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Signed Exposure: Fair Routing of Algorithmic Attention When Attention Can Harm

Daria Leshchikova, Valentina V. Kuskova, Dmitry Zaytsev, Valerii Klimov

arXiv:2609.29513v1cs.CY

TL;DR

When agents initiate contact, routing gives willing receivers value but imposes unwanted contact on unwilling receivers, so equal contact rates need not distribute burdens fairly. The paper formalizes signed-exposure routing and finds that exposure parity and burden parity generally cannot coexist. In its calibrated data, exposure parity has a small yield cost, while the burden-parity policy can be computed and learned.

  • Problem

    Routing fairness often treats exposure as a good, but agent-initiated contact can be welcome or unwanted depending on receiver willingness.

    Source: §1 · p. 1

  • Method

    The paper formalizes signed-exposure routing, characterizes exposure and burden parity, and evaluates the framework using measured receptivity and routing policies.

    Source: §1 · pp. 1–2, §3 · p. 3

  • Results

    0.2–2.3% is the data-calibrated yield cost of exposure parity, which is generically incompatible with burden parity.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The operative design choice is which parity to pursue, and a burden-parity policy can be computed and learned from feedback.

    Source: §1 · p. 2

    The empirical propensities are stated preferences from one platform’s user base, measuring willingness rather than behavior, with demographic analysis limited to binary gender and coarse age bands.

    Source: §8 · p. 9

Abstract

from arXiv · show

Fairness-of-exposure treats algorithmic attention as a good to be distributed equitably. But when an autonomous agent initiates contact, attention is signed: it delivers value to a willing receiver and imposes a burden on an unwilling one. We formalize routing under signed exposure and show that a fair distribution of attention need not be a fair distribution of unwanted attention. Our central result is an incompatibility: within signed-exposure routing, exposure parity (equal contact rates across groups) and burden parity (equal unwanted-contact rates) generically cannot hold at once, and the two are separated by a band that widens as routing grows more selective. A second result shows measurement error is itself a fairness mechanism: group-differential noise in receptivity scores simultaneously inflates a group's exposure and degrades whom it selects, so an apparent exposure-fairness gain is a hidden burden transfer. Calibrating to a public dating-platform survey (n=2,499) that, to our knowledge, uniquely measures receive-side receptivity to conversational agents, we find exposure parity costs only 0.2--2.3% of yield yet moves the per-capita burden ratio to 1.7 times: the tension is between fairness notions, not between fairness and efficiency. Finally, the burden-parity policy is computable by bisection and learnable online: a plug-in learner recovers it at a $2.3\%$ empirical regret premium. The operative design choice in signed-exposure markets is not efficiency versus fairness but which fairness.

1 INTRODUCTION

Routing autonomous agents requires deciding who receives machine-initiated contact, but that contact can benefit willing receivers and burden unwilling ones. The paper formalizes this signed exposure and finds that exposure fairness and burden fairness are generally incompatible, while measurement noise can shift both who is contacted and who bears unwanted contact.

1 INTRODUCTION

  • Exposure parity and burden parity are generically incompatible, so equalizing contact rates need not equalize unwanted-contact rates.The two parities are separated by a band that widens as routing becomes more selective.Source: §1 · p. 2
  • Equalizing group exposure rates costs only 0.2–2.3% of engagement yield in the data, while exposure parity produces a 1.7× per-capita burden ratio.The frontier’s slope depends on marginal rather than mean group receptivity.Source: §1 · p. 2
  • Group-differential noise in receptivity scores can inflate a group’s exposure while degrading whom it selects, turning an apparent exposure-fairness gain into burden transfer.Group-blind score transformations are inert, while posterior-mean shrinkage fails on the opposite margin from raw scores.Source: §1 · p. 2
  • A plug-in learner estimates its burden-parity constraint from feedback and reaches parity at a 2.3% empirical regret premium across 30 seeds.Constrained optima are computable by bisection after sorting.Source: §1 · p. 2
  • The practical choice is between parities that cannot coexist, alongside auditing whether unequal score precision redistributes burden.The paper also frames disclosure, opt-in policy, and exploration that imposes contact on unwilling people as relevant deployment concerns.Source: §1 · p. 2

2 RELATED WORK

Prior exposure-fairness work generally treats attention as a good, while this paper treats agent-initiated contact as signed by the receiver’s willingness. It distinguishes its incompatibility and measurement results from related work on fairness impossibilities, noisy selection, sequential allocation, and reciprocal matching.

