<p>To make things weird, although Frisch was fully aware of the importance of random distribution in economics relations, he never mention the randomness in binary preference relations!</p>
<p>How to define preference? I learned that <span class="math-container">$x\succ y$</span> means the decision maker is more likely to choose <span class="math-container">$x$</span>, but I don't know the sources of this.</p>
<p>I found the following definition on Wikipedia:</p>
<blockquote>
<p>Suppose a person is offered apples (x) and oranges (y), and is asked to choose one of the two.</p>
<p>Under several repetitions of this experiment (and assuming laboratory conditions controlling outside factors), if the scientist observes that apples are chosen 51% of the time it would mean that <span class="math-container">$x\succ y$</span>. If half of the time oranges are chosen, then <span class="math-container">$x\sim y$</span>. Finally, if 51% of the time she chooses oranges it means that <span class="math-container">$y\succ x$</span>. Preference is here being identified with a greater frequency of choice.</p>
</blockquote>
<p>I see that Block, Marschak, Tversky, and Luce use this definition, but their first occupation is not economist I guess. My question is, did Frisch (or other old famous economists except Debreu) used this definition?</p>
<hr />
<p>Debreu wrote: &quot;The relation <span class="math-container">$p(a, b) &gt; 1/2$</span> is read &quot;<span class="math-container">$a$</span> is preferred to <span class="math-container">$b$</span>&quot;</p>
<p>For example, see &quot;Topological Methods in Cardinal Utility Theory&quot; and &quot; STOCHASTIC CHOICE AND CARDINAL UTILITY (Econometrica)&quot;</p>
<p>Tversky use the same thing, for example, in his 1969 &quot;Intransitivity of preferences&quot;.</p>
<hr />
<p>To clarify, the &quot;<strong>observable</strong> definition&quot;, emphasized in the title, means an equivalent condition of &quot;<span class="math-container">$x$</span> is preferred <span class="math-container">$y$</span>&quot; that is economically observable, economically intuitive, experimentally or empirically testable. Of course, everyone who exposed to any microeconomics courses understands the mathematical definition of preference. In contrast, this question asks what is the meaning of &quot;preference&quot; in economic experiments and real world.</p>

CC BY-SA 4.0
2020-10-10T04:10:37.840Z
@KennyLJ Debreu did use this definition. But he is more like a mathematician than economist.
High GPA
CC BY-SA 4.0
2020-10-11T13:17:31.773Z
@KennyLJ For your first comment, do you mean that: if $x\succsim y$, then the agent is more likely to choose $x$?
High GPA
CC BY-SA 4.0
2020-11-10T19:10:24.327Z
The definition of $x\succ y$ used by Debreu is that $x\succeq y$ holds but not $y\succeq x$.
Michael Greinecker
CC BY-SA 4.0
2020-11-10T22:16:24.003Z
@MichaelGreinecker Could you please check the literature mentioned above?
High GPA
CC BY-SA 4.0
2020-11-10T22:24:08.700Z
Debreu does not ever use the symbol "$\succ$" in that paper.
Michael Greinecker
CC BY-SA 4.0
2020-11-10T22:52:24.270Z
@MichaelGreinecker Could you please read out "$\succ$" loud?
High GPA
CC BY-SA 4.0
2020-11-10T22:57:54.777Z
Sure. I just did.
Michael Greinecker
<microeconomics><econometrics><preferences><decision-theory><philosophy-of-economics>
What is the observable definition of "preference" by Frisch?
High GPA
# What is the observable definition of "preference" by Frisch?

(Asked by: username_0 on 2020-10-09)

To make things weird, although Frisch was fully aware of the importance of random distribution in economics relations, he never mention the randomness in binary preference relations!

How to define preference? I learned that $x\succ y$ means the decision maker is more likely to choose $x$, but I don't know the sources of this.

I found the following definition on Wikipedia:

> Suppose a person is offered apples (x) and oranges (y), and is asked to choose one of the two.
>
> Under several repetitions of this experiment (and assuming laboratory conditions controlling outside factors), if the scientist observes that apples are chosen 51% of the time it would mean that $x\succ y$. If half of the time oranges are chosen, then $x\sim y$. Finally, if 51% of the time she chooses oranges it means that $y\succ x$. Preference is here being identified with a greater frequency of choice.

I see that Block, Marschak, Tversky, and Luce use this definition, but their first occupation is not economist I guess. My question is, did Frisch (or other old famous economists except Debreu) used this definition?

---

Debreu wrote: "The relation $p(a, b) > 1/2$ is read "$a$ is preferred to $b$"

For example, see "Topological Methods in Cardinal Utility Theory" and " STOCHASTIC CHOICE AND CARDINAL UTILITY (Econometrica)"

Tversky use the same thing, for example, in his 1969 "Intransitivity of preferences".

---

To clarify, the "**observable** definition", emphasized in the title, means an equivalent condition of "$x$ is preferred $y$" that is economically observable, economically intuitive, experimentally or empirically testable. Of course, everyone who exposed to any microeconomics courses understands the mathematical definition of preference. In contrast, this question asks what is the meaning of "preference" in economic experiments and real world.

**Tags:** microeconomics, econometrics, preferences, decision-theory, philosophy-of-economics
> **Comments:**
> **username_0**: @KennyLJ Debreu did use this definition. But he is more like a mathematician than economist.  
> **username_0**: @KennyLJ For your first comment, do you mean that: if $x\succsim y$, then the agent is more likely to choose $x$?  
> **username_1**: The definition of $x\succ y$ used by Debreu is that $x\succeq y$ holds but not $y\succeq x$.  
> **username_0**: @MichaelGreinecker Could you please check the literature mentioned above?  
> **username_1**: Debreu does not ever use the symbol "$\succ$" in that paper.  
> **username_0**: @MichaelGreinecker Could you please read out "$\succ$" loud?  
> **username_1**: Sure. I just did.  

---

## 0 answers

