Consider a simple situation when two kids fight each other over a cookie. Let's assume that there is only one cookie. How do we divide the cookie so that both kids will be satisfied? This is not such an easy assignment. Now, let's consider a similar situation between adults. For example, assets acquired during the marriage must be divided fairly between spouses during divorce proceedings. This is also not such a simple assignment. Some will define it as a hard-to-do assignment. But, in some cases, science can help with relatively simple and straightforward roles. The rules are based on a well-known Cake-Cutting algorithm that is a part of the fair division concept.
Fair division is a concept in mathematics and economics that allocates goods or resources among individuals so that each person perceives their share as equitable or fair. This could involve dividing a cake, sharing property, assigning tasks, or distributing any other divisible item among multiple parties.
The history of the fair division concept goes back to the
1940s when Polish mathematician Hugo Steinhaus was considered the first to
study the “cake-cutting procedure.” Since then, many studies have taken place
in the field of fair division. The
formal research of fair division gained momentum in the 20th century with the
emergence of game theory. The fair division became a central topic in
cooperative game theory, where researchers developed algorithms and solution
concepts for dividing resources among multiple parties.
Let’s go straight to the topic.
How can we apply this Cake-Cutting algorithm in real–life
situations?
Simple. Consider dividing one small cake between two people.
One person cuts the cake into two portions, and the other chooses which
portion they want. This ensures fairness in the eyes of both parties.
This simple approach was mentioned in the Bible when Abraham and Lot divided the land of Cannan.
The next question is how to implement it in real-life
situations. Here are two examples that will help with that.
Imagine two siblings, Alex and Sam, inheriting a collection
of valuable vintage comics from their grandparents. Both siblings are
interested in comics but have different preferences and values for each item in
the collection.
To divide the collection fairly, Alex and Sam can use the "divide and choose" method:
- Dividing:
One sibling (Alex) divides the collection into two portions they believe
to be of equal value. Alex carefully divides the comics, trying to make
each portion as equal as possible, considering factors like rarity,
condition, and personal preference.
- Choosing:
Sam, the other sibling, gets to choose which portion they want. Sam
carefully examines both portions, assessing each comic's value and
considering their preferences. After careful consideration, Sam decides
the portion they believe to be more valuable or desirable.
This method ensures fairness because the sibling dividing
the collection is incentivized to make the portions as equal as possible to prevent
the other sibling from choosing the more valuable portion. Meanwhile, the other
sibling can choose the portion they perceive to be more valuable, thereby
ensuring both parties are satisfied with the outcome.
Another example:
Let's say two friends, Sarah and John, are planning a weekend road trip together.
They must decide how to divide the driving responsibilities fairly since they'll share one car.
- Dividing:
Sarah suggests splitting the driving equally, with each person driving for
half of the journey. However, John is concerned about driving through
heavy traffic in a city they'll be passing through. To make the division
fair, Sarah proposes dividing the driving based on time rather than distance.
She suggests that they break the trip into two equal time segments, each
driving for one segment.
- Choosing:
John agrees to Sarah's proposal. To determine who drives first, they flip
a coin. Sarah wins the coin toss and gets to choose whether she wants to
drive the first or second segment. After considering factors like traffic
patterns and rest stops, Sarah drives the first segment.
This method ensures fairness because Sarah, as the person
dividing the driving time, is incentivized to create two segments of equal
duration. Meanwhile, John, as the person choosing which segment to drive, can
select the segment that best fits his preferences and concerns. They can reach
a fair agreement that satisfies both parties by dividing and choosing.
Below is a more practical and sophisticated example that requires additional knowledge of the Cutting Cake algorithm.
Let's consider a hypothetical divorce settlement scenario between Alice and Bob, a married couple who are separating and need to divide their assets fairly. We'll use a little bit more sophisticated cake-cutting algorithm than described above to help them reach a fair distribution of their shared resources.
Here's how the process might unfold:
- Inventory
of Assets:
- Alice
and Bob create an inventory of all their shared assets, including
property, savings, investments, vehicles, household items, and other
valuable possessions.
- Preferences
and Priorities:
- Each
of them lists their preferences and priorities regarding the division of
assets. For example, Alice might prioritize keeping the family home for
stability for their children, while Bob might prioritize retaining
investments for long-term financial security.
- Fair
Division:
- They
agree to use a cake-cutting algorithm to divide their assets fairly.
- Ranking
of Assets:
- Alice
and Bob individually rank the assets in the inventory based on their
preferences and perceived value. They may assign numerical values or
rankings to each asset, indicating their relative importance.
- Algorithm
Execution:
- They
input their rankings into the cake-cutting algorithm, which processes the
data to determine a fair division of assets that minimizes envy between
them. The algorithm aims to allocate assets to maximize the overall
satisfaction of both parties.
- Negotiation
and Adjustments:
- After
the algorithm generates a proposed division of assets, Alice and Bob
review the results and negotiate any necessary adjustments or
modifications. They may discuss trade-offs, compromises, or additional
considerations to ensure the division meets their needs and preferences.
- Final
Agreement:
- Once
they reach a consensus on the division of assets, Alice and Bob formalize
their agreement in a legally binding document, such as a divorce
settlement agreement. The document outlines the distribution of assets,
liabilities, and any other relevant terms or provisions related to their
separation.
- Legal
Approval:
- They
may seek legal advice to review the settlement agreement and ensure its
compliance with applicable laws and regulations. Once approved, they
finalize the divorce proceedings, and the agreed-upon division of assets
takes effect.
By using a cake-cutting algorithm in their divorce
settlement process, Alice and Bob can achieve a fair and equitable distribution
of their shared assets, minimizing conflicts and promoting a smoother
transition to their new lives post-divorce. The algorithm helps them objectively navigate the complexities of asset division, considering their preferences and priorities.
If you want to widen your understanding of the field, link
to one of the recommended books.
The pictures in this post were taken from Unsplash.