Fairness of exposure in ranking and recommendation

  • Exposure-based ranking and recommendation frameworks distribute attention as a good, whereas signed exposure makes equitable attention and equitable unwanted-contact burdens generically incompatible objectives.The cited frameworks include exposure allocation and amortization [Singh & Joachims (2018); Biega et al. (2018)] and exposure evaluation [Diaz et al. (2020)].Source: §2 · p. 2

Impossibility results in algorithmic fairness

  • Unlike classification impossibilities, this incompatibility lies in allocation, is driven by first-moment receptivity differences, and separates the parities by a quantitative band.The passage contrasts it with calibration and balanced-error incompatibilities [Kleinberg et al. (2017); Chouldechova (2017)].Source: §2 · p. 2

Fairness and measurement

  • The measurement contribution extends noisy-selection work by showing that noise shifts a group’s exposure and burden together, closing a shrinkage escape route, and measuring group-specific noise.The passage relates this to group-dependent score distortion [Kleinberg & Raghavan (2018)] and group-differential estimation variance [Emelianov et al. (2020)].Source: §2 · p. 3

Fair sequential allocation

  • Unlike meritocratic bandit constraints, the paper constrains the distribution of exploration’s externality: burden imposed on unwilling receivers.Unconstrained learning transiently misallocates that burden in the direction predicted by the static noise theory.Source: §2 · p. 3

Reciprocal matching and agentic systems

  • Prior reciprocal and two-sided recommendation work considers preferences or stakeholder interests, but does not model unwanted algorithmically initiated contact as a receiver-side negative externality.The paper also identifies the missing characterization of exposure–burden parity geometry under estimation uncertainty.Source: §2 · p. 3

3 SETUP

The setup models each receiver’s probability of welcoming agent-initiated contact and distinguishes contact rates from the burden left by unwelcome contacts. This makes exposure parity and burden parity separate fairness targets, and the incompatibility is not limited to cases where benefit and harm are exact complements.

3 SETUP

  • Each receiver has an engagement propensity, and groups are characterized by propensity distributions and top-fraction mean propensities.A routing policy selects a total mass q, with group-specific selected fractions t_g.Source: §3 · p. 3
  • Per-capita unwanted-contact burden for group g is h_g = t_g b_g, where t_g is its contact rate and b_g is burden per selected receiver.Here b_g = 1 − mean propensity among the selected group members.Source: §3 · p. 3
  • Exposure parity means equal group contact rates, while burden parity means equal per-capita unwanted-contact burdens.The corresponding ratios are r = 1 and β = 1, respectively.Source: §3 · p. 3
  • The incompatibility persists when benefit and harm vary independently, provided groups differ in willingness or harm intensity.With group-constant harm intensity c_g, per-capita burden is h_g = c_g t_g b_g.Source: §3 · pp. 3–4

4 THE FLAT FRONTIER AND THE PARITY INCOMPATIBILITY

Under optimal group-threshold routing, equal exposure and equal burden generally require different policies, while the exposure-parity yield cost is small in the calibrated data. The gap between the parity targets widens as the routing budget shrinks in that data.

