Matchmaking Systems

Matchmaking systems recommend pairs where both sides matter: dating, hiring, mentoring, marketplaces, or team formation. Unlike one-sided ranking, a high score from side A to side B is insufficient if side B would reject or be overloaded.

Reciprocal scoring

A simple reciprocal score combines directional preferences:

$$s(a,b)=\sqrt{s_{A\to B}(a,b)s_{B\to A}(b,a)}.$$

The geometric mean penalizes one-sided interest. A serving system still uses candidate generation, eligibility rules, and list-quality controls such as diversity.

Worked example

Suppose two people on side A are being matched to three people on side B. Directional scores alone would overvalue one-sided interest, so the reciprocal score uses the geometric mean:

Pair	$s_{A\to B}$	$s_{B\to A}$	$\sqrt{s_{A\to B}{s}_{B\to A}}$	Interpretation
A0-B0	0.90	0.70	0.794	Strong mutual match.
A0-B1	0.40	0.60	0.490	Moderate from both sides.
A0-B2	0.20	0.20	0.200	Weak from both sides.
A1-B0	0.30	0.50	0.387	One side is not very interested.
A1-B1	0.80	0.90	0.849	Best reciprocal match.
A1-B2	0.60	0.80	0.693	Good but not top.

Pair A1-B1 wins because both sides score each other highly. A one-sided recommender might over-contact the same popular candidate and create a feedback loop.

Caveats

Capacity constraints, fairness, safety, and strategic behavior are central. Optimizing total matches can overload high-demand participants or reduce diversity. Online experiments need marketplace-level metrics because one user’s recommendation can remove an opportunity from another user.

References

• Adomavicius and Tuzhilin, 2005, Toward the Next Generation of Recommender Systems
• Li et al., 2010, A Contextual-Bandit Approach to Personalized News Article Recommendation

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