<p><em>@OfriRaviv provided a great answer, but I thought I'd add a third alternative I am aware of for completeness.</em></p>
<p>The Tversky &amp; Shafir result is only a violation of classical probability. This approach to probability usually goes unquestioned (since people often assume <a href="http://en.wikipedia.org/wiki/Classical_logic" rel="noreferrer">classical logic</a> is the only reasonable logic), but could be put under scientific scrutiny. In physics, this scrutiny lead to the development of quantum mechanics and the associated <a href="http://en.wikipedia.org/wiki/Free_probability" rel="noreferrer">non-commutative (or free) probability</a> (see also: <a href="http://www.uni-math.gwdg.de/mitch/free.pdf" rel="noreferrer">more technical lecture notes</a>).</p>
<p>Recently, this approach has also been pursued in cognitive science (most notably by <a href="http://mypage.iu.edu/%7Ejbusemey/home.html" rel="noreferrer">Jerome R. Busemeyer</a>) to develop a theory of <a href="http://mypage.iu.edu/%7Ejbusemey/quantum/Quantum%20Cognition%20Notes.htm" rel="noreferrer">quantum decision-making</a>. Note that this approach does not assume that the brain is quantum mechanical in the physics sense, instead it questions if the assumption of classical logic is reasonable, or if human behavior is better modeled by non-<a href="http://en.wikipedia.org/wiki/Probability_axioms" rel="noreferrer">Kolmogorov probability</a>.</p>
<p>In this setting, the behavior displayed by humans is rational in accordance to their system of probability. This is similar to, but subtly different from, rule-rationality versus act-rationality in Ofri Raviv's answer. In particular these dynamic models of decision-making can explain the observed 'violations of rationality' in Tversky &amp; Shafir.</p>
<h3>References</h3>
<ul>
<li><p>Busemeyer, J. R., Wang, Z., &amp; Townsend, J. T. (2006) &quot;Quantum dynamics of human decision making.&quot;  Journal of Mathematical Psychology, 50, 220-241. [<a href="http://mypage.iu.edu/%7Ejbusemey/QD.pdf" rel="noreferrer">pdf</a>]</p>
</li>
<li><p>Pothos, E. M. &amp; Busemeyer, J. R. (2009)  &quot;A Quantum Probability Explanation for Violations of ‘Rational’ Decision Theory&quot;. Proceedings of the Royal Society B, 276 (1165),  2171-2178. [<a href="http://mypage.iu.edu/%7Ejbusemey/quantum/QDT.pdf" rel="noreferrer">pdf</a>]</p>
</li>
<li><p>Busemeyer, J. R., Pothos, E. &amp; Franco, R., Trueblood, J. S. (2011) &quot;A quantum theoretical explanation for probability judgment ‘errors’&quot;.  Psychological Review, 108, 193-218. [<a href="http://mypage.iu.edu/%7Ejbusemey/quantum/PJudge6.pdf" rel="noreferrer">pdf</a>]</p>
</li>
</ul>

CC BY-SA 3.0
2012-02-09T00:23:20.053Z
2012-02-09T00:23:20.053Z
2020-06-17T09:55:31.633Z
Artem Kaznatcheev
<p>I know 2 explanations to such seemingly irrational behaviour in cognitive science. Both of them don't really justify the usage of the simple reward-maximizing model in economics.</p>

<h2>Rule Rationality versus Act Rationality</h2>

<p><strong>Act Rationality</strong> is the notion that <strong>every decision</strong> an agent makes is made in order to maximize his utility. <strong>Rule Rationality</strong> is the notion that decision making follows rules. These rules are rational, in the sense that among all possible rules, the chosen rule is the one that <strong>on average</strong> (over choices made) maximizes the agent's utility. Importantly, not every decision is optimal. </p>

<p>In the example you stated, this can be seen as the following: Usually, my actions towards others affect their actions towards me. In this specific game it is not the case, but people cannot take that into account, because of their rule. Their rule says "Assume people are good, try to cooperate, and defect only as a last resort, or if the gain is very high". If they are told explicitly what the other player has chosen, than it is obvious that their choice cannot affect his (so they compute the utility of both choices and choose the higher one). If they're not told the other player's decision, then they assume their decision will affect his to some extent, <strong>because that is the way it usually works in the real world</strong>.</p>

