- Choice 1:
- Option A: A 100% chance of winning
1 million, a 10% chance of winning 1 million and an 89% chance of winning nothing. - Option D: A 10% chance of winning
2^1 =![Rendered by QuickLaTeX.com 5 million and a 90% chance of winning nothing. Most people choose <strong>Option D</strong>, as the odds are similar for a much larger potential payout.</li> <!-- /wp:list-item --></ul> <!-- /wp:list --></li> <!-- /wp:list-item --></ul> <!-- /wp:list --> <!-- wp:paragraph --> <strong>The Paradox:</strong> When you calculate the expected utility for these choices, a person who chose Option A in the first choice should, to be consistent with the independence axiom, also choose Option C in the second choice. The fact that most people choose Option A and Option D shows a <strong>preference reversal</strong> that contradicts the theory. <!-- /wp:paragraph --> <!-- wp:separator --> <hr class="wp-block-separator has-alpha-channel-opacity"/> <!-- /wp:separator --> <!-- wp:html --> <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-3196649779609103" crossorigin="anonymous"></script> <!-- Inside Content --> <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-3196649779609103" data-ad-slot="4855547878" data-ad-format="auto" data-full-width-responsive="true"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script> <!-- /wp:html --> <!-- wp:separator --> <hr class="wp-block-separator has-alpha-channel-opacity"/> <!-- /wp:separator --> <!-- wp:heading --> <h2 class="wp-block-heading"><strong>2. Ellsberg Paradox</strong></h2> <!-- /wp:heading --> <!-- wp:paragraph --> The <strong>Ellsberg paradox</strong> highlights <strong>ambiguity aversion</strong>, which is a preference for choices with <strong>known probabilities</strong> over choices with <strong>unknown or ambiguous probabilities</strong>.<sup></sup> This violates the subjective expected utility theory, which assumes people can assign a subjective probability to any event and make decisions based on that. <!-- /wp:paragraph --> <!-- wp:paragraph --> <strong>The Setup:</strong> You have an urn containing 90 balls. You know that 30 are <strong>red</strong>, and the remaining 60 are a mix of <strong>black</strong> and <strong>yellow</strong> in unknown proportions.<sup></sup> <!-- /wp:paragraph --> <!-- wp:list --> <ul class="wp-block-list; tabtab"><!-- wp:list-item --> <li><strong>Choice 1:</strong><!-- wp:list --> <ul class="wp-block-list"><!-- wp:list-item --> <li><strong>Option A:</strong> Bet that a red ball is drawn. (Known probability: 30/90 = 1/3)</li> <!-- /wp:list-item --> <!-- wp:list-item --> <li><strong>Option B:</strong> Bet that a black ball is drawn. (Ambiguous probability: between 0/90 and 60/90) Most people choose <strong>Option A</strong> because the probability is known.</li> <!-- /wp:list-item --></ul> <!-- /wp:list --></li> <!-- /wp:list-item --> <!-- wp:list-item --> <li><strong>Choice 2:</strong><!-- wp:list --> <ul class="wp-block-list"><!-- wp:list-item --> <li><strong>Option C:</strong> Bet that a red or yellow ball is drawn.</li> <!-- /wp:list-item --> <!-- wp:list-item --> <li><strong>Option D:</strong> Bet that a black or yellow ball is drawn. The probability of a black or yellow ball is exactly 60/90 (since there are 60 of them in total), while the probability of a red or yellow ball is ambiguous. Most people choose <strong>Option D</strong>.</li> <!-- /wp:list-item --></ul> <!-- /wp:list --></li> <!-- /wp:list-item --></ul> <!-- /wp:list --> <!-- wp:paragraph --> <strong>The Paradox:</strong> In the first choice, people prefer the known probability of a red ball over the ambiguous probability of a black ball.<sup></sup> However, in the second choice, people prefer the known probability of a black or yellow ball over the ambiguous probability of a red or yellow ball.<sup></sup> The choices demonstrate a general human aversion to situations where probabilities are unknown, even if the expected outcome might be the same.<sup></sup> <!-- /wp:paragraph --> <!-- wp:separator --> <hr class="wp-block-separator has-alpha-channel-opacity"/> <!-- /wp:separator --> <!-- wp:html --> <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-3196649779609103" crossorigin="anonymous"></script> <!-- Inside Content --> <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-3196649779609103" data-ad-slot="4855547878" data-ad-format="auto" data-full-width-responsive="true"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script> <!-- /wp:html --> <!-- wp:separator --> <hr class="wp-block-separator has-alpha-channel-opacity"/> <!-- /wp:separator --> <!-- wp:heading --> <h2 class="wp-block-heading"><strong>3. St. Petersburg Paradox</strong></h2> <!-- /wp:heading --> <!-- wp:paragraph --> The <strong>St. Petersburg paradox</strong> shows a disconnect between the <strong>mathematical expected value</strong> of a game and the amount a person would actually be willing to pay to play it.<sup></sup> The paradox challenges the idea that people make decisions by simply maximizing expected monetary value.<sup></sup> <!-- /wp:paragraph --> <!-- wp:paragraph --> <strong>The Setup:</strong> Imagine a game where a coin is flipped until it lands on heads. The payout is determined by the number of flips it takes. <!-- /wp:paragraph --> <!-- wp:list --> <ul class="wp-block-list; tabtab"><!-- wp:list-item --> <li>If heads is on the 1st flip, you win](https://www.SuperBusinessManager.com/wp-content/ql-cache/quicklatex.com-8480acb9832814cc22de64974288306a_l3.png)
2^2 = 2^3 = 2) + (1/4 * 8) + … EV = 1 + 100 feels more painful than the pleasure of gaining $100. This asymmetry in our response to gains and losses is a central pillar of the theory.
