What Does Fair Mean In This Calculator?

Fair means approximately envy-free under the recorded choices: the method searches for prices where different roommates prefer different rooms. The displayed tolerance is important because the interactive Sperner procedure approaches an exact result through finer approximations rather than claiming arbitrary preferences can be solved exactly in a fixed number of questions.

Why Do Some Trial Prices Jump So Far?

After checking the equal split, the constructive search may deliberately test broad boundary prices, including a free room or temporary credit. Those screens are preference comparisons, not proposed rent. The calculator records the roommate's actual choice instead of guessing which free room they prefer, then narrows the range as the search continues.

How Many Roommates Can Use It?

The session supports two through eight roommates with the same number of rooms. More roommates create a higher-dimensional search and can require more choices before the tolerance becomes narrow.

Do The Final Prices Add Up To The Exact Rent?

Yes. Displayed prices are allocated in whole cents and any rounding remainder is assigned deterministically so the final total matches the rent exactly. The fairness conclusion remains approximate to the tolerance shown.

Does This Create A Lease Agreement?

No. The export is a nonbinding planning summary. Everyone should review the final room, price and affordability before changing a lease or payment arrangement.

Fair Rent Split Calculator

Divide a fixed total rent among unequal rooms so every roommate prefers their assigned room at its price.

1Set Up
2Room Choices
3Agreement

Guided Roommate Session

Set Up The Apartment

Gather everyone before you begin. Each person will answer a series of room choices at different trial prices until the method finds an approximate envy-free split.

Equal Split Comes FirstThe session checks equal room prices automatically. If everyone chooses a different room, that split becomes the result immediately.

Session Basics

The number of roommates must match the number of rooms.

Total Monthly Rent$

Roommates And Rooms

Name The Roommates

Use names everyone can recognize during the choice rounds.

Roommate ARoommate BRoommate C

Describe The Rooms

A short detail such as “Private Bath” or “Street View” keeps each choice clear.

01Room NameShort Description

02Room NameShort Description

03Room NameShort Description

Method And Assumptions

How The Session Works

The session first checks whether equal room prices already produce different choices. If they do not, the total rent stays fixed while the tool tests other combinations. Early comparisons can be intentionally broad and may include a temporary credit; they are not proposals.

Required Assumptions

Everyone must find at least one room acceptable at every trial, answer consistently, and not choose the most expensive room when another room is free or carries a trial credit. Preferences should change continuously as prices change. Ties may be broken either way.

Mathematical Basis

Based on Francis Su’s rental-harmony construction using Sperner’s lemma and the Fair Division Calculator developed with Elisha Peterson and Patrick Vinograd.

Read The Original Paper Visit The Harvey Mudd Project

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What Is the Fair Rent Split Calculator?

The Fair Rent Split Calculator is a guided roommate decision session for assigning unequal bedrooms and dividing one fixed monthly rent. It implements the interactive rental-harmony approach developed from Francis Su's constructive use of Sperner's lemma: the tool asks one roommate at a time which room they would choose at a proposed set of prices, then follows those choices toward an approximate envy-free split. In that result, each roommate is assigned a different room they preferred at a nearby tested price combination.

How It Works

Gather every roommate, enter the total rent, and give each person and room a clear name. The session first asks everyone at the equal split and immediately returns that exact result when different roommates choose different rooms. If choices conflict, answer every later trial truthfully; the calculator never chooses among free rooms on anyone's behalf. Early trial prices can be deliberately broad or include a temporary credit because they measure preference boundaries rather than propose actual rent. When a proposal appears, review its stated dollar tolerance, accept it, or continue refining before downloading the agreement summary.

When to Use It

Use it when the number of roommates matches the number of bedrooms and the rooms differ in size, privacy, light, storage, bathroom access or other qualities people value differently. It is especially useful when an equal split or a square-footage formula cannot capture each roommate's personal tradeoffs. Everyone should be present, able to afford at least one room throughout the session and willing to make consistent choices.

Frequently Asked Questions

What Does Fair Mean In This Calculator?: Fair means approximately envy-free under the recorded choices: the method searches for prices where different roommates prefer different rooms. The displayed tolerance is important because the interactive Sperner procedure approaches an exact result through finer approximations rather than claiming arbitrary preferences can be solved exactly in a fixed number of questions.
Why Do Some Trial Prices Jump So Far?: After checking the equal split, the constructive search may deliberately test broad boundary prices, including a free room or temporary credit. Those screens are preference comparisons, not proposed rent. The calculator records the roommate's actual choice instead of guessing which free room they prefer, then narrows the range as the search continues.
How Many Roommates Can Use It?: The session supports two through eight roommates with the same number of rooms. More roommates create a higher-dimensional search and can require more choices before the tolerance becomes narrow.
Do The Final Prices Add Up To The Exact Rent?: Yes. Displayed prices are allocated in whole cents and any rounding remainder is assigned deterministically so the final total matches the rent exactly. The fairness conclusion remains approximate to the tolerance shown.
What Assumptions Does Rental Harmony Require?: Every roommate must find at least one room acceptable at every trial, answer consistently as prices change, and avoid choosing the most expensive room when another room is free or carries a trial credit. Preferences must also behave continuously as prices change. If those conditions fail, the mathematical guarantee does not apply.
Does This Create A Lease Agreement?: No. The export is a nonbinding planning summary. Everyone should review the final room, price and affordability before changing a lease or payment arrangement.

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