Skip to main content

Questions tagged [choice-theory]

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

Filter by
Sorted by
Tagged with
9 votes
5 answers
1k views

Are terrorists rational?

Terrorism in general, and suicidal terrorism in particular, is popularly seen as “irrational,” but many economists and political scientists argue otherwise. This quote is from Terrorism: The ...
emeryville's user avatar
  • 6,945
8 votes
1 answer
2k views

Condorcet's paradox: Is the majority rule transitive?

From this wikipedia link I would say that the majority rule is not transitive. Also I'm not sure I understand exactly what is transitivity in this situation... With a usual preference relation $x\...
An old man in the sea.'s user avatar
7 votes
1 answer
6k views

(Preference Relation/Set) Continuous $\succsim$ imply closedness of upper and lower contour sets

[ADDED/MODIFIED] : I have put my proof where the commodity space is simply $\mathbb{R_+}$(e.g. nonnegative reals) for simplicity below. Please share your 2 cent. I have put words to aid my own ...
Frank Swanton's user avatar
7 votes
2 answers
9k views

What is the difference between "Social Choice Theory", "Public Choice Theory", and "Collective decision-making?

I need to know the difference between Social Choice, Public Choice and collective decision-making. Also, Is public choice, social choice the same as collective choice? Thank you
Christopher Tamina's user avatar
6 votes
2 answers
1k views

Continuous rational and monotone preference relation implies $x\succsim0$?

I updated my proof to a general version as follows: please share your thoughts & 2cent. Thanks Show a monotone continuous complete preorder on $\mathbb{R}^L_+$ has $y\geq x\rightarrow y\succsim x$....
Frank Swanton's user avatar
6 votes
3 answers
2k views

What is the point of the indirect utility function?

Where does this have application? I understand how the demand function may be arrived at using the utility maximization problem but I don't understand where the indirect utility function is used and I ...
TheEconomist's user avatar
6 votes
1 answer
429 views

Envelope theorem for discrete choice sets?

If we have a function $$f(x)=\max_yg(x,y)$$ Then we can find the derivative $d/dx \ f(x)$ by realizing that $$(1): \quad \frac {\partial }{\partial y}g(x,y^*)=0$$ because of the first order ...
user56834's user avatar
  • 845
6 votes
1 answer
1k views

Prove that a continuous $\succsim$ is quasilinear

This question is closely related to Mas-colell, Whinston, Green: Microeconomic Theory, Question 3.C.5b Let $\succsim$ be a strictly monotone, continuous, and rational preference relation on $(-\...
möbius's user avatar
  • 553
5 votes
3 answers
352 views

The 'Economic Man' (Reference Request)

We are writing a paper about the 'economic man.' By this, we mean that the choices he makes epitomize a rational economic thinker. However, we also acknowledge the fact that there are other, non-...
DornerA's user avatar
  • 1,568
5 votes
3 answers
3k views

intertemporal utility function usage : calculating consumption

I have encountered this a lot in my exams and can not seem to understand how to use these functions here is an easy exemple : A consumer who will only live 2 periods receives 1000€ in the first ...
Amr El Aswar's user avatar
5 votes
0 answers
47 views

Comparing voting methods when there are only two voters

Consider the Schulze, Kemeny-Young, Ranked Pairs and Borda count voting methods. (The last is obviously the odd one out in this list!) Suppose that there are only two voters. Each voter gives a ...
cfp's user avatar
  • 252
5 votes
0 answers
135 views

Afriat theorem for negative goods

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 ...
High GPA's user avatar
  • 1,916
4 votes
1 answer
125 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 ...
Polime's user avatar
  • 71
4 votes
1 answer
174 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-...
dewewdew's user avatar
  • 105
4 votes
1 answer
481 views

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), ...
decisionsdecisions's user avatar
4 votes
1 answer
93 views

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 ...
Beerus's user avatar
  • 505
4 votes
1 answer
83 views

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 ...
High GPA's user avatar
  • 1,916
4 votes
1 answer
127 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 $\...
decisionsdecisions's user avatar
4 votes
1 answer
485 views

What is the economic incentive to cheat? How does an experiment capture exogenous deviations?

In my undergraduate career an economic experiment was conducted on my class: one class was the control two classes were the experimental (I was in an experimental class) The basic premise was a ...
Bluebird's user avatar
  • 242
4 votes
1 answer
108 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 ...
Pavel Kocourek's user avatar
4 votes
1 answer
334 views

Microeconomic foundation of discrete choice model

(1) Does the following result in a "valid" (in the sense of being consistent with the economic theory) market demand function? A consumer $i$ maximizes a utility $u_{ij}$ in choosing one of J ...
berter's user avatar
  • 43
4 votes
0 answers
171 views

Proof of Proposition 1.4 from Microfoundations I by Kreps

Regardless of the size of X (set of all possible objects), if a preference relation which is complete and transitive is defined on it, then the corresponding choice function generated by it will ...
subrat's user avatar
  • 63
3 votes
2 answers
333 views

a risk lover agent preferences and the preference of risk natural agent may be the same

Consider two lotteries $N$ and $M$. Agent $i$ is risk-averse and prefers $N$. Agent $j$ is risk-neutral and prefers $M$. Would any risk-loving agent $k$ also prefer $M$? That is, would $j$ and $k$ ...
none009's user avatar
  • 153
3 votes
2 answers
162 views

Convex rationalization when the budget sets are segments?