<ul>
<li><a href="http://carbon.videolectures.net/2008/pascal2/eccs08_jerusalem/aumann_rrvar/eccs08_aumann_rrvar_01.pdf" rel="nofollow">A presentation by Nobel laurate Robert Aumann on the subject</a>.</li>
</ul>

<p>This explanation is closely related to the concept of '<strong><a href="http://en.wikipedia.org/wiki/Bounded_rationality" rel="nofollow">Bounded Rationality</a></strong>' that assumes rational decisions with some bounds on the amount of information or processing power.</p>

<h3>Relation to Homo economicus</h3>

<p>This explanation contradicts the assumptions of <em>H.economicus</em> - Actions are not taken to optimize a utility function in every situation. Actions are taken according to rules (that are themselves optimized perhaps during evolution to optimize <strong>average</strong> reward).</p>

<h2>Unknown optimization function</h2>

<p>People choose optimally, just not trying to optimize what you think they are. </p>

<p>For example, if we add some 'reputation' that the agent has, and he is also worried about how his choice will affect (in addition to minimizing the time spent in prison, in the prisonner's dillema), perhaps we can explain the result you mentioned. When the 'time in prison' outcome is clear (other person's choice is known) then it gets a high weight in the combined optimization problem. When the 'time in prison' outcome is not clear (other person's choice is not known) then it gets a smaller weight (no point in working too hard to optimize goals you can't predict) and the reputation result (I want to be perceived as a 'good'/'cooperating' person) is given more weight.</p>

<p>This explanation is more 'rationalistic' by nature: It <strong>assumes</strong> behaviour is an optimization problem - we (the experimenters/scientists) just don't necessarily know the optimization function. </p>

<h3>Relation to Homo economicus</h3>

<p>This explanation is somewhat consistent with H.economicus. The problem is, we don't know the utility function in the general case. It can be very complex, and take into account different factors in different situations. This means that the H.economicus' basic assumtion (optimizing some utility function) is correct, but it makes the model less useful by making the specific function used not known in the general case.</p>

CC BY-SA 3.0
2012-02-04T10:58:03.697Z
2014-11-11T10:16:45.200Z
2014-11-11T10:16:45.200Z
Ofri Raviv
<p>In the early 90s Tversky &amp; Shafir observed several violations of rationality in human participants, in particular violation of the disjunction effect and sure-thing principle. This has lead to much work on questioning the rationalist assumptions of <a href="http://en.wikipedia.org/wiki/Homo_economicus" rel="noreferrer"><em>Homo economicus</em></a>.</p>
<h3>Example</h3>
<p>An example of the violation they saw was in the Prisoners' dilemma: if a person knew their partner defected then also defected (only a 3% cooperation rate), if a person knew their partner cooperated then they usually still defected (only a 16% cooperation rate). However, if they were not sure if their partner defected or cooperated, then they cooperated at much higher rates (a 37% cooperation rate). This violates the naive rationalist expectation of some % between 3 and 16 in the unknown-condition case.</p>
<p>Shafir &amp; Tversky explained this effect through <em>quasi-magical thinking</em>. Even though the participants knew they had no causal effect on their partner's choice, when the choice was unknown they still &quot;did their part&quot; to cause a favorable outcome.</p>
<p>Note that given the false-belief that your actions magically effect the outcome of the other participant's decision, it is no longer irrational to cooperate at a higher rate when you don't know the partner's decision.</p>
<h3>Question</h3>
<p>However, <em>H.econ</em> is still a popular model in economics. For some, this is a pragmatic choice (&quot;the assumption holds in most situation and allows us to build nice models, so we are okay with it being broken <em>sometimes</em>&quot;), but others have strong justifications for why rationality is still a good principle. What is a popular way for rationalists to defend against the apparent violations of rationality brought up by Tversky and Shafir that go beyond false-beliefs or quasi-magical thinking?</p>
<h3>References</h3>
<p>Shafir, E., &amp; Tversky, A. (1992). Thinking through uncertainty: Nonconsequential reasoning and choice. Cognitive Psychology, 24, 449-474. <a href="http://uwch-4.humanities.washington.edu/Texts/JOSH-H/Philosophy%20Guides,%20Analysis%27%20and%20Resources%20(ver.2)/Preference,%20Belief,%20and%20Similarity%20Selected%20Writings%20(Bradford%20Books).pdf#page=720" rel="noreferrer">PDF</a></p>
<p>Tversky, A., &amp; Shafir, E. (1992). The disjunction effect in choice under uncertainty. Psychological Science, 3, 305-309.</p>

