# Questions tagged [choice-theory]

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

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### Non decreasing function for utility transformation

I was going through the Theorem 2 : Suppose $u(x)$ represents agents preferences, $\succsim$ and $f : \mathbb{R} \rightarrow \mathbb{R}$ is a strictly increasing function. Then the new new utility ...
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### Question About Proof of Proposition 3.C.1 in MWG - Step 1

I have difficulties understanding the first step of the proof of Proposition 3.C.1 in MWG. Proposition 3.C.1$\quad$ Suppose that the rational preference relation $\succsim$ on $X$ is continuous. Then ...
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### Understanding the definition of monotone

In Microeconomic Theory by Mas-Colell, Whinston, and Green, the definition of monotone preference relations is given as follows: Definition 3.B.2$\quad$ The preference relation $\succsim$ on $X$ is ...
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### Prove: The law of demand holds if WA, Walras' law, homogeneity of degree 0, and homogeneity of degree 1 in wealth hold for Walrasian demand functions

Problem I am asked to prove the following result (MWG Exercise 2.F.5): The law of demand always holds if the walrasian demand function $x(\mathbf{p},w)$ satisfies the weak axiom of revealed ...
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### Proof for Marshallian Demand function

If you have a Marshallian demand function that is strictly convex, then it satisfies WARP. How to prove this?
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### Proving the Choice with Recommendations

Suppose that there are two types of outcomes, i.e. $X=X_1 \cup X_2$ with $X_1 \cap X_2=∅$. All outcomes in $X_2$ are the same to the decision maker (he doesn't understand these kind of products). He ...
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### In revealed preference (RP), is any two points $x,y$ related by the indirect revealed preference relation?

Let $X$ be the closed compact convex set of alternative and $B$ be a closed compact convex subset of $X$. $C$ is defined on all closed compact convex set $B\subseteq X$. $X$ is ordered by a strictly ...
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### Find a choice function such that WARP or SARP is violated

WARP implies choice function is raionalizable. Say we have a choice function $C(B)$, $B$ is a closed convex compact set. I am looking for a intuitive example of $C$. The $C$ is economic meaningful, ...
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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 ...
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### 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 ...
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### 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
37 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, ...
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### 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 ...
181 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 ...
134 views

### 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 ...
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### 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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Consider a Nested Logit demand model with two nests, $N_1, N_2$: $N_1$ contains the outside option only (labelled "0"), $N_2$ contains all the remaining alternatives (labelled "$j=1,...,... • 368 0 votes 1 answer 258 views ### max{x1,x2} where P1not=p2 I have seen min{x1,x2} functions representing perfect compliments but have never seen a max{x1,x2} function anywhere in my book or lectures, I also have never seen anything about p1 not equaling p2. ... 2 votes 1 answer 102 views ### Market with changing number of goods and services In the General Equilibrium framework of Arrow, Debreau and others, there are a fixed number of commodities, which I feel is a valid assumption in the short run but maybe not in the long run. Over time,... 3 votes 1 answer 196 views ### Understanding the Choice Rule in MWG I am reading the Microeconomics Theory book by MWG, and I am having a tough time interpreting what things mean to a real life example, so any help would be appreciated. For example, it gave this. ... • 99 2 votes 1 answer 785 views ### Can the Certainty Equivalent be negative? I am questioning if the CE of a lottery can be negative? For me it doesn't make much sense by definition. I encountered this problem on the following exercise: Imagine a case where we have a lottery(... 4 votes 1 answer 130 views ### Utility representation of single peaked preferences Is it true that a single-peaked preference (with the peak at some finite point) over the set of real numbers, always has a utility representation ?? If yes, can you please hint towards the proof or ... • 71 0 votes 0 answers 74 views ### Binary relation on the set$X = \{v, w, x, y , z\}$that is asymmetric and transitive but not negatively transitive So I am trying to find a binary relation on the set$X = \{v, w, x, y, z\}$that is asymmetric and transitive but not negatively transitive, and is quite tricky. Will$R = (v, w)$be asymmetric and ... 0 votes 1 answer 189 views ### Prove that Choice Coherence Implies IIA Prove that Choice Coherence implies Independence of Irrelevant Alternatives (IIA). From the definition of choice coherence, we have this: A choice function c satisfies choice coherence if, for every ... • 3 4 votes 1 answer 132 views ### Doesn't the Pareto-extension rule invalidate Eliaz's (2004) unified theorem of social choice? Eliaz (2004) uses social aggregators to provide a unique "meta-theorem" from which Arrow and Gibbard-Satterthwaite follow as corollaries. He defines social aggregators as follows. Let$\...
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 $\mathcal{V}$. ...