The measure of risk aversion
... We will say that u is a linear function on a mixture set M if it is a real-valued function for which
u(λx⊕(1−λ)y) = λu(x)+(1−λ)u(y) for all λ and x, y ∈ M . Two linear functions u and v are related
by a positive affine transformation if there are real numbers a > 0 and b such that v(x) = au(x) + b
pse14 VanLong 19108260 en
... one has to decipher the necessary conditions for a diﬀerential equation to have
a (unique) solution, a question about which little is known without imposing
more structure. Suﬃcient conditions are easier to explore9 , but are of course
more restrictive than one would like, in particular those requir ...
Category Theory Lecture Notes for ESSLLI Michael Barr Department
... The significance of the fact that the composite c is defined on G2 is that g ◦ f is defined if and only
if the source of g is the target of f . This means that composition is a function whose domain is an
equationally defined subset of G1 × G1 : the equation requires that the source of g equal the t ...
Lecture 04: Risk Preferences and Risk Preferences and Expected
... A preference ordering is (i) complete, (ii) transitive, (iii)
continuous and [(iv) relatively stable] can be represented
by a utility function, i.e.
(c0,cc1,…,ccS) Â (c
⇔ U(c0,c1,…,cS) > U(c’0,c’1,…,c’S)
(preference ordering over lotteries –
A Course in Modal Logic - Sun Yat
... concepts, whereas these differences are actually supported by
different intuitive semantics (even philosophical background). The
reader who is interested in this can refer to the related literature.
(Ⅱ) The cardinality of At is finite or countable infinite, but, in fact,
most of results given in thi ...
Harmony, Normality and Stability
... Dummett singles out two features of the use of expressions that are of central importance for specifying their meanings. The two features are intended
to apply very generally to all kinds of expressions, but I’m only concerned
with the logical constants. ‘The first category [of principles governing ...
Social Preferences, Beliefs, and the Dynamics of Free Riding in
... cooperation” is an interesting candidate for explaining the fragility of cooperation because
this motivation depends directly on how others behave or are believed to behave. Conditional
cooperators who observe (or believe) that others free ride, will reduce their contributions and
thus contribute to ...
The Z/EVES 2.0 User`s Guide - Department of Computer Science
... of order; if such a specification is imported into Z/EVES it is necessary to move the paragraphs into
a suitable checking order. Order is also important for theorems, as the proof of a given theorem can
only use other theorems that precede the given theorem in the specification. Thus, lemmas must
Random Expected Utility,
... identical characteristics each facing the same decision problem presents the observer with
a frequency distribution over outcomes. Typically, such data is interpreted as the outcome
of independent random choice by a group of identical individuals. Even when repeated
decisions of a single individual ...
Marginal Utility Theory of Household Behavior
... Or, the household consumes enough of each commodity so that the marginal
utility per dollar of the last unit consumed is equal for all goods
household could increase its welfare by reallocating consumption
away from the low ratio ...
A survey on Interactive Theorem Proving
... The history of mathematics has stories about false results that went
undetected for long periods of time. However, it is generally believed
that if a published mathematical argument is not valid, it will be
eventually detected as such. While the process of finding a proof may
require creative insigh ...
Proof-Net Categories - Matematički Institut SANU
... definitions, and also for motivation from the perspective of general proof
theory or categorial proof theory. At some key points, we rely on results
proved before. In Chapter 2 we rely on matters proved in ,  and ,
and in particular on a coherence result from  (Symmetric Net Coherenc ...
Proof-Net Categories - Matematički Institut SANU
... categories. This result involves a proviso concerning the units, but does
not exclude them completely (as we announced in the preceding section).
This coherence of star-autonomous categories is a powerful tool for verifying
whether a diagram of arrows commutes in star-autonomous categories.
After al ...
Henkin`s Method and the Completeness Theorem
... In addition to formal manipulation of the formulas of this system we shall be concerned
with their meaning according to the following interpretation. The propositional constants are to denote one of the truth values, T or F, the symbol “f ” denoting F, and
the propositional variables are to have the ...
Everything Else Being Equal: A Modal Logic for Ceteris Paribus
... modally equivalent, written M, w M , v, iff they satisfy exactly the same
formulas of LP .
Definition 4 (Bisimulation) Two pointed models M, w and M , v are bisimilar
(written M, w ↔ M , v) iff there is a relation E ⊆ M × M such that, for all
states s ∈ M and t ∈ M :
1. If sEt then for all p ...
1- ISSN 1045-6333 NOTIONS OF FAIRNESS
... reader to contemplate the converse: suppose that no matter how much the degree of fairness
differed between two regimes, a notion of fairness never implied that one regime was superior to
another when all else was equal, namely, when everyone had the same level of well-being.
Clearly, there is no se ...
Barwise: Infinitary Logic and Admissible Sets
... become isomorphic if the set-theoretic world were extended in such a way as
to collapse the cardinalities of both structures to ℵ0 . There is one special case
where potential isomorphism does imply isomorphism. Using Cantor’s original
argument, one can show that any two countable structures which ar ...
Expected Uncertain Utility Theory,
... prior of B. Hence, both decision makers perceive the same range of uncertainty.
(ii) Two decision makers have the same uncertainty attitude (the same von NeumannMorgenstern index) if and only if 1’s certainty equivalent of the bet yAx is the same
as 2’s uncertainty equivalent of the bet yBx for all ...
Combining Paraconsistent Logic with Argumentation
... moreover, allow for the full reasoning power of a deductive logic. Although for many
cases less expressiveness may suffice, a full theory of the logic of argumentation cannot
exclude the general case.
Caminada, Carnielli and Dunne  formulated a new set of rationality postulates
in addition to tho ...
Arrow's impossibility theorem
In social choice theory, Arrow’s impossibility theorem, the General Possibility Theorem, or Arrow’s paradox, states that, when voters have three or more distinct alternatives (options), no rank order voting system can convert the ranked preferences of individuals into a community-wide (complete and transitive) ranking while also meeting a pre-specified set of criteria. These pre-specified criteria are called unrestricted domain, non-dictatorship, Pareto efficiency, and independence of irrelevant alternatives. The theorem is often cited in discussions of election theory as it is further interpreted by the Gibbard–Satterthwaite theorem.The theorem is named after economist Kenneth Arrow, who demonstrated the theorem in his doctoral thesis and popularized it in his 1951 book Social Choice and Individual Values. The original paper was titled ""A Difficulty in the Concept of Social Welfare"".In short, the theorem states that no rank-order voting system can be designed that always satisfies these three ""fairness"" criteria: If every voter prefers alternative X over alternative Y, then the group prefers X over Y. If every voter's preference between X and Y remains unchanged, then the group's preference between X and Y will also remain unchanged (even if voters' preferences between other pairs like X and Z, Y and Z, or Z and W change). There is no ""dictator"": no single voter possesses the power to always determine the group's preference.Voting systems that use cardinal utility (which conveys more information than rank orders; see the subsection discussing the cardinal utility approach to overcoming the negative conclusion) are not covered by the theorem. The theorem can also be sidestepped by weakening the notion of independence. Arrow rejected cardinal utility as a meaningful tool for expressing social welfare, and so focused his theorem on preference rankings.The axiomatic approach Arrow adopted can treat all conceivable rules (that are based on preferences) within one unified framework. In that sense, the approach is qualitatively different from the earlier one in voting theory, in which rules were investigated one by one. One can therefore say that the contemporary paradigm of social choice theory started from this theorem.