Backgroud: SARP can be defined on general budget set. SARP: Assume for all $B$ the choice $c(B)$ is only one element. If $x_i,x_{i+1}\in B_i$, and $x_i = c(B_i)$, for all $i\in \{1,N-1\}$, then $x_1=...
High GPA's user avatar
  • 1,916
3 votes
1 answer
412 views

Hick's and Slutsky's approaches lead to different income effects. Why?

Suppose a cup of coffee and a plate of beans are sold at € 1 and € 3 respectively during the winter. In summer, the government decides to remove the subsidy on coffee and its new price per cup goes up ...
Isa's user avatar
  • 87
3 votes
1 answer
190 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. ...
Alex's user avatar
  • 99
3 votes
2 answers
16k views

Relation between linear utility function and U=max{x,y}

I'm studying general equilibrium theory, and in the study guide I came across a utility function of the type $U=\max\{x,y\}$, which I'm not that familiar with. I study mainly from two books: ...
José Julián Parra's user avatar
3 votes
2 answers
90 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 $\mathcal{V}$. ...
Star's user avatar
  • 436
3 votes
1 answer
79 views

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 ...
homo-economitux's user avatar
3 votes
1 answer
393 views

Convexity of preferences (dissimilar definitions)

Varian's Intermediate Microeconomics describes convexity as $$\text{Given } x, y \in X: x \sim y \implies \forall t \in [0,1], tx + (1-t)y \succeq x,y$$ The other definition I read everywhere is: $$\...
Kur_Kush's user avatar
3 votes
1 answer
81 views

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 ...
Beerus's user avatar
  • 505
3 votes
1 answer
69 views

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 ...
Beerus's user avatar
  • 505
3 votes
0 answers
67 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 ...
High GPA's user avatar
  • 1,916
3 votes
2 answers
470 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 ...
Star's user avatar
  • 436
3 votes
0 answers
614 views

Choice rule and path independence

Question: A choice rule $C$ satisfies path independence if for all $A, B \in 2^X \setminus \emptyset$, $C(A \cup B) = C(C(A) \cup C(B))$. Prove that if $C$ is nonempty and rationalizable, then $C$ ...
TeTs's user avatar
  • 181
2 votes
2 answers
278 views

Discontinuous function $U$ with continuous preferences can be written as a composition of discontinuous & monotone function and a continuous function

Conjecture: Every discontinuous utility function $U$ representing continuous preferences can be written as $U = f \circ g$ for some continuous $g$ and discontinuous strictly monotone $f$. The goal is ...
not tdm's twin's user avatar
2 votes
1 answer
780 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(...
Gonçalo Gameiro's user avatar
2 votes
2 answers
159 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 ...
High GPA's user avatar
  • 1,916
2 votes
1 answer
101 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,...
Ishan Kashyap Hazarika's user avatar
2 votes
1 answer
173 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 ...
Yun's user avatar
  • 101
2 votes
1 answer
664 views

Choice correspondence notation

My question is about the following notation: I have noticed in several places (for example here (page 15) and here (page 1)) that different authors use different notations for choice correspondences....
thekiciminister's user avatar
2 votes
2 answers
427 views

Can there be sensible choice behavior that violates the Weak Axiom of Revealed Preference?

Following the notation of Mas-Collel, Whinston, and Green, consider a family of budget sets $\mathcal{B}=\{\{x,y\},\{x,y,z\}\}$. To make the example concrete, let's let $x$ be a book $y$ be a left ...
EthanAlvaree's user avatar
2 votes
1 answer
153 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 ...
desi arthshastri's user avatar
2 votes
1 answer
241 views

Proof of the tangency condition in UMP

When an indifference curve is tangent to the budget line such that the preferences are convex and monotone, why is the point of tangency an optimal for an UMP? Given the budget line $p_1 x + p_2 y = I$...
xyz123's user avatar
  • 23
2 votes
1 answer
57 views

Proof for Marshallian Demand function

If you have a Marshallian demand function that is strictly convex, then it satisfies WARP. How to prove this?
babededeeptido's user avatar
2 votes
1 answer
287 views

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 ...
Ishan Kashyap Hazarika's user avatar
2 votes
1 answer
246 views

Consumer demand: a function of present endowment?

I don't know about you, but each time I go shopping for groceries, my purchasing decision takes into account what I already have at home. I don't make only one demand decision for my entire life the ...
EthanAlvaree's user avatar
2 votes
1 answer
86 views

If the income increases by $\$d$, will it mean the utility at the optimal point increases by $\lambda d$?

I read that if the income increases by $\\\$d$, then the utility at the optimal point will increase by $\lambda d$. How do I get a sense of this, both mathematically and intuitively? Can we write that ...
cris's user avatar
  • 21
2 votes
1 answer
92 views

Part of proof of Gibbard-Satterthwaite Theorem

I'm currently working through Nisan's Algorithmic Game Theory, Chapter 9 (Introduction to Mechanism Design). A part of the proof for the Gibbard-Satterthwaite Theorem is given as "obvious," ...
andrew's user avatar
  • 51
2 votes
2 answers
2k views

Weak axiom of revealed preference and choice coherence - how to show they are equivalent

$B$ and $B'$ are elements of the family of subsets of $X$ WARP For every pair $x,y \in B \cap B' $ and if $x \in c(B)$ , then if $y \in c(B'), x$ must $\in c(B').$ Choice Coherence For very pair $x,...
subrat's user avatar
  • 63