28, 1940 in Concord, New Hampshire) is an American game theory, game theorist and political scientist at the New York University Department of Politics. Brams is best known for using the techniques of game theory, public choice theory, and social choice theory to analyze voting systems and fair division. He is one of the independent discoverers of approval voting, as well as extensions of approval voting to multiple-winner elections to give proportional representation of different interests. Brams was a co-discoverer, with Alan D. Taylor, Alan Taylor, of the first envy-free cake-cutting solution for ''n'' people. Previous to the Brams-Taylor procedure, the cake-cutting problem had been one of the most important open problems in contemporary mathematics. He is co-inventor with Taylor of the fair-division procedure, adjusted winner, which was patented by New York University in 1999 (# 5,983,205). Adjusted winner has been licensed to a Boston law firm, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 system can convert the ranked preferences of individuals into a community-wide (complete and transitive) ranking while also meeting the specified set of criteria: '' unrestricted domain'', '' non-dictatorship'', ''Pareto efficiency'', and ''independence of irrelevant alternatives''. The theorem is often cited in discussions of voting theory as it is further interpreted by the Gibbard–Satterthwaite theorem. The theorem is named after economist and Nobel laureate Kenneth Arrow, who demonstrated the theorem in his doctoral thesis and popularized it in his 1951 book ''Social Choice and Individual Values''. The original paper was titled "A Difficulty in the Concept of Social Welfare". In short, the theorem states that no rank-order electoral syst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plurality Voting
Plurality voting refers to electoral systems in which a candidate, or candidates, who poll more than any other counterpart (that is, receive a plurality), are elected. In systems based on single-member districts, it elects just one member per district and may also be referred to as first-past-the-post (FPTP), single-member plurality (SMP/SMDP), single-choice voting (an imprecise term as non-plurality voting systems may also use a single choice), simple plurality or relative majority (as opposed to an ''absolute majorit''y, where more than half of votes is needed, this is called ''majority voting''). A system which elects multiple winners elected at once with the plurality rule, such as one based on multi-seat districts, is referred to as plurality block voting. Plurality voting is distinguished from ''majority voting'', in which a winning candidate must receive an absolute majority of votes: more than half of all votes (more than all other candidates combined if each voter ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
