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Condorcet's Jury Theorem
Condorcet's jury theorem is a political science theorem about the relative probability of a given group of individuals arriving at a correct decision. The theorem was first expressed by the Marquis de Condorcet in his 1785 work ''Essay on the Application of Analysis to the Probability of Majority Decisions''. The assumptions of the theorem are that a group wishes to reach a decision by majority rule, majority vote. One of the two outcomes of the vote is ''correct'', and each voter has an independent probability ''p'' of voting for the correct decision. The theorem asks how many voters we should include in the group. The result depends on whether ''p'' is greater than or less than 1/2: * If ''p'' is greater than 1/2 (each voter is more likely to vote correctly), then adding more voters increases the probability that the majority decision is correct. In the limit, the probability that the majority votes correctly approaches 1 as the number of voters increases. * On the other hand, if ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Myth Of The Rational Voter
''The Myth of the Rational Voter: Why Democracies Choose Bad Policies'' is a 2007 book by the economist Bryan Caplan, in which the author challenges the idea that voters are reasonable people whom society can trust to make laws. Rather, Caplan contends that voters are irrational in the political sphere and have systematically biased ideas concerning economics. Summary Throughout the book, Caplan focuses on voters' opinion of economics since so many political decisions revolve around economic issues (immigration, trade, welfare, economic growth, and so forth). Using data from the Survey of Americans and Economists on the Economy (SAEE), Caplan categorizes the roots of economic errors into four biases: anti-market, anti-foreign, make-work, and pessimistic. Anti-market bias Caplan refers to the anti-market bias as a "tendency to underestimate the benefits of the market mechanism." People tend to view themselves as victims of the market, rather than as participants in it, according t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wisdom Of The Crowd
"Wisdom of the crowd" or "wisdom of the majority" expresses the notion that the collective opinion of a diverse and independent group of individuals (rather than that of a single expert) yields the best judgement. This concept, while not new to the Information Age, has been pushed into the spotlight by social information sites such as Quora, Reddit, Stack Exchange, Wikipedia, Yahoo! Answers, and other web resources which rely on collective human knowledge. An explanation for this supposition is that the idiosyncratic noise associated with each individual judgment is replaced by an average of that noise taken over a large number of responses, tempering the effect of the noise. Trial by jury can be understood as at least partly relying on wisdom of the crowd, compared to bench trial which relies on one or a few experts. In politics, sometimes sortition is held as an example of what wisdom of the crowd would look like. Decision-making would happen by a diverse group instead of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Law Of Large Numbers
In probability theory, the law of large numbers is a mathematical law that states that the average of the results obtained from a large number of independent random samples converges to the true value, if it exists. More formally, the law of large numbers states that given a sample of independent and identically distributed values, the sample mean converges to the true mean. The law of large numbers is important because it guarantees stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins. Any winning streak by a player will eventually be overcome by the parameters of the game. Importantly, the law applies (as the name indicates) only when a ''large number'' of observations are considered. There is no principle that a small number of observations will coincide with the expected value or that a stre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jury Theorem
A jury theorem is a mathematical theorem proving that, under certain assumptions, a decision attained using majority voting in a large group is more likely to be correct than a decision attained by a single expert. It serves as a formal argument for the idea of wisdom of the crowd, for decision of questions of fact by jury trial, and for democracy in general. The first and most famous jury theorem is Condorcet's jury theorem. It assumes that all voters have independent probabilities to vote for the correct alternative, these probabilities are larger than 1/2, and are the same for all voters. Under these assumptions, the probability that the majority decision is correct is strictly larger when the group is larger; and when the group size tends to infinity, the probability that the majority decision is correct tends to 1. There are many other jury theorems, relaxing some or all of these assumptions. Setting The premise of all jury theorems is that there is an ''objective truth'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Condorcet Paradox
