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The free will theorem states: Given the axioms, if the choice about what measurement to take is not a function of the information accessible to the experimenters (free will assumption), then the results of the measurements cannot be determined by anything previous to the experiments. That is an "outcome open" theorem:
Download as PDF; Printable version; In other projects ... This list may not reflect recent ... Fluctuation–dissipation theorem; Free will theorem; G. Goldstone ...
Download as PDF; Printable version; ... This list may not reflect recent changes. ... Free will in theology; Free will theorem;
Stone's theorem on one-parameter unitary groups (functional analysis) Stone–Tukey theorem ; Stone–von Neumann theorem (functional analysis, representation theory of the Heisenberg group, quantum mechanics) Stone–Weierstrass theorem (functional analysis) Strassmann's theorem (field theory) Strong perfect graph theorem (graph theory)
The above example restricted to candidates Alice and Bob also serves as an example of highest median rules failing the majority criterion, although highest medians can pass the majority criterion with normalized ballots (i.e. ballots scaled to use the whole 0-100 range). However, normalization cannot recover the Archimedean criterion.
In 2004, Conway and Simon B. Kochen, another Princeton mathematician, proved the free will theorem, a version of the "no hidden variables" principle of quantum mechanics. It states that given certain conditions, if an experimenter can freely decide what quantities to measure in a particular experiment, then elementary particles must be free to ...
The problem of free will has been identified in ancient Greek philosophical literature. The notion of compatibilist free will has been attributed to both Aristotle (4th century BCE) and Epictetus (1st century CE): "it was the fact that nothing hindered us from doing or choosing something that made us have control over them".
Moulin's characterizations consider only rules that are "peak only", that is, the rule depends only on the n peaks. Ching [2] proved that all rules that are strategyproof and continuous, even if they are not "peak only", are augmented median rules, that is, can be described by a variant of the median rule with some 2 n parameters.