# Questions tagged [choice-theory]

a conglomerate of models and results concerning the aggregation of individual choices into collective choices

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### Question About Stochastic Choice - MWG Exercise 1.D.5

I am studying microeconomic theory using MWG. I got stuck on Exercise 1.D.5, specifically part (c), but I would also like to have my part (a) and (b) checked by someone. Here is the exercise and my ...
57 views

### In Debreu's representation theorem of ordinal utility, is the assumption of "second countability" necessary?

Debreu's representation theorems Debreu 1959 states that: second countability, continuity, and weak ordering sufficiently implies the existence of real (continuous) utility function. The second and ...
127 views

### Minimal assumption for a “certainty equivalence” exists

Let $R$ be the set of real number. Let $N$ be an infinite set. Let utility $u:R^N\to R$. The utility function is strictly monotonic. My question is, does the certainty equivalence $CE$ exist? Do we ...
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### Is the relation $\mathcal{R}=\{(1,2),(2,3),(1,3)\}$ on $X=\{1,2,3\}$ complete?

Is the relation $\mathcal{R}=\{(1,2),(2,3),(1,3)\}$ on $X=\{1,2,3\}$ complete? By looking at the completeness definition in preference: Definition 1.1(c), this is same as the connected relation in the ...
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### Choice theory vs decision theory

I always thought that Decision Theory and Choice Theory are the same fields. But when reading the Wikipedia entry for Decision Theory recently, I read the explicit clarification: "not to be ...
1 vote
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### Can the following statement be rationalized if it yields a choice function?

A person choose an alternative to maximize another person's suffering. I thought we could define a sort of relation where the person suffers more from x than y. And if we can always do this, we can ...
1 vote
31 views

### Can the following behavior be rationalized if it yields a choice function?

The decision maker has an ideal point in mind and chooses the alternative closest to it. I am not sure if I am right, but in order to rationalize it, we first have to construct a choice function. So, ...
103 views

### Example of consumer preferences that switches from being concave to being convex

Question Is there an example of consumer preferences over consumption bundles $(x,y)\in \Bbb R^2$ that would be concave when $x$ is abundant relative to $y$ and convex otherwise? Are there known ...
92 views

### State dependent preferences vs state independent preferences in utility theory

I am working on changes in preferences and found papers on state-independent preference. What is the difference between state-dependent and state-independent preferences and utility functions? What ...
41 views

### Which Choice Rule follows Always Chosen axiom and No Binary Cycle axiom?

Source: taken from ISI PhD entrance exam questions.
1 vote
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### Consumer surplus in Logit model should minus actural payment?

In Logit model, as Train(2003) said in his book(page 55) said, "By definition, a person’s consumer surplus is the utility, in dollar terms, that the person receives in the choice situation. The ...
148 views

### Choice Function and Empty Set [duplicate]

Can the choice function of a non-empty and finite set be the empty set? Or is this by definition of the choice function impossible? Does there need to be always at least one winner if we evaluate non-...
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### Difference between social choice functions and social decision functions?

A social decision function (SDF) à la Sen (1970) is defined as a collective choice rule whose range is restricted to social preference relations which generate a choice function. From Gaertner (2009), ...
89 views

### Exact definition of one-player Bayesian Correlated Equilibrium

Consider a game where a decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world $V$. The state of the world has support $\mathcal{V}$. ...
148 views

### Why does Figure 2.F.1(b) (MWG page 30) satisfy the WARP (Definition 2.F.1)?

I can see that Figure 2.F.1(a) satisfies the WARP (Definition 2.F.1) in MWG (page 30). However, as the choice $x(p',w')$ is only feasible under the price-income level $(p',w')$ and $x(p'',w'')$ is ...
1 vote
63 views

### Risk neutrality in single-agent choice problem under uncertainity

Consider the following static single-agent choice problem under uncertainty. Let $V$ be the state of the world with support $\mathcal{V}$ and probability distribution $P_V\in \Delta(\mathcal{V})$. ...
424 views

### Sen's property $\alpha$ holds when limited attention in choice?

Consider the limited attention choice framework by Matejka and McKay (2015). This framework can give rise to consideration sets, as roughly summarised below. Consideration sets in the limited ...
1 vote
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### Is the set of optimal strategies convex in a single-agent decision choice problem?

EDITED with insights from the comment below. Consider a decision maker who has to choose an action among $\mathcal{Y}\equiv \{1,2,...,L\}$. The payoff from choosing action $y\in \mathcal{Y}$ depends ...
1 vote
196 views

### Boots' Theory by Pratchett

Consider the following quote from the book, $\textit{Men at Arms}$ by Terry Pratchett. “The reason that the rich were so rich, Vimes reasoned, was because they managed to spend less money. ...
I understand from an intuitive sense that decreasing monotonic transformations will skew the choices and ordinality. But mathematically the $F'(U(x,y))$ just cancels out each other out in numerator ...
GARP and Afrait theorem assume that the alternative $x\in\mathbb R_+$ is always positive. In some economic contexts, such as financial choices, the attribute can be negative. I wonder if we can ...