Talk:Gale–Shapley algorithm/GA1

GA Review
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Reviewer: Femke (talk · contribs) 20:27, 13 January 2024 (UTC)

I remember reviewing an article from you a couple years back where I gave a single suggestion for improvement. I think this article again shows how science communication is done. I've read the article twice, and have only four comments:


 * Optional: the gif is not as clear as could be. I think it's better to have the preferences on top, have the solution highlighted in the same way for proposers/acceptors, and to use a larger font size for the text top right.
 * "If an applicant X and an employer Y could form an unstable pair, Y would have made an offer to their preferred match X, before making another offer to their actual match. But X would have accepted this offer and kept it in preference to the offer they ended up with. Therefore, no such pair is possible.[9]" - this is difficult to understand. It's a confusing that we start by contemplating an unstable pair (X is not the preferred match), and then call some other preferred match X too. Could you reword?
 * optional: The method is complicated by side constraints that make the problem it solves not exactly the stable matching problem.-- the word side reads off to me. Is extra constraints better wording?
 * "A stable matching instance can have multiple stable matchings." I read this initially as " a stable matching solution can have multiple solutions". Can we have a different word for instance? Such as problem? Or problem instance?

Will do a spot check later. —Femke 🐦 (talk) 20:27, 13 January 2024 (UTC)


 * I spot checked 6 statements using 3 sources. No problems found. —Femke 🐦 (talk) 20:42, 13 January 2024 (UTC)
 * Re the animation: Unfortunately I'm not really set up to create or modify animated gifs.
 * Re "side constraints": changed "side" to "additional".
 * Re "It's a confusing that we start by contemplating an unstable pair (X is not the preferred match), and then call some other preferred match X too." (in the matches are stable part of the correctness argument): no, it really is the same X both times. But I rewrote this to avoid the appearance of proof by contradiction: now we show that each pair is not unstable, rather than assuming an unstable pair and showing that its existence contradicts the outcome of the algorithm. I hope this is less confusing.
 * Re "A stable matching instance": "instance" is the correct technical word here for a specific input to a general computational problem, but I suppose that being technical and using jargon is not really the point. Reworded to "There may be many stable matchings for the same system of preferences."
 * —David Eppstein (talk) 02:32, 14 January 2024 (UTC)
 * Brilliant, thanks. The new wording for the unstable matching is clearer, but the first sentence is still a bit confusing. The following sounds better to my ears: There cannot be an applicant X and employer Y who prefer each other over their final match. The "unmatched pair" makes it sound like we're in the middle of the algorithm where they haven't been matched yet. —Femke 🐦 (talk) 10:02, 14 January 2024 (UTC)
 * Reworded. —David Eppstein (talk) 18:23, 14 January 2024 (UTC)