Source Clarifications

Source: User-Item Fairness Tradeoffs in Recommendations.

Theorem 4: population masses and positive tolerance (Section 5, p. 7; Appendix E, p. 39)

• Cold-start mass 1-beta → 1-2 beta, alongside two known-type masses of beta each. The corrected masses sum to one and match Appendix E’s item equation. Theorem 4 retains 1/n < beta < 1/2, where n is the number of items.

Appendix E Lemma 15: center display (Appendix E, p. 38)

• The center formula omitting one mirrored known type → lambda=1/(1+L_t), where lambda is the common normalized item utility and L_t the center pivot’s utility-ratio sum. The center-equation note gives the equation and a numerical witness.