The Prospect Theory Value Function: Prospect theory is often visualized with a value function that is S-shaped. It’s steeper for losses than for gains, illustrating loss aversion. This function is also concave for gains (explaining risk aversion when dealing with gains) and convex for losses (explaining risk-seeking behavior when dealing with losses).
6. The Endowment Effect
The endowment effect is a bias where people place a disproportionately higher value on an item simply because they own it. This contradicts the Coase Theorem in economics, which suggests that in the absence of transaction costs, an item’s value should be independent of who owns it.
The Setup:
- Group 1 (Sellers): Given a coffee mug and asked the minimum price they would sell it for.
- Group 2 (Buyers): Not given a mug and asked the maximum price they would pay for it.
The Paradox: Studies consistently show that the sellers demand a much higher price for the mug than the buyers are willing to pay. The mere fact of owning the mug “endows” it with a higher perceived value. This is a direct consequence of loss aversion from prospect theory: the sellers see giving up the mug as a loss, which feels more significant than the buyers’ potential gain of acquiring it.
These concepts and biases, alongside the classic paradoxes, have profoundly influenced behavioral economics and finance.
They provide a more realistic and psychologically grounded understanding of how people make decisions, revealing that our choices are often shaped by cognitive shortcuts, emotions, and the way information is presented, rather than by pure, objective rationality.
Decision-making paradoxes are situations where an individual’s choices appear to be inconsistent or irrational when judged against the principles of classical economic theories, like expected utility theory.
These paradoxes highlight how human behavior often deviates from the predictions of traditional models, revealing the influence of cognitive biases and psychological factors.
Here are some of the most common paradoxes:
1. Allais Paradox
The Allais paradox demonstrates that people’s choices can violate the independence axiom of expected utility theory. This axiom suggests that if you add an identical outcome to two different lotteries, the preference between the two lotteries should not change. The paradox shows this isn’t always true, as people often place a disproportionately high value on a certain outcome, a phenomenon known as the certainty effect.
The Setup: Participants are presented with two pairs of choices.
- Choice 1:
- Option A: A 100% chance of winning
1 million, a 10% chance of winning 1 million and an 89% chance of winning nothing. - Option D: A 10% chance of winning
2^1 =![Rendered by QuickLaTeX.com 5 million and a 90% chance of winning nothing. Most people choose <strong>Option D</strong>, as the odds are similar for a much larger potential payout.</li> <!-- /wp:list-item --></ul> <!-- /wp:list --></li> <!-- /wp:list-item --></ul> <!-- /wp:list --> <!-- wp:paragraph --> <strong>The Paradox:</strong> When you calculate the expected utility for these choices, a person who chose Option A in the first choice should, to be consistent with the independence axiom, also choose Option C in the second choice. The fact that most people choose Option A and Option D shows a <strong>preference reversal</strong> that contradicts the theory. <!-- /wp:paragraph --> <!-- wp:separator --> <hr class="wp-block-separator has-alpha-channel-opacity"/> <!-- /wp:separator --> <!-- wp:html --> <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-3196649779609103" crossorigin="anonymous"></script> <!-- Inside Content --> <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-3196649779609103" data-ad-slot="4855547878" data-ad-format="auto" data-full-width-responsive="true"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script> <!-- /wp:html --> <!-- wp:separator --> <hr class="wp-block-separator has-alpha-channel-opacity"/> <!-- /wp:separator --> <!-- wp:heading --> <h2 class="wp-block-heading"><strong>2. Ellsberg Paradox</strong></h2> <!-- /wp:heading --> <!-- wp:paragraph --> The <strong>Ellsberg paradox</strong> highlights <strong>ambiguity aversion</strong>, which is a preference for choices with <strong>known probabilities</strong> over choices with <strong>unknown or ambiguous probabilities</strong>.<sup></sup> This violates the subjective expected utility theory, which assumes people can assign a subjective probability to any event and make decisions based on that. <!-- /wp:paragraph --> <!-- wp:paragraph --> <strong>The Setup:</strong> You have an urn containing 90 balls. You know that 30 are <strong>red</strong>, and the remaining 60 are a mix of <strong>black</strong> and <strong>yellow</strong> in unknown proportions.<sup></sup> <!-- /wp:paragraph --> <!-- wp:list --> <ul class="wp-block-list; tabtab"><!-- wp:list-item --> <li><strong>Choice 1:</strong><!-- wp:list --> <ul class="wp-block-list"><!