A Tale of Two Friends, Two Loves, and Two Economic Perspectives

A love story that helps you demystify Preference-based and Choice-based approaches in Mircoeconomics

A Tale of Two Friends, Two Loves

In the sun-kissed coastal town of Portobello, two young souls, Dante and Emilia, grew up as inseparable companions. Their bond, forged in childhood, blossomed into a love story as timeless as the sea itself. Dante, the son of the town's revered leader, Aldo, and Emilia, the spirited daughter of Antonio, shared a deep connection that transcended the ordinary.

Their love story unfolded in simple yet meaningful moments. After school, Dante would surprise Emilia with her favorite treats, their weekend walks along the beach becoming a cherished ritual. As time painted their days with shared laughter and whispered secrets, Emilia's preferences became Dante's sacred knowledge. "Chocolate is my absolute favorite," she had declared one summer day, when Dante presented her with Mint and Vanilla ice cream. Her nose wrinkled playfully as she added, "I'll take the Vanilla, but Mint? Only if Uncle Bello's shop runs completely dry!" Their love grew in these small moments of understanding, like when Emilia saved for weeks to buy Dante his treasured soccer shirt.

As their relationship deepened, Dante became an expert in Emilia's tastes. He could navigate her preferences blindfolded – from her precise coffee order (latte with oat milk, never regular) to her cooking essentials (Bertolli oil, not De Cecco). The rare occasions when her beloved Molisana pasta was unavailable, forcing him to substitute with Rummo, would earn him a fleeting pout that he found endearing.

Their world expanded when Vincenzo, a tough newcomer to Portobello, entered their lives. What began as brotherhood between Dante and Vincenzo in street scuffles evolved into a warm friendship among the three. Vincenzo observed their dynamics with keen interest, noting Emilia's chocolate ice cream preference, her favorite pasta Rummo, and her best drink Latte, though his conclusions about her pasta choices were based on limited observations.

But fate had other plans. War erupted like a thunderstorm on a clear day, conscripting both young men into its merciless machine. The news of Dante's disappearance in battle struck like lightning, shattering Emilia's world into countless pieces. Years passed, marked by grief and silent prayers, until peace finally returned – bringing home Vincenzo, but not Dante.

In their shared loss, Emilia and Vincenzo found solace in each other's company. As their relationship evolved, Vincenzo discovered new layers to Emilia's preferences. He learned that her love for vanilla ice cream emerged when chocolate wasn't available, and that Rummo pasta was merely a compromise when Molisana couldn't be found. Through patient observation and countless shared moments, Vincenzo came to understand Emilia's heart as completely as Dante once had, though his path to this understanding followed a different star.

Two Economic Perspectives

Preference-Based Approach (represented by Dante):

1. Preference-based approach tries to understand decision-making process inside out via a direct knowledge of preferences (as Emilia tells Dante her preference).

2. Assumes individuals (Emilia) have clear, consistent, and complete preferences: she behaves consistently without contradiction in her choice of ice scream (Chocolate > Vanilla > Mint).

3. Assumption of "clear, consistent, and complete preferences" is quite strong and might not always hold in reality. Not every Dante has a childhood friend Emilia who share her preference to him directly and completely.

4. Focuses on understanding the underlying rationale and order of preferences.

5. Can predict choices across different scenarios once preferences are known (latte with oat milk).

6. Example: Dante knew Emilia would choose Vanilla over Mint because he understood her preference ordering (Chocolate > Vanilla > Mint).

Choice-Based Approach (represented by Vincenzo):

1. Choice-based approach tries to understand decision-making process outside in by observing the individual across revealed preference.

2. Builds understanding through observing actual choices in different situations.

3. Initially may lead to incomplete or incorrect conclusions (like assuming Rummo was preferred).

4. Requires observing choices under various conditions to understand true preferences.

5. More empirical and based on revealed preferences through actions.

6. Example: Vincenzo learned about Emilia's ice cream preferences by observing her choices under different availability conditions.

Relationship between the approaches:

1. The equivalence between preference-based and choice-based approaches holds under specific conditions:

   1. Complete observation: The choice function must be observed over all possible budget sets (B contains all subsets of X)

   2. WARP satisfaction: If Molisana is chosen when both Molisana and Rummo are available, then Rummo cannot be chosen in any other situation where Molisana is also available

   In the story's context: Only when Vincenzo observes Emilia's pasta choices across all possible combinations ({Rummo}, {Molisana}, {Rummo, Molisana}), AND her choices satisfy WARP, can his choice-based understanding match Dante's preference-based knowledge.

2. Choice-based approach may require more time and observations to reach the same conclusions.

3. Preference-based knowledge can predict choices more accurately in new situations (or so-called new budget set B).

4. Known Prefrence Relation implies Weak Axiom: Emilia would choose Vanilla ice scream only if Chocolate is unavailable. When both flavours present, she will choose Chocolate.

5. Choice-based approach might be more practical when direct preference information isn't available.

6. Both approaches complement each other: preferences inform choices, and choices reveal preferences.