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The idea of a social choice function, or of a ranked-choice voting system, is to take the preferences of everyone in society, and to combine them all to get one preference that represents the preferences of society. This is modeled in Arrow's theorem as a mathematical function taking in a list of preferences and outputting one preference.
The concept of proof is formalized in the field of mathematical logic. [ 12] A formal proof is written in a formal language instead of natural language. A formal proof is a sequence of formulas in a formal language, starting with an assumption, and with each subsequent formula a logical consequence of the preceding ones.
Proof theory is a major branch [1] of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees, which are constructed ...
In political science, Duverger's law ( / ˈduvərʒeɪ / DOO-vər-zhay) holds that in political systems with single-member districts (as in the U.S.), two main parties tend to emerge with minor parties typically splitting votes away from the most similar major party. [ 1][ 2] In contrast, systems with proportional representation usually have ...
Coase theorem. In law and economics, the Coase theorem ( / ˈkoʊs /) describes the economic efficiency of an economic allocation or outcome in the presence of externalities. The theorem is significant because, if true, the conclusion is that it is possible for private individuals to make choices that can solve the problem of market externalities.
This is a list of mathematical theories. Almgren–Pitts min-max theory; Approximation theory; Arakelov theory; ... Proof theory; Quantum theory; Queue theory; Ramsey ...
In mathematics, an impossibility theorem is a theorem that demonstrates a problem or general set of problems cannot be solved. These are also known as proofs of impossibility, negative proofs, or negative results. Impossibility theorems often resolve decades or centuries of work spent looking for a solution by proving there is no solution.
Fundamental theorems of welfare economics. There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information, and in perfect competition, will be Pareto optimal (in the sense that no further exchange would make one person better off without making another ...