An intuitionistic version of Zermelo's proof that every choice set can be well-ordered

2001 ◽  
Vol 66 (3) ◽  
pp. 1121-1126
Author(s):  
J. Todd Wilson
Keyword(s):  
Choice Function ◽  
Direct Generalization ◽  
Intuitionistic Version ◽  
Choice Set

AbstractWe give a proof, valid in any elementary topos, of the theorem of Zermelo that any set possessing a choice function for its set of inhabited subsets can be well-ordered. Our proof is considerably simpler than existing proofs in the literature and moreover can be seen as a direct generalization of Zermelo's own 1908 proof of his theorem.

scholarly journals Evolving Choice Inconsistencies in Choice of Prescription Drug Insurance

2016 ◽  
Vol 106 (8) ◽  
pp. 2145-2184 ◽  
Author(s):  
Jason Abaluck ◽  
Jonathan Gruber
Keyword(s):  
Prescription Drug ◽  
Choice Function ◽  
The Elderly ◽  
Structural Framework ◽  
The Individual ◽  
Cost Plan ◽  
Study Choice ◽  
Over Time ◽  
Out Of Pocket Costs ◽  
Choice Set

We study choice over prescription insurance plans by the elderly using government administrative data to evaluate how these choices evolve over time. We find large “foregone savings” from not choosing the lowest cost plan that has grown over time. We develop a structural framework to decompose the changes in “foregone welfare” from inconsistent choices into choice set changes and choice function changes from a fixed choice set. We find that foregone welfare increases over time due primarily to changes in plan characteristics such as premiums and out-of-pocket costs; we estimate little learning at either the individual or cohort level. (JEL G22, H51, I13, I18, J14)

scholarly journals Path-Independent Consideration

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 21
Author(s):  
Juan Lleras ◽  
Yusufcan Masatlioglu ◽  
Daisuke Nakajima ◽  
Erkut Ozbay
Keyword(s):  
Decision Maker ◽  
Choice Function ◽  
Path Independence ◽  
Choice Set

In the context of choice with limited consideration, where the decision-maker may not pay attention to all available options, the consideration function of a decision maker is path-independent if her choice cannot be manipulated by the presentation of the choice set. This paper characterizes a model of choice with limited consideration with path independence, which is equivalent to a consideration function that satisfies both the attention filter and consideration filter properties from Masatlioglu et al. (2012) and Lleras et al. (2017), respectively. Despite the equivalence of path-independent consideration with the consideration structures from these two papers, we show that, to have a choice with limited consideration that is path-independent, satisfying both axioms on the choice function that characterize choice limited consideration with attention and consideration filters unilaterally (from Masatlioglu et al. (2012) and Lleras et al. (2017)) is necessary but not sufficient.

scholarly journals Choice Set Definition Issues in a Kuhn-Tucker Model of Recreation Demand

1999 ◽  
Vol 14 (4) ◽  
pp. 343-355 ◽  
Author(s):  
DANIEL J. PHANEUF ◽  
JOSEPH A. HERRIGES
Keyword(s):  
Recreation Demand ◽  
Choice Set

A Comment on Arrow’s Impossibility Theorem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Alec Sandroni ◽  
Alvaro Sandroni
Keyword(s):  
Social Choice ◽  
Choice Function ◽  
Social Preference ◽  
Social Choice Function ◽  
Individual Preference ◽  
Impossibility Theorem ◽  
Preference Order ◽  
Individual Choice ◽  
Choice Functions ◽  
Preference Orders

AbstractArrow (1950) famously showed the impossibility of aggregating individual preference orders into a social preference order (together with basic desiderata). This paper shows that it is possible to aggregate individual choice functions, that satisfy almost any condition weaker than WARP, into a social choice function that satisfy the same condition (and also Arrow’s desiderata).

scholarly journals A BOUND FOR THE INDEX OF A QUADRATIC FORM AFTER SCALAR EXTENSION TO THE FUNCTION FIELD OF A QUADRIC

2018 ◽  
Vol 19 (2) ◽  
pp. 421-450 ◽  
Author(s):  
Stephen Scully
Keyword(s):  
Quadratic Form ◽  
Upper Bound ◽  
Function Field ◽  
The Other ◽  
Direct Generalization ◽  
Other Hand ◽  
General Field ◽  
The One ◽  
Anisotropic Quadratic Form

Let $q$ be an anisotropic quadratic form defined over a general field $F$. In this article, we formulate a new upper bound for the isotropy index of $q$ after scalar extension to the function field of an arbitrary quadric. On the one hand, this bound offers a refinement of an important bound established in earlier work of Karpenko–Merkurjev and Totaro; on the other hand, it is a direct generalization of Karpenko’s theorem on the possible values of the first higher isotropy index. We prove its validity in two key cases: (i) the case where $\text{char}(F)\neq 2$, and (ii) the case where $\text{char}(F)=2$ and $q$ is quasilinear (i.e., diagonalizable). The two cases are treated separately using completely different approaches, the first being algebraic–geometric, and the second being purely algebraic.

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