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Gibbard's theorem can be proven using Arrow's impossibility theorem. [citation needed] Gibbard's theorem is itself generalized by Gibbard's 1978 theorem [3] and Hylland's theorem, [4] which extend these results to non-deterministic processes, i.e. where the outcome may not only depend on the agents' actions but may also involve an element of ...
Gibbard's theorem shows that any strategyproof game form (i.e. one with a dominant strategy) with more than two outcomes is dictatorial. The Gibbard–Satterthwaite theorem is a special case showing that no deterministic voting system can be fully invulnerable to strategic voting in all circumstances, regardless of how others vote.
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2]
Sturm's theorem (theory of equations) Sturm–Picone comparison theorem (differential equations) Subspace theorem (Diophantine approximation) Superrigidity theorem (algebraic groups) Supersymmetry nonrenormalization theorems ; Supporting hyperplane theorem (convex geometry) Švarc-Milnor lemma (geometric group theory) Swan's theorem (module theory)
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Gibbard's theorem is itself generalized by Gibbard's 1978 theorem [11] and Hylland's theorem, which extend these results to non-deterministic processes, i.e. where the outcome may not only depend on the agents' actions but may also involve an element of chance. The Gibbard's theorem assumes the collective decision results in exactly one winner ...
Gleason's theorem highlights a number of fundamental issues in quantum measurement theory. As Fuchs argues, the theorem "is an extremely powerful result", because "it indicates the extent to which the Born probability rule and even the state-space structure of density operators are dependent upon the theory's other postulates". In consequence ...
The von Neumann entropy formula is an extension of the Gibbs entropy formula to the quantum mechanical case. It has been shown [ 1 ] that the Gibbs Entropy is equal to the classical "heat engine" entropy characterized by d S = δ Q T {\displaystyle dS={\frac {\delta Q}{T}}\!} , and the generalized Boltzmann distribution is a sufficient and ...