CC BY-SA 3.0
2012-02-03T23:15:45.667Z
Rationalists would not disagree that humans are generally not rational, and would be receptive to evidence that people tend to be irrational in a particular way. This helps them to form a good model of how people will behave. Did you mean to ask how *economists* who model people as rational defend against apparent violations of rationality?
JGWeissman
<rationality><decision-making><economics>
What are popular rationalist responses to Tversky & Shafir?
Artem Kaznatcheev
# What are popular rationalist responses to Tversky & Shafir?

(Asked by: username_0 on 2012-02-03)

In the early 90s Tversky & Shafir observed several violations of rationality in human participants, in particular violation of the disjunction effect and sure-thing principle. This has lead to much work on questioning the rationalist assumptions of [*Homo economicus*](http://en.wikipedia.org/wiki/Homo_economicus).

### Example

An example of the violation they saw was in the Prisoners' dilemma: if a person knew their partner defected then also defected (only a 3% cooperation rate), if a person knew their partner cooperated then they usually still defected (only a 16% cooperation rate). However, if they were not sure if their partner defected or cooperated, then they cooperated at much higher rates (a 37% cooperation rate). This violates the naive rationalist expectation of some % between 3 and 16 in the unknown-condition case.

Shafir & Tversky explained this effect through *quasi-magical thinking*. Even though the participants knew they had no causal effect on their partner's choice, when the choice was unknown they still "did their part" to cause a favorable outcome.

Note that given the false-belief that your actions magically effect the outcome of the other participant's decision, it is no longer irrational to cooperate at a higher rate when you don't know the partner's decision.

### Question

However, *H.econ* is still a popular model in economics. For some, this is a pragmatic choice ("the assumption holds in most situation and allows us to build nice models, so we are okay with it being broken *sometimes*"), but others have strong justifications for why rationality is still a good principle. What is a popular way for rationalists to defend against the apparent violations of rationality brought up by Tversky and Shafir that go beyond false-beliefs or quasi-magical thinking?

### References

Shafir, E., & Tversky, A. (1992). Thinking through uncertainty: Nonconsequential reasoning and choice. Cognitive Psychology, 24, 449-474. [PDF](http://uwch-4.humanities.washington.edu/Texts/JOSH-H/Philosophy%20Guides,%20Analysis%27%20and%20Resources%20(ver.2)/Preference,%20Belief,%20and%20Similarity%20Selected%20Writings%20(Bradford%20Books).pdf#page=720)

Tversky, A., & Shafir, E. (1992). The disjunction effect in choice under uncertainty. Psychological Science, 3, 305-309.

**Tags:** rationality, decision-making, economics

> **Comments:**
> **username_1**: Rationalists would not disagree that humans are generally not rational, and would be receptive to evidence that people tend to be irrational in a particular way. This helps them to form a good model of how people will behave. Did you mean to ask how *economists* who model people as rational defend against apparent violations of rationality?  

---

## 2 answers

### Answer by username_2 on 2012-02-04. Score: 19 | Accepted answer

I know 2 explanations to such seemingly irrational behaviour in cognitive science. Both of them don't really justify the usage of the simple reward-maximizing model in economics.

## Rule Rationality versus Act Rationality

**Act Rationality** is the notion that **every decision** an agent makes is made in order to maximize his utility. **Rule Rationality** is the notion that decision making follows rules. These rules are rational, in the sense that among all possible rules, the chosen rule is the one that **on average** (over choices made) maximizes the agent's utility. Importantly, not every decision is optimal.

In the example you stated, this can be seen as the following: Usually, my actions towards others affect their actions towards me. In this specific game it is not the case, but people cannot take that into account, because of their rule. Their rule says "Assume people are good, try to cooperate, and defect only as a last resort, or if the gain is very high". If they are told explicitly what the other player has chosen, than it is obvious that their choice cannot affect his (so they compute the utility of both choices and choose the higher one). If they're not told the other player's decision, then they assume their decision will affect his to some extent, **because that is the way it usually works in the real world**.