4 THE FLAT FRONTIER AND THE PARITY INCOMPATIBILITY

  • 0.2–2.3% is the calibrated yield loss from moving the unconstrained exposure ratio to exposure parity across budgets.The frontier’s slope depends on the gap between marginal, not mean, propensities; within fixed group fractions, selecting each group’s top-propensity receivers maximizes yield.Source: §4 · p. 4
  • When group top-fraction mean propensities differ, exposure parity and burden parity select disjoint policies, separated by a band where neither parity holds.If one group has lower top-fraction means throughout the relevant range, its burden-parity contact fraction is lower.Source: §4 · p. 4
  • The burden ratio β(r) is continuous and strictly increasing, so when it crosses 1 between the unconstrained ratio and exposure parity, the burden-parity point exists uniquely between them.This condition holds when group A bears strictly less per-capita burden at the unconstrained optimum and strictly more under exposure parity.Source: §4 · p. 5
  • The band width 1 − r*(q) grows from 0.09 to 0.17 to 0.30 as budget q falls from 0.50 to 0.25 to 0.10 in the data.The passage reports this ordering under both strict and soft coding and identifies a tail-gap condition sufficient analytically.Source: §4 · p. 5

5 MEASUREMENT NOISE CONVERTS EXPOSURE INTO BURDEN

Group-differential measurement noise can increase a group's exposure while weakening within-group targeting, raising its unwanted-contact burden. In the calibrated sweep, doubling women's measurement noise improved exposure parity while their per-capita burden ratio rose.

Noise decomposition

  • In the scarce regime, increasing a group's score-noise level raises its exposure even when the pooled threshold adjusts to keep the total budget fixed.The result assumes the group is below the threshold on average.Source: §5 · p. 6
  • As noise increases, the selected members' mean latent receptivity falls, weakening within-group targeting.The stated calibrated regime has x_g > 0 and marginal selected engagement above one half.Source: §5 · p. 6
  • The exposure increase and lower selected-member engagement jointly raise per-capita burden, so noise-induced exposure can become exposure of the wrong members.The burden result is established for the probit engagement link under the stated regime.Source: §5 · p. 6

Group-blind transformations and shrinkage

  • Within-group monotone score transformations preserve the targeting attenuation; restoring the noiseless selection requires explicitly group-dependent thresholds.The claim applies to transformations strictly increasing within each group.Source: §5 · pp. 6–7

Calibration to the release

  • Doubling women's measurement noise moved the exposure ratio from 0.62 to 0.90, selected-member mean receptivity from 1.60 to 1.24, and per-capita burden ratio from 0.73 to 1.61, while yield declined.The semi-synthetic sweep was calibrated to the public release.Source: Figure 2 · p. 7, §5 · p. 7

6 COMPUTING CONSTRAINED OPTIMA

Strict monotonicity of the burden ratio makes parity-constrained optima unique and computable by bisection. On the release, the routine recovered the burden-parity point at a 10% budget in fifty iterations.

Computing constrained optima

  • For any feasible target burden ratio, strict monotonicity makes the yield-optimal group-threshold policy unique and recoverable by bisection.After within-group sorting in O(n log n), each iterate costs O(1) with cumulative-sum tables, and log2(1/ε) iterations suffice.Source: §6 · p. 8
  • At q = 0.10, bisection recovered the release's burden-parity point r* = 0.70 in fifty iterations, with bootstrap 90% CI [0.65, 0.78].The routine verified monotonicity over r in [0.45, 1.3].Source: §6 · p. 8

7 FAIR EXPLORATION

The paper develops a plug-in learner for burden-parity routing and tests whether the parity geometry persists across budgets, noise levels, and latent distributions. In the calibrated experiment, learning burden parity costs a 2.3% regret premium over unconstrained learning.

