|
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 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 ''p'' is les ... [...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." In Caplan's view, people tend to view themselves as victims of the market, rather than participants of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wisdom Of The Crowd
The wisdom of the crowd is the collective opinion of a diverse independent group of individuals rather than that of a single expert. This process, while not new to the Information Age, has been pushed into the mainstream 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 phenomenon is that there is idiosyncratic noise associated with each individual judgment, and taking the average over a large number of responses will go some way toward canceling the effect of this 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 by a fairly homogenous political group or party. Research within cog ... [...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
The Condorcet paradox (also known as the voting paradox or the paradox of voting) in social choice theory is a situation noted by the Marquis de Condorcet in the late 18th century, in which collective preferences can be cyclic, even if the preferences of individual voters are not cyclic. This is paradoxical, because it means that majority wishes can be in conflict with each other: Suppose majorities prefer, for example, candidate A over B, B over C, and yet C over A. When this occurs, it is because the conflicting majorities are each made up of different groups of individuals. Thus an expectation that transitivity on the part of all individuals' preferences should result in transitivity of societal preferences is an example of a fallacy of composition. The paradox was independently discovered by Lewis Carroll and Edward J. Nanson, but its significance was not recognized until popularized by Duncan Black in the 1940s. Example Suppose we have three candidates, A, B, and C, and ... [...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, that is, a candidate preferred by more voters than any others, whenever there is such a candidate. A candidate with this property, the ''pairwise champion'' or ''beats-all winner'', is formally called the ''Condorcet winner''. 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 (but rare) that every candidate has an opponent that defeats them in a two-candidate contest.(This is similar to the game rock paper scissors, where each hand shape wins against one opponent and loses to another one). The possibility of such cyclic preferences is known as the Condorcet paradox. However, a smallest group of candidates that beat al ... [...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 (or Lebesgue measure 1). In other words, the set of possible exceptions may be non-empty, but it has probability 0. The concept is analogous to the concept of "almost everywhere" in measure theory. In probability experiments on a finite sample space, there is no difference between ''almost surely'' and ''surely'' (since having a probability of 1 often 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, and the continuity of the paths of Brownian motion. The terms almost certainly (a.c.) and almost always (a.a.) are also used. Almost never describes the opposite of ''almost surely'': an event that h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A Priori Probability
An ''a priori'' probability is a probability that is derived purely by deductive reasoning. One way of deriving ''a priori'' probabilities is the principle of indifference, which has the character of saying that, if there are ''N'' mutually exclusive and collectively exhaustive events and if they are equally likely, then the probability of a given event occurring is 1/''N''. Similarly the probability of one of a given collection of ''K'' events is ''K'' / ''N''. One disadvantage of defining probabilities in the above way is that it applies only to finite collections of events. In Bayesian inference, " uninformative priors" or "objective priors" are particular choices of ''a priori'' probabilities. Note that "prior probability" is a broader concept. Similar to the distinction in philosophy between a priori and a posteriori, in Bayesian inference ''a priori'' denotes general knowledge about the data distribution before making an inference, while ''a posteriori'' denotes knowledge t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prior Probability
In Bayesian statistical inference, a prior probability distribution, often simply called the prior, of an uncertain quantity is the probability distribution that would express one's beliefs about this quantity 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. Bayes' theorem calculates the renormalized pointwise product of the prior and the likelihood function, to produce the ''posterior probability distribution'', which is the conditional distribution of the uncertain quantity given the data. Similarly, the prior probability of a random event or an uncertain proposition is the unconditional probability that is assigned before any relevant evidence is taken into account. Priors can be created using a num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bryan Caplan
Bryan Douglas Caplan (born April 8, 1971) is an American economist and author. Caplan is a professor of economics at George Mason University, research fellow at the Mercatus Center, adjunct scholar at the Cato Institute, and former contributor to the ''Freakonomics'' blog and EconLog. 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. Education Caplan holds a B.A. in economics from the University of California, Berkeley (1993) and a Ph.D. in economics from Princeton University (1997). Writings ''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 earlier academic writing. It draws heavily from the ''Survey of Americans and Economists on the Economy'' in making the argume ... [...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, and the analysis of political activities, political thought, political behavior, and associated constitutions and laws. Modern political science can generally be divided into the three subdisciplines of comparative politics, international relations, and political theory. Other notable subdisciplines are public policy and administration, domestic politics and government, political economy, and political methodology. Furthermore, political science is related to, and draws upon, the fields of economics, law, sociology, history, philosophy, human geography, political anthropology, and psychology. Political science is methodologically diverse and appropriates many methods originating in psychology, social research, and political philosophy. Approaches include positivism, interpretivism, rational choice theory, behaviouralism, structuralism, post-struct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Machine Learning
Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine learning algorithms build a model based on sample data, known as training data, in order to make predictions or decisions without being explicitly programmed to do so. Machine learning algorithms are used in a wide variety of applications, such as in medicine, email filtering, speech recognition, agriculture, and computer vision, where it is difficult or unfeasible to develop conventional algorithms to perform the needed tasks.Hu, J.; Niu, H.; Carrasco, J.; Lennox, B.; Arvin, F.,Voronoi-Based Multi-Robot Autonomous Exploration in Unknown Environments via Deep Reinforcement Learning IEEE Transactions on Vehicular Technology, 2020. A subset of machine learning is closely related to computational statistics, which focuses on making predicti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
