Understanding the Stable Marriage Problem

What makes the stable marriage problem unique compared to traditional mathematics?

• It is based on geometry.

• It involves complex calculations.

• It uses no numbers or calculations.

• It requires advanced algebra.

What is the main goal in arranging marriages in the stable marriage problem?

• To achieve stability by avoiding mutual preferences for others.

• To minimize the number of rejections.

• To maximize the number of marriages.

• To ensure everyone is happy with their partner.

What is the key question addressed in the stable marriage problem?

• Can we always find a stable marriage arrangement?

• How to calculate the number of possible marriages?

• What is the best way to make everyone happy?

• How to minimize the number of proposals?

Who developed the algorithm that solves the stable marriage problem?

• Alan Turing and John von Neumann

• Pythagoras and Euclid

• David Gale and Lloyd Shapley

• Albert Einstein and Isaac Newton

In the Gale-Shapley algorithm, what happens on the first day?

• Everyone gets married immediately.

• All proposals are rejected.

• Women propose to their top choice.

• Men propose to women.

What is the role of men in the Gale-Shapley algorithm?

• To propose to women.

• To reject all proposals.

• To accept the first proposal they receive.

• To reject all but their top suitor.

What happens if a woman is rejected in the Gale-Shapley algorithm?

• She is automatically engaged.

• She leaves the process.

• She waits for another proposal.

• She proposes to her next choice.

What is the outcome when the Gale-Shapley algorithm terminates?

• All engagements are stable.

• Some participants remain unengaged.

• All participants are unhappy.

• The process restarts.

In the example provided, who does Charlotte end up engaged to?

• Wickham

• Collins

• Darcy

• Bingley

What is demonstrated through the example with Charlotte, Elizabeth, Jane, and Lydia?

• The algorithm is too complex to understand.

• The process is random.

• The algorithm is flawed.

• The algorithm leads to stable engagements.