-- wp:list-item --> <li><strong>Option A:</strong> Bet that a red ball is drawn. (Known probability: 30/90 = 1/3)</li> <!-- /wp:list-item --> <!-- wp:list-item --> <li><strong>Option B:</strong> Bet that a black ball is drawn. (Ambiguous probability: between 0/90 and 60/90) Most people choose <strong>Option A</strong> because the probability is known.</li> <!-- /wp:list-item --></ul> <!-- /wp:list --></li> <!-- /wp:list-item --> <!-- wp:list-item --> <li><strong>Choice 2:</strong><!-- wp:list --> <ul class="wp-block-list"><!-- wp:list-item --> <li><strong>Option C:</strong> Bet that a red or yellow ball is drawn.</li> <!-- /wp:list-item --> <!-- wp:list-item --> <li><strong>Option D:</strong> Bet that a black or yellow ball is drawn. The probability of a black or yellow ball is exactly 60/90 (since there are 60 of them in total), while the probability of a red or yellow ball is ambiguous. Most people choose <strong>Option D</strong>.</li> <!-- /wp:list-item --></ul> <!-- /wp:list --></li> <!-- /wp:list-item --></ul> <!-- /wp:list --> <!-- wp:paragraph --> <strong>The Paradox:</strong> In the first choice, people prefer the known probability of a red ball over the ambiguous probability of a black ball.<sup></sup> However, in the second choice, people prefer the known probability of a black or yellow ball over the ambiguous probability of a red or yellow ball.<sup></sup> The choices demonstrate a general human aversion to situations where probabilities are unknown, even if the expected outcome might be the same.<sup></sup> <!-- /wp:paragraph --> <!-- wp:separator --> <hr class="wp-block-separator has-alpha-channel-opacity"/> <!-- /wp:separator --> <!-- wp:html --> <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-3196649779609103" crossorigin="anonymous"></script> <!-- Inside Content --> <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-3196649779609103" data-ad-slot="4855547878" data-ad-format="auto" data-full-width-responsive="true"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script> <!-- /wp:html --> <!-- wp:separator --> <hr class="wp-block-separator has-alpha-channel-opacity"/> <!-- /wp:separator --> <!-- wp:heading --> <h2 class="wp-block-heading"><strong>3. St. Petersburg Paradox</strong></h2> <!-- /wp:heading --> <!-- wp:paragraph --> The <strong>St. Petersburg paradox</strong> shows a disconnect between the <strong>mathematical expected value</strong> of a game and the amount a person would actually be willing to pay to play it.<sup></sup> The paradox challenges the idea that people make decisions by simply maximizing expected monetary value.<sup></sup> <!-- /wp:paragraph --> <!-- wp:paragraph --> <strong>The Setup:</strong> Imagine a game where a coin is flipped until it lands on heads. The payout is determined by the number of flips it takes. <!-- /wp:paragraph --> <!-- wp:list --> <ul class="wp-block-list; tabtab"><!-- wp:list-item --> <li>If heads is on the 1st flip, you win](https://www.SuperBusinessManager.com/wp-content/ql-cache/quicklatex.com-8480acb9832814cc22de64974288306a_l3.png)
2^2 = 2^3 = 2) + (1/4 * 8) + … EV = 1 + 100 feels more painful than the pleasure of gaining $100. This asymmetry in our response to gains and losses is a central pillar of the theory.
The Prospect Theory Value Function: Prospect theory is often visualized with a value function that is S-shaped. It’s steeper for losses than for gains, illustrating loss aversion. This function is also concave for gains (explaining risk aversion when dealing with gains) and convex for losses (explaining risk-seeking behavior when dealing with losses).
6. The Endowment Effect
The endowment effect is a bias where people place a disproportionately higher value on an item simply because they own it. This contradicts the Coase Theorem in economics, which suggests that in the absence of transaction costs, an item’s value should be independent of who owns it.
The Setup:
- Group 1 (Sellers): Given a coffee mug and asked the minimum price they would sell it for.
- Group 2 (Buyers): Not given a mug and asked the maximum price they would pay for it.
The Paradox: Studies consistently show that the sellers demand a much higher price for the mug than the buyers are willing to pay. The mere fact of owning the mug “endows” it with a higher perceived value. This is a direct consequence of loss aversion from prospect theory: the sellers see giving up the mug as a loss, which feels more significant than the buyers’ potential gain of acquiring it.
These concepts and biases, alongside the classic paradoxes, have profoundly influenced behavioral economics and finance.
They provide a more realistic and psychologically grounded understanding of how people make decisions, revealing that our choices are often shaped by cognitive shortcuts, emotions, and the way information is presented, rather than by pure, objective rationality.
- Option A: A 100% chance of winning
- Option A: A 100% chance of winning