11
votes
Accepted
Condorcet's paradox: Is the majority rule transitive?
As you stated, transitivity is that overall $x \succeq y$ and $y \succeq z$ implies $x \succeq z$. I will show an example where majority rule isn't transitive and hopefully it will answer your ...
- 1,563
11
votes
Are terrorists rational?
I guess you might already know this, but I wanted to add a little detail to the other answers for the sake of any layman who comes here and gets the wrong end of the stick.
What is meant by ...
- 16.6k
8
votes
Accepted
(Preference Relation/Set) Continuous $\succsim$ imply closedness of upper and lower contour sets
Looking more closely at your question, I think things should not be overly complicated. From Mas-Colell et.al.
Definition 3.C.1:
The preference relation $\succsim$ on X is continuous if it is ...
- 6,409
7
votes
The 'Economic Man' (Reference Request)
I would point you firstly to work pioneered by the late Gary Becker on applying the principles of economic optimisation to non-market behaviour.
Becker's insight was that the kinds of trade-offs ...
- 16.6k
7
votes
Accepted
Can the Certainty Equivalent be negative?
If you start out with €0, then the certainty equivalent of losing €2.5 with probability 1 is -€2.5.
Your exercise basically asks you to calculate what difference winning the lottery with a small ...
- 26.2k
6
votes
a risk lover agent preferences and the preference of risk natural agent may be the same
Don't commit the cardinal mistake of equating preferences with choices.
In the context of Expected Utility Theory, the fact that a risk-averse agent ($RA$) would choose $N$ over $M$ implies that
$...
- 31.8k
6
votes
Accepted
Utility representation of single peaked preferences
No. Basically, you can encode a form of lexicographic preferences, probably the most familiar example of non-representable preferences, as single-peaked preferences on $\mathbb{R}$.
Define $\succeq$ ...
- 9,705
5
votes
What is the point of the indirect utility function?
Recall that if $x$ and $y$ are consumption bundles, $u(x)$ is the consumer's utility function, and $u(x)>u(y)$ means the consumer strictly prefers bundle $x$ to bundle $y$.
The indirect utility ...
- 382
5
votes
intertemporal utility function usage : calculating consumption
This is the two-period budget constraint:
C1 + C2/(1+r) = Y1 + Y2/(1+r)
Derivation is straightforward. On the LHS, you have the present value of consumption (considered during period 1), and on ...
- 71
5
votes
What is the difference between "Social Choice Theory", "Public Choice Theory", and "Collective decision-making?
Social choice theory or social choice is a theoretical framework for analysis of combining individual opinions, preferences, interests, or welfares to reach a collective decision or social welfare in ...
- 151
5
votes
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The 'Economic Man' (Reference Request)
Amartya Sen, a 1998 Nobel Laureate, has a well cited article on the subject:
"Rational Fools: A Critique of the Behavioral Foundations of Economic Theory", Philosophy & Public Affairs, 1977.
...
- 14.4k
5
votes
Accepted
What is one dimensional, ordered type?
Judging from the reference you provide, this refers to whether the set $\Theta$ is ordered or not. For example, natural numbers or the alphabet are ordered sets. In the context of moral hazard ...
- 8,437
5
votes
Accepted
Envelope theorem for discrete choice sets?
There is an envelope theorem for the setting you describe.
Have a look at “Envelope Theorems for Arbitrary Choice Sets” by Milgrom and Segal (2002).
- 2,097
5
votes
Understanding the Choice Rule in MWG
I am having trouble understanding what $C(\{x, y, z\}) = \{x, y\}$ means.
MWG already explain this on p.10:
When [$C(B)$ contains more than one element], the elements of $C(B)$ are the alternatives ...
- 14.4k
5
votes
Market with changing number of goods and services
I think the best candidate would be monopolistic competition as introduced by
Dixit and Stiglitz (1977) Monopolistic Competition and Optimum Product Diversity,
in which two models are introduced. ...
- 3,247
5
votes
Accepted
Weak preferences and negative transitivity
Probably it can be done easier if you do both steps separately ($\implies$ and $\impliedby$), but here is a proof that does both at the same time:
\begin{align*}
&x\succ y \vee x\sim y\\
\iff\;&...
- 454
4
votes
Accepted
Continuous rational and monotone preference relation implies $x\succsim0$?
If we take the definition of monotonicity to be if $x\geqq y$ then $x \succeq y$, you can simplify the proof (though it looks right).
Note $\mathbf{0}\leq x$ for all $x\in \mathbb{R}_+^l$. So by ...
- 2,167
4
votes
Are terrorists rational?
I don't think we have enough data on that matter. They would be irrational, for example, if transitivity of their preferences does not hold. How do we get their preferences? Through the axiom of ...
- 10.4k
4
votes
Accepted
Prove that a continuous $\succsim$ is quasilinear
First off it seems to me you are proceeding in a manner more complicated than necessary. (Perhaps this is intentional because you wish to face a harder exercise.) Since it is given that $v(x)$ ...
- 26.2k
4
votes
Accepted
Boots' Theory by Pratchett
Rampini elaborates on your idea (and also the Pratchett quote) in his AER article "Financing Durable Assets". See the abstract:
This paper studies how the durability of assets affects ...
- 5,090
4
votes
Why does Figure 2.F.1(b) (MWG page 30) satisfy the WARP (Definition 2.F.1)?
Intuitively, this just says that if the bundle you choose was possible under wealth $w$ and price $p$ but it is not $x(p, w)$, then it must be that you cannot obtain it when price is $p'$ and wealth ...
- 2,764
4
votes
Accepted
Difference between social choice functions and social decision functions?
Let $X$ be the set of alternatives.
A social decision function maps profiles of preference orderings to relations on $X$ such that every nonempty subset of $X$ has at least one maximum under this ...
- 9,705
4
votes
Discontinuous function $U$ with continuous preferences can be written as a composition of discontinuous & monotone function and a continuous function
If the preference is continuous, reflexive, transitive and complete, then there exists a continuous utility representation $g$, and since $U$ also represents the same preference, so there must be a ...
- 5,082
3
votes
Are terrorists rational?
We can not prove terrorists are not rational. We can only have a failure to find a tractable utility function that adequately models their behavior.
On the practical side, one cannot see enough ...
- 3,322
3
votes
Are terrorists rational?
Ron Wintrobe has a book on Rational Extremism, which explains how behavior of terrorists, in particular suicide bombers may be "rationalized". He theorizes that the act of blowing up oneself is a form ...
- 14.4k
3
votes
Accepted
Relation between linear utility function and U=max{x,y}
The optimal choice set for a max function and a perfect substitutes function with equal relative prices share some solutions [i.e, boundary solutions], but in general, the indifference curves, and ...
- 154
3
votes
Accepted
Vocabulary/Name for Utility of a Set of Choices
What you seem to be interested is the subfield of decision theory that goes by the name of "menu choice." The starting point of this literature is the paper
Kreps, David M. "A representation theorem ...
- 9,705
3
votes
Accepted
a risk lover agent preferences and the preference of risk natural agent may be the same
Another way of looking at this problem is to consider the means and variances of the lotteries.
A risk averse agent (RA) likes high mean and low variance
A risk neutral agent (RN) likes high mean ...
- 14.4k
3
votes
Accepted
Exact definition of one-player Bayesian Correlated Equilibrium
The concept of the BCE from their 2016 paper is similar to what you have. I think Bergemann and Morris' intuitive explanation is valuable so I'll paraphrase it here.
Each player in the game has a ...
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