In social choice theory, Condorcet's voting paradox is a fundamental discovery by the Marquis de Condorcet that majority rule is inherently self-contradictory. The result implies that it is logically impossible for any voting system to guarantee that a winner will have support from a majority of voters; for example, there can be rock-paper-scissors scenarios where a majority of voters will prefer A to B, B to C, and also C to A, even if every voter's individual preferences are rational and avoid self-contradiction. Examples of Condorcet's paradox are called Condorcet cycles or cyclic ties. In such a cycle, every possible choice is rejected by the electorate in favor of another alternative, who is preferred by more than half of all voters. Thus, any attempt to ground social decision-making in majoritarianism must accept such self-contradictions (commonly called spoiler effects). Systems that attempt to do so, while minimizing the rate of such self-contradictions, are called Condo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, whenever there is such a candidate. A candidate with this property, the ''pairwise champion'' or ''beats-all winner'', is formally called the ''Condorcet winner'' or ''Pairwise Majority Rule Winner'' (PMRW). The head-to-head elections need not be done separately; a voter's choice within any given pair can be determined from the ranking. Some elections may not yield a Condorcet winner because voter preferences may be cyclic—that is, it is possible that every candidate has an opponent that defeats them in a two-candidate contest. The possibility of such cyclic preferences is known as the Condorcet paradox. However, a smallest group of candidates that beat all candidates not in the group, known as the Smith set, always exists. The Smith set is guaranteed to have the Condorcet winner in it should one exist. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Almost Surely
In probability theory, an event is said to happen almost surely (sometimes abbreviated as a.s.) if it happens with probability 1 (with respect to the probability measure). In other words, the set of outcomes on which the event does not occur has probability 0, even though the set might not be empty. The concept is analogous to the concept of "almost everywhere" in measure theory. In probability experiments on a finite sample space with a non-zero probability for each outcome, there is no difference between ''almost surely'' and ''surely'' (since having a probability of 1 entails including all the sample points); however, this distinction becomes important when the sample space is an infinite set, because an infinite set can have non-empty subsets of probability 0. Some examples of the use of this concept include the strong and uniform versions of the law of large numbers, the continuity of the paths of Brownian motion, and the infinite monkey theorem. The terms almost certai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A Priori Probability
A prior probability distribution of an uncertain quantity, simply called the prior, is its assumed probability distribution before some evidence is taken into account. For example, the prior could be the probability distribution representing the relative proportions of voters who will vote for a particular politician in a future election. The unknown quantity may be a parameter of the model or a latent variable rather than an observable variable. In Bayesian statistics, Bayes' rule prescribes how to update the prior with new information to obtain the posterior probability distribution, which is the conditional distribution of the uncertain quantity given new data. Historically, the choice of priors was often constrained to a conjugate family of a given likelihood function, so that it would result in a tractable posterior of the same family. The widespread availability of Markov chain Monte Carlo methods, however, has made this less of a concern. There are many ways to constru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bryan Caplan
Bryan Douglas Caplan (born April 8, 1971) is an American economist and author. He is a professor of economics at George Mason University, a senior research fellow at the Mercatus Center, an adjunct scholar at the Cato Institute, and a former contributor to the '' Freakonomics'' blog. He currently publishes his own blog, ''Bet on It''. Caplan is a self-described " economic libertarian". The bulk of Caplan's academic work is in behavioral economics and public economics, especially public choice theory. Early life and education Caplan was born to a Jewish father and a Catholic mother, in Northridge, California, on April 8, 1971. He obtained a B.A. in economics from the University of California, Berkeley in 1993 and a Ph.D. in economics from Princeton University in 1997. Career ''The Myth of the Rational Voter'' '' The Myth of the Rational Voter: Why Democracies Choose Bad Policies'', published in 2007, further develops the "rational irrationality" concept from Caplan's earli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Political Science
Political science is the scientific study of politics. It is a social science dealing with systems of governance and Power (social and political), power, and the analysis of political activities, political philosophy, political thought, political behavior, and associated constitutions and laws. Specialists in the field are political scientists. History Origin Political science is a social science dealing with systems of governance and power, and the analysis of political activities, political institutions, political thought and behavior, and associated constitutions and laws. As a social science, contemporary political science started to take shape in the latter half of the 19th century and began to separate itself from political philosophy and history. Into the late 19th century, it was still uncommon for political science to be considered a distinct field from history. The term "political science" was not always distinguished from political philosophy, and the modern dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
