A recommender whose items get tired: expert matching fused by rank, not by score

The opinion in this design lives in the arithmetic of k=60. On a single list, the distance between first and second place is about 0.00026 ^[6]. Turning up fiftieth on a *second* retriever's list adds roughly 0.0091 to the same expert, about 34 times as much ^[2]. The fusion therefore prices agreement between independent views far above position within any one of them, and agreement is a thing you can show a member, which is what the write-up says a push surface owes them ^[3].

The weight table says it again. Seven components sum to exactly 1.00 ^[1], and the heaviest is the one the author labels explicit and directional ^[7]: the term that turns into a sentence you can defend out loud, of the kind the post demands, one ladder level ahead of you in systems design ^[3]. The profile-embedding cosine that a content recommender would lead with sits below it, at 0.20 ^[7].

Then the part that decides whether the expert pool grows. An untested expert is handed 0.5 on quality rather than 0 ^[8]. Run the published formula on someone with five completed sessions, a 4.0 rating and the default 0.6 acceptance and you get 0.681 ^[3]; at a weight of 0.12, that whole record is worth 0.022 of the final score ^[3]. A flawless record tops out at 0.06 above the untested prior ^[4]. Against that, ten prior recommendations already cost 0.018 through the log-damped exposure term ^[5], so being recommended ten times cancels most of what five completed sessions buys you ^[5]. Both curves bend the same way on purpose: the author's stated reason for exponential saturation on experience is that 0 versus 5 sessions is a real difference and 40 versus 45 is noise, and a linear term would have put veterans out of reach ^[10], while a linear exposure penalty would have made a good expert unrecommendable after a handful of cycles ^[12].

None of those gradations matter as much as whether the person has room. Capacity is scored at 0.15 and is also a hard gate ^[7], and then it binds again when scored pairs are allocated globally, greedy in descending order, each pair spending one unit of its expert's budget ^[14]. One constraint, enforced once softly and once absolutely.

Two things the excerpt does not settle. The fairness term is written as a factor returning exactly 1.0 at zero exposures ^[12] but listed as a 0.03 weight ^[7], and the code that combines the components is not shown, so whether it scales the score or is added to it stays open. The allocate() listing is also cut off mid-loop, with per_requester in the signature and no visible use in the shown lines ^[15]. A smaller wrinkle: the fusion loop indexes ranks from zero, so the top item actually contributes 1/60, not the 1/61 the prose computes ^[6]. It changes no ordering, which is presumably why nobody caught it.