User-item fairness tradeoffs in recommendations

TL;DR

A model of recommendations with user and item fairness objectives and the solutions of fairness-constrained optimization are developed, identifying two phenomena: when user preferences are diverse, there is"free"item and user fairness; and users whose preferences are misestimated can be especially disadvantaged by item fairness constraints.

Abstract

In the basic recommendation paradigm, the most (predicted) relevant item is recommended to each user. This may result in some items receiving lower exposure than they "should"; to counter this, several algorithmic approaches have been developed to ensure item fairness. These approaches necessarily degrade recommendations for some users to improve outcomes for items, leading to user fairness concerns. In turn, a recent line of work has focused on developing algorithms for multi-sided fairness, to jointly optimize user fairness, item fairness, and overall recommendation quality. This induces the question: what is the tradeoff between these objectives, and what are the characteristics of (multi-objective) optimal solutions? Theoretically, we develop a model of recommendations with user and item fairness objectives and characterize the solutions of fairness-constrained optimization. We identify two phenomena: (a) when user preferences are diverse, there is "free" item and user fairness; and (b) users whose preferences are misestimated can be especially disadvantaged by item fairness constraints. Empirically, we prototype a recommendation system for preprints on arXiv and implement our framework, measuring the phenomena in practice and showing how these phenomena inform the design of markets with recommendation systems-intermediated matching.

Figures (11)

• Figure 1: Empirical (using our arXiv recommender) tradeoff between the minimum user (Y axis) and item (X axis) utility. Recall $\gamma$ is the fraction of the best possible minimum normalized item utility $I_{\min{}}^*$ guaranteed. (a) Illustrating \ref{['thm:pofdecreasing']} empirically -- homogeneous populations have a higher price of fairness. Empirically, however, the price of fairness is small except with strict item fairness constraints $\gamma \to 1$. (b) For a set of users, holding other users fixed, the cost to the worst-off user of misestimating preferences, at varying $\gamma$. Empirically, the cost of misestimation is already so high that it is not worsened with item fairness constraints, as in the worst case analysis of \ref{['thm:misestimation']}.
• Figure 2: We repeat the experiment of Figure \ref{['fig:empiricaltradeoffs']} from the original paper but replace max-min fairness with Nash welfare fairness. That is, in the objective we replace $U_{\min{}}$ with the user Nash welfare $U_{\textnormal{NW}}$. We must be more careful with the item fairness constraint: we know that the normalized utilities satisfy $0 \leq U_i, I_j \leq 1$, so $U_{\textnormal{NW}}, I_{\textnormal{NW}} < 0$. This means that in Problem \ref{['eqn:originalconcaveproblem']} we must replace the item fairness constraint $I_{\min{}}(\rho) \geq \gamma I_{\min{}}^*$ with the constraint $I_{\textnormal{NW}}(\rho) \geq (1/\gamma) I_{\textnormal{NW}}^*$. When $\gamma = 0$, this corresponds to $I_{\textnormal{NW}}(\rho) \geq -\infty$; when $\gamma = 1$, this corresponds to $I_{\min{}}(\rho) \geq I_{\min{}}^*$. Thus as before, when $\gamma = 0$ there is effectively no item fairness constraint, and $\gamma = 1$ constrains item fairness to be maximal.
• Figure 3: We repeat the experiment of Figure \ref{['fig:empiricaltradeoffs']} from the original paper but replace max-min fairness with max-sum-$k$-min fairness for $k = 3$. In the optimization in Problem \ref{['eqn:originalconcaveproblem']}, we replace $U_{\min{}}$ and $I_{\min{}}$ with $U_{k-\textnormal{min}}$ and $I_{k-\textnormal{min}}$ respectively.
• Figure 4: Robustness of empirical findings without symmetry assumption: user-item fairness trade-offs and diversity as item utilities become less correlated with user utilities. Here, we take the user utilities $w^U$ to be derived from the arXiv recommendation engine similarity scores as in Figure \ref{['fig:tradeoff:diversity']}. For each plot the item utilities are a linear interpolation between the users' utilities and exposure. Formally, $w_{ij}^I = \Delta \cdot 1 + (1-\Delta)\cdot w_{ij}^U$. When $\Delta = 0$, item and user utilities agree; when $\Delta = 1$ items derive utility solely from exposure.
• Figure 5: Robustness of empirical findings without symmetry assumption: item fairness constraints still do not increase the price of mis-estimation empirically. Here, we take the user utilities $w^U$ to be derived from the arXiv recommendation engine similarity scores as in Figure \ref{['fig:tradeoff:misest']}. For each plot the item utilities are a linear interpolation between the users' utilities and exposure. Formally, $w_{ij}^I = \Delta \cdot 1 + (1-\Delta)\cdot w_{ij}^U$. When $\Delta = 0$, item and user utilities agree; when $\Delta = 1$ items derive utility solely from exposure.

Theorems & Definitions (64)

• Proposition 0
• Proposition 0
• Example 1
• Theorem 1
• proof : Proof sketch for Theorem \ref{['thm:pofdecreasing']}
• Theorem 2
• proof : Proof sketch
• Lemma 1
• proof
• Proposition 2