# Questions tagged [fair-division]

For various problems related to dividing a resource among several parties.

12
questions

**29**

votes

**5**answers

898 views

### Fair cutting of the plane with lines

An infinite countable family $\cal{L}$ of lines in the plane $\mathbb{R}^2$ forms a fair cutting of the plane if the following conditions are satisfied:
$\bullet$ No circle intersects infinitely many ...

**34**

votes

**4**answers

1k views

### Dividing a cake between $n-1$, $n$, or $n+1$ guests

A housewife is waiting for guests and has prepared a cake. She doesn't know how many guests will come, but it will be $n-1$, $n$, or $n+1$.
What is the minimal number $f(n)$ of pieces the cake ...

**19**

votes

**3**answers

1k views

### What is the fairest order for stage-striking (and is it the Thue-Morse sequence)?

Here's a fair-sequencing problem that doesn't quite match the usual fair-division problems. I think that, like those, the answer should also be the Thue-Morse sequence ("balanced alternation"), ...

**1**

vote

**0**answers

34 views

### rank-choice shared-resource fair-division

I'm looking for an algorithm or a paper that solves a problem with a particular set of properties.
Imagine you have some number of rooms and some greater number of people. Each person should be ...

**3**

votes

**1**answer

223 views

### Is there a moving knife procedure for envy-free cake cutting with connected pieces?

In the wikipedia page on envy-free cake cutting, continuous "moving knife" algorithms for envy free cake cutting to connected pieces is only mentioned for up to 4 players. As the wikipedia article ...

**4**

votes

**2**answers

331 views

### How many cuts are required for a weighted-proportional cake-cutting?

In proportional cake-cutting, there are $n$ agents with equal entitlements to a "cake" (an interval). Each agent $i$ has a nonatomic value measure $V_i$ over the cake, and it is required to create a ...

**7**

votes

**0**answers

158 views

### Cutting a piece of cake that $n$ people value as exactly $w$

Stromquist and Woodall (1985) study the problem of Sets on which several measures agree. There are $n$ non-atomic value measures on the unit circle, and a parameter $w\in(0,1)$. The goal is to find a ...

**15**

votes

**4**answers

731 views

### Fair cake-cutting between groups

The cake-cutting game is usually played between individuals. What if we try to play it between groups?
A certain land has to be divided between two states. There are $n$ citizens in each state. ...

**13**

votes

**1**answer

806 views

### Stromquist's 3 knives procedure

(copied from math.SE)
BACKGROUND: A cake has to be divided among 3 people with possibly different tastes, such that each person receives a single connected piece, and no person prefers another person'...

**4**

votes

**2**answers

8k views

### Seeking a solution algorithm to the 3-partition problem

I need to divide 48 pieces of jewelry between 3 inheritors so as to give equal, or nearly equal value, to each. I have learned that this is called the 3-partition problem. I solved it for 9 pieces of ...

**21**

votes

**4**answers

1k views

### Fairest way to choose gifts

Suppose that a parent brings home from a trip $2n$ gifts of roughly
equal value for his/her two children. The children get to choose one
at a time which gifts they want. What is the fairest way to do ...

**1**

vote

**2**answers

285 views

### Mediated envy-free and efficient cake cutting with n=2?

Is there an algorithm in literature to compute an efficient (pareto optimal) and envy-free cake cutting when there are only $n=2$ players and a mediator?