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In the fields of mechanism design and social choice theory, Gibbard's theorem is a result proven by philosopher Allan Gibbard in 1973. [1] It states that for any deterministic process of collective decision, at least one of the following three properties must hold: The process is dictatorial, i.e. there is a single voter whose vote chooses the ...
Allan Fletcher Gibbard (born 1942) is the Richard B. Brandt Distinguished University Professor of Philosophy Emeritus at the University of Michigan, Ann Arbor. [1] Gibbard has made major contributions to contemporary ethical theory, in particular metaethics, where he has developed a contemporary version of non-cognitivism.
In metaphilosophy and ethics, metaethics is the study of the nature, scope, ground, and meaning of moral judgment, ethical belief, or values.It is one of the three branches of ethics generally studied by philosophers, the others being normative ethics (questions of how one ought to be and act) and applied ethics (practical questions of right behavior in given, usually contentious, situations).
The revelation principle shows that, while Gibbard's theorem proves it is impossible to design a system that will always be fully invulnerable to strategy (if we do not know how players will behave), it is possible to design a system that encourages honesty given a solution concept (if the corresponding equilibrium is unique). [3] [4]
In statistical quality control, the ¯ and s chart is a type of control chart used to monitor variables data when samples are collected at regular intervals from a business or industrial process. [1] This is connected to traditional statistical quality control (SQC) and statistical process control (SPC).
If the mean =, the first factor is 1, and the Fourier transform is, apart from a constant factor, a normal density on the frequency domain, with mean 0 and variance / . In particular, the standard normal distribution φ {\displaystyle \varphi } is an eigenfunction of the Fourier transform.
In meta-ethics, expressivism is a theory about the meaning of moral language.According to expressivism [citation needed], sentences that employ moral terms – for example, "It is wrong to torture an innocent human being" – are not descriptive or fact-stating; moral terms such as "wrong", "good", or "just" do not refer to real, in-the-world properties.
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 [1] and then proved independently by the philosopher Allan Gibbard in 1973 [2] and economist Mark Satterthwaite in 1975. [3]