<p>My math is a bit rusty, but I believe you can show that, for a well-behaved (e.g., open and connected) feasible set <span class="math-container">$T$</span> and a consideration set <span class="math-container">$T'$</span>, <span class="math-container">$x \in S \subseteq T' \subseteq T$</span>, e.g. Sen's property <span class="math-container">$\alpha$</span> holds.</p>

<p>That doesn't seem like a very interesting question/result though, as it just follows directly from the definition of "well-behaved".  Maybe I'm missing something.</p>

CC BY-SA 4.0
2019-10-10T20:54:03.820Z
2019-10-10T20:54:03.820Z
heh
<p>Consider the limited attention choice framework by <a href="https://economics.yale.edu/sites/default/files/matejka-140218.pdf" rel="nofollow noreferrer">Matejka and McKay (2015)</a>.</p>

<p>This framework can give rise to consideration sets, as roughly summarised below. </p>

<p><strong>Consideration sets in the limited attention choice framework:</strong>
  Since attention is a scarce resource, the agents may be induced to contemplate only a subset of the available alternatives, ignoring all the others. More precisely, this framework assumes that the decision maker (hereafter, DM) knows the feasible set but is not fully aware of the value of each alternative in the feasible set. The DM is endowed with a prior on the value of each alternative in the feasible set and can "buy" an  <em>information structure</em> to update such a prior.  An information structure consists of a  signal that, once realised, allows the DM to update her prior and then choose the alternative from the feasible set maximising the <em>expected</em> utility given the refined information. On one hand,  the DM prefers a  signal that is as informative as possible on the value of each alternative  in order to minimise ex-post regret. On the other hand, limited attention constraints imply that a more informative  signal is more costly because it requires more cognitive effort to be processed. Such a trade-off can lead to equilibria featuring information structures such that some alternatives in the feasible set are never chosen by the DM for any realisation of the signal. Hence, these alternatives are not part of the DM's consideration set. Complementarily, the DM consideration set's consists of the alternatives which are chosen by the DM with positive probability  for at least some realisations of the signal. </p>

<p><strong>Question:</strong> Consider <a href="https://en.wikipedia.org/wiki/Independence_of_irrelevant_alternatives" rel="nofollow noreferrer">the Sen's property <span class="math-container">$\alpha$</span></a> stating that 
if an alternative <span class="math-container">$x$</span> is chosen from a set <span class="math-container">$T$</span>, and <span class="math-container">$x$</span> is also an element of a subset <span class="math-container">$S$</span> of <span class="math-container">$T$</span>, then <span class="math-container">$x$</span> must be chosen from <span class="math-container">$S$</span>. Does this property hold in the the limited attention choice framework by Matejka and McKay (2015)? The authors have a discussion about IIA (independence of irrelevant alternatives) but I couldn't understand whether the Sen's property <span class="math-container">$\alpha$</span> holds or not. </p>

<decision-theory><choice-theory><rational-expectations>
Sen's property $\alpha$ holds when limited attention in choice?
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# Sen's property $\alpha$ holds when limited attention in choice?

(Asked by: username_0 on 2019-09-18)

Consider the limited attention choice framework by [Matejka and McKay (2015)](https://economics.yale.edu/sites/default/files/matejka-140218.pdf).

This framework can give rise to consideration sets, as roughly summarised below.

**Consideration sets in the limited attention choice framework:**
Since attention is a scarce resource, the agents may be induced to contemplate only a subset of the available alternatives, ignoring all the others. More precisely, this framework assumes that the decision maker (hereafter, DM) knows the feasible set but is not fully aware of the value of each alternative in the feasible set. The DM is endowed with a prior on the value of each alternative in the feasible set and can "buy" an *information structure* to update such a prior. An information structure consists of a signal that, once realised, allows the DM to update her prior and then choose the alternative from the feasible set maximising the *expected* utility given the refined information. On one hand, the DM prefers a signal that is as informative as possible on the value of each alternative in order to minimise ex-post regret. On the other hand, limited attention constraints imply that a more informative signal is more costly because it requires more cognitive effort to be processed. Such a trade-off can lead to equilibria featuring information structures such that some alternatives in the feasible set are never chosen by the DM for any realisation of the signal. Hence, these alternatives are not part of the DM's consideration set. Complementarily, the DM consideration set's consists of the alternatives which are chosen by the DM with positive probability for at least some realisations of the signal.

**Question:** Consider [the Sen's property $\alpha$](https://en.wikipedia.org/wiki/Independence_of_irrelevant_alternatives) stating that
if an alternative $x$ is chosen from a set $T$, and $x$ is also an element of a subset $S$ of $T$, then $x$ must be chosen from $S$. Does this property hold in the the limited attention choice framework by Matejka and McKay (2015)? The authors have a discussion about IIA (independence of irrelevant alternatives) but I couldn't understand whether the Sen's property $\alpha$ holds or not.

**Tags:** decision-theory, choice-theory, rational-expectations

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## 1 answers

### Answer by username_1 on 2019-10-10. Score: 0

My math is a bit rusty, but I believe you can show that, for a well-behaved (e.g., open and connected) feasible set $T$ and a consideration set $T'$, $x \in S \subseteq T' \subseteq T$, e.g. Sen's property $\alpha$ holds.

That doesn't seem like a very interesting question/result though, as it just follows directly from the definition of "well-behaved". Maybe I'm missing something.


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