<p>No, weak orderings are not mutually exclusive, but strict orderings are, exactly as for the usual comparison of real numbers: you can have $x \geq y$ and $y \geq x$ (if $x=y$), but $x&gt;y$ and $y&gt;x$ are incompatible with each other.</p>

<p>The weak orderings $A \succeq B$ and $B \succeq A$ mean that the decision-maker is indifferent between $A$ and $B$: he might therefore choose any of these options indifferently.</p>

CC BY-SA 3.0
2016-03-06T04:06:28.120Z
Thank you. That clears up a few things.    
If A ⪰ B mean that the decision-maker is indifferent between A and B, then why does the author raise a third possibility that if A ⪰ B and B ⪰ A, then A ∼ B ( The consumer is indifferent between the two).  

Precisely, What I'm asking is: What is the difference between A ⪰ B and A ∼ B if both notations mean that the consumer is unable to make a decision?
WorldGov
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2016-03-06T08:15:56.050Z
@AkalankPrakash $A \succeq B$ does not mean that the consumer is indifferent: it means that he weakly prefers $A$ to $B$ (but not strictly). It is the opposite of $B \succ A$. It is only the combination of $A \succeq B$ and $B \succeq A$ that is equivalent to $A \sim B$. Thinking of $A$ and $B$ as real numbers instead of bundles.might help you.
Oliv
CC BY-SA 3.0
2016-03-05T10:40:41.700Z
2016-03-05T10:40:41.700Z
Oliv
<p>From Perloff, Microecomics, 6th edition (Pg. 75): </p>

<p>A consumer chooses between bundles of goods by ranking them as to the pleasure
the consumer gets from consuming each. We summarize a consumer’s ranking using
a preference relation, such as the consumer weakly prefers Bundle a to Bundle b, if the consumer likes Bundle a at least as much as Bundle b.</p>

<p>Given this weak preference relation, we can derive two other relations. If the consumer weakly prefers Bundle a to b, but the consumer does not weakly prefer
b to a, then we say that the consumer strictly prefers a to b—would definitely
choose a rather than b if given a choice—which we write as a b.</p>

<p>If the consumer weakly prefers a to b and weakly prefers b to a —— then we say that the consumer is indifferent between the bundles, or likes the
two bundles equally.</p>

<hr>

<p>My question is: When you have declared that a consumer weakly prefers A to B, how could you then argue that a consumer could also prefer (weakly) B to A? Aren't they mutually exclusive?</p>

CC BY-SA 3.0
2016-03-05T15:28:55.630Z
This has a voting score of 1, has only one answer but is a 'hot network question' ?
BCLC
CC BY-SA 3.0
2016-03-06T04:29:33.180Z
Ranked by views. @BCLC
Kitsune Cavalry
<microeconomics>
Consumer choice: How could a consumer weakly prefer A to B *and* B to A?
WorldGov
# Consumer choice: How could a consumer weakly prefer A to B *and* B to A?

(Asked by: username_0 on 2016-03-05)

From Perloff, Microecomics, 6th edition (Pg. 75):

A consumer chooses between bundles of goods by ranking them as to the pleasure
the consumer gets from consuming each. We summarize a consumer’s ranking using
a preference relation, such as the consumer weakly prefers Bundle a to Bundle b, if the consumer likes Bundle a at least as much as Bundle b.

Given this weak preference relation, we can derive two other relations. If the consumer weakly prefers Bundle a to b, but the consumer does not weakly prefer
b to a, then we say that the consumer strictly prefers a to b—would definitely
choose a rather than b if given a choice—which we write as a b.

If the consumer weakly prefers a to b and weakly prefers b to a —— then we say that the consumer is indifferent between the bundles, or likes the
two bundles equally.

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My question is: When you have declared that a consumer weakly prefers A to B, how could you then argue that a consumer could also prefer (weakly) B to A? Aren't they mutually exclusive?

**Tags:** microeconomics
> **Comments:**
> **username_1**: This has a voting score of 1, has only one answer but is a 'hot network question' ?  
> **username_2**: Ranked by views. @BCLC  

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## 1 answers

### Answer by username_3 on 2016-03-05. Score: 3

No, weak orderings are not mutually exclusive, but strict orderings are, exactly as for the usual comparison of real numbers: you can have $x \geq y$ and $y \geq x$ (if $x=y$), but $x>y$ and $y>x$ are incompatible with each other.

The weak orderings $A \succeq B$ and $B \succeq A$ mean that the decision-maker is indifferent between $A$ and $B$: he might therefore choose any of these options indifferently.

> **Comments:**
> **username_0**: Thank you. That clears up a few things.     If A ⪰ B mean that the decision-maker is indifferent between A and B, then why does the author raise a third possibility that if A ⪰ B and B ⪰ A, then A ∼ B ( The consumer is indifferent between the two).    Precisely, What I'm asking is: What is the difference between A ⪰ B and A ∼ B if both notations mean that the consumer is unable to make a decision?  
> **username_3**: @AkalankPrakash $A \succeq B$ does not mean that the consumer is indifferent: it means that he weakly prefers $A$ to $B$ (but not strictly). It is the opposite of $B \succ A$. It is only the combination of $A \succeq B$ and $B \succeq A$ that is equivalent to $A \sim B$. Thinking of $A$ and $B$ as real numbers instead of bundles.might help you.  

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