Recommender Popularity Bias: The Rich-Get-Richer Feedback Loop

Feedback Loop Controls

Popularity bias α 1.5

Exploration rate ε 0.10

Recommendation list size K 5

Simulation speed (rounds/s) 10

Catalogue Exposure

Gini coefficient

0.000

Top-10% share

10.0%

Long tail (never recommended)

0.0%

Rounds simulated

How it works

72 catalogue items each start with one unit of exposure (a small seed rating so no item has zero probability). Every round the recommender fills a list of K slots by drawing items with probability:

P(i) = (1-ε) · (c_i+1)^α / Σ_j (c_j+1)^α  +  ε · (1/N)

where c_i is item i's exposure count so far, α is how strongly the algorithm favours already-popular items (pure collaborative-filtering popularity ranking), and ε is the fraction of picks replaced by a uniform random exploration slot. Whichever items get picked have their exposure count incremented, which is fed straight back into next round's probabilities — the same closed loop a live recommender runs on real click/watch/purchase data.

At α = 0 every item is equally likely regardless of history (no bias). As α grows past ~1, small early leads compound: popular items get recommended more, which makes them more popular, which gets them recommended even more — the "Matthew effect" or rich-get-richer dynamic documented in real collaborative-filtering and engagement-ranking systems. Raising ε injects deliberate diversity/cold-start exploration that slows the collapse.

Bar height and colour encode each item's current exposure (log-scaled so early differences stay visible). Three summary statistics track catalogue-wide concentration:

Gini coefficient — 0 means every item has identical exposure, 1 means one item has captured everything.
Top-10% share — the fraction of all exposure held by the most-exposed 10% of items; 10% is the "no concentration" baseline.
Long tail — the percentage of items still sitting at their starting seed, i.e. never once recommended.

Low exposure High exposure

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.