* [A presentation by Nobel laurate Robert Aumann on the subject](http://carbon.videolectures.net/2008/pascal2/eccs08_jerusalem/aumann_rrvar/eccs08_aumann_rrvar_01.pdf).

This explanation is closely related to the concept of '**[Bounded Rationality](http://en.wikipedia.org/wiki/Bounded_rationality)**' that assumes rational decisions with some bounds on the amount of information or processing power.

### Relation to Homo economicus

This explanation contradicts the assumptions of *H.economicus* - Actions are not taken to optimize a utility function in every situation. Actions are taken according to rules (that are themselves optimized perhaps during evolution to optimize **average** reward).

## Unknown optimization function

People choose optimally, just not trying to optimize what you think they are.

For example, if we add some 'reputation' that the agent has, and he is also worried about how his choice will affect (in addition to minimizing the time spent in prison, in the prisonner's dillema), perhaps we can explain the result you mentioned. When the 'time in prison' outcome is clear (other person's choice is known) then it gets a high weight in the combined optimization problem. When the 'time in prison' outcome is not clear (other person's choice is not known) then it gets a smaller weight (no point in working too hard to optimize goals you can't predict) and the reputation result (I want to be perceived as a 'good'/'cooperating' person) is given more weight.

This explanation is more 'rationalistic' by nature: It **assumes** behaviour is an optimization problem - we (the experimenters/scientists) just don't necessarily know the optimization function.

### Relation to Homo economicus

This explanation is somewhat consistent with H.economicus. The problem is, we don't know the utility function in the general case. It can be very complex, and take into account different factors in different situations. This means that the H.economicus' basic assumtion (optimizing some utility function) is correct, but it makes the model less useful by making the specific function used not known in the general case.


---

### Answer by username_0 on 2012-02-09. Score: 11

*@OfriRaviv provided a great answer, but I thought I'd add a third alternative I am aware of for completeness.*

The Tversky & Shafir result is only a violation of classical probability. This approach to probability usually goes unquestioned (since people often assume [classical logic](http://en.wikipedia.org/wiki/Classical_logic) is the only reasonable logic), but could be put under scientific scrutiny. In physics, this scrutiny lead to the development of quantum mechanics and the associated [non-commutative (or free) probability](http://en.wikipedia.org/wiki/Free_probability) (see also: [more technical lecture notes](http://www.uni-math.gwdg.de/mitch/free.pdf)).

Recently, this approach has also been pursued in cognitive science (most notably by [Jerome R. Busemeyer](http://mypage.iu.edu/%7Ejbusemey/home.html)) to develop a theory of [quantum decision-making](http://mypage.iu.edu/%7Ejbusemey/quantum/Quantum%20Cognition%20Notes.htm). Note that this approach does not assume that the brain is quantum mechanical in the physics sense, instead it questions if the assumption of classical logic is reasonable, or if human behavior is better modeled by non-[Kolmogorov probability](http://en.wikipedia.org/wiki/Probability_axioms).

In this setting, the behavior displayed by humans is rational in accordance to their system of probability. This is similar to, but subtly different from, rule-rationality versus act-rationality in username_2's answer. In particular these dynamic models of decision-making can explain the observed 'violations of rationality' in Tversky & Shafir.

### References

* Busemeyer, J. R., Wang, Z., & Townsend, J. T. (2006) "Quantum dynamics of human decision making." Journal of Mathematical Psychology, 50, 220-241. [[pdf](http://mypage.iu.edu/%7Ejbusemey/QD.pdf)]
* Pothos, E. M. & Busemeyer, J. R. (2009) "A Quantum Probability Explanation for Violations of ‘Rational’ Decision Theory". Proceedings of the Royal Society B, 276 (1165), 2171-2178. [[pdf](http://mypage.iu.edu/%7Ejbusemey/quantum/QDT.pdf)]
* Busemeyer, J. R., Pothos, E. & Franco, R., Trueblood, J. S. (2011) "A quantum theoretical explanation for probability judgment ‘errors’". Psychological Review, 108, 193-218. [[pdf](http://mypage.iu.edu/%7Ejbusemey/quantum/PJudge6.pdf)]


---