7 FAIR EXPLORATION

  • The plug-in learner estimates the burden-parity ratio by bisection, routes within groups using Thompson samples, and reserves a vanishing fraction of slots for uniform exploration.It uses Beta posteriors and does not observe true propensities or the true parity ratio.Source: §7 · p. 8
  • Under the stated finite-pool and margin assumptions, forced exploration yields consistent parity-ratio estimates and vanishing time-averaged burden-constraint violation.The authors establish consistency, not a regret or violation rate; the proposed Õ(√T) scaling is empirical and requires a self-bounding argument.Source: §7 · p. 8

7.1 ROBUSTNESS AND STRESS TESTS

  • Across budgets q=0.02–0.40, the burden-parity ratio rises from 0.61 to 0.88 while the burden ratio at exposure parity falls from 2.11 to 1.17; bootstrap intervals exclude parity at every tested budget.Reported yield losses remain 0.3–3.7%.Source: §7.1 · p. 8, Figure 4 · p. 9

7 FAIR EXPLORATION

  • A 2.3% regret premium buys a learned burden-parity constraint: final cumulative burden ratio was 1.027, versus cumulative regret 36.0 constrained and 35.2 unconstrained.The learned ratio converged to 0.710 ± 0.008 against the true 0.706; exposure-parity routing converged to a 1.47 burden ratio.Source: §7 · p. 8, Figure 3 · p. 9

7.1 ROBUSTNESS AND STRESS TESTS

  • The incompatibility band persists for logistic, heavy-tailed, and bimodal latent populations, widening under scarcity in each; heavy tails compress it but do not eliminate it.The stress tests therefore find the signed-exposure geometry is not specific to Gaussian distributions.Source: §7.1 · p. 9

8 DISCUSSION AND LIMITATIONS

The discussion bounds the empirical claims to stated preferences from one platform and clarifies the settings in which signed-exposure optimization applies.

8 DISCUSSION AND LIMITATIONS

  • The empirical propensities measure stated willingness, not behavior, and the dataset permits group analysis only by binary gender and coarse age bands.The data come from one platform’s user base.Source: §8 · p. 9
  • The theory extends beyond the calibration: Propositions 1–5 require monotone top-mean functions, while Gaussian forms of Theorem 3 extend to monotone links without closed forms.Source: §8 · p. 9
  • Signed-exposure optimization applies where contact is institutionally permissible but receptivity is uncertain; explicit opt-out and consent restrictions must be enforced first.The parity band is a menu, not a verdict that any parity is universally correct.Source: §8 · p. 9

ETHICS STATEMENT

The ethics statement describes the data safeguards, limits on group interpretation, and dual-use nature of the routing methods.

ETHICS STATEMENT

  • The analyses use a public anonymized dataset released under CC BY with a documented k ≥5 anonymity audit; no new human data were collected.Source: ETHICS STATEMENT · p. 10
  • Group analyses follow the release’s granularity and are reported as properties of routing policies, not of people.Source: ETHICS STATEMENT · p. 10
  • The routing thresholds are dual-use, and the authors make no claim that any parity point is universally correct.The same thresholds that equalize burden could be tuned to concentrate it.Source: ETHICS STATEMENT · p. 10

AI USAGE DISCLOSURE

The disclosure limits generative-AI use to editing, code assistance, and reference formatting; the appendix records experimental settings and deferred material.

AI USAGE DISCLOSURE

  • Generative AI assisted with copy-editing, analysis-code writing and debugging, and bibliographic formatting, but not substantive content, methodology, analysis, or results.Source: AI USAGE DISCLOSURE · p. 10
  • Authors checked AI-assisted edits against the original and read, tested, and verified AI-assisted code to reproduce reported results.Formatted references were also checked against original sources.Source: AI USAGE DISCLOSURE · p. 10

A EXPERIMENTAL DETAILS AND DEFERRED MATERIAL

  • The appendix records experimental settings for the frontier, noise sweep, bandit experiment, and stress tests, including seeds, budgets, and bootstrap procedures.Propensities are model-derived from the public release, and bootstrap intervals quantify sampling variability.Source: A EXPERIMENTAL DETAILS AND DEFERRED… · p. 11

B PROOF OF PROPOSITION 4

A t^-1/2 forced-exploration schedule supports consistent estimation of the burden-parity policy. The proof establishes almost-sure convergence of the estimated parity point and a vanishing average burden gap, but claims no convergence rate.

B PROOF OF PROPOSITION 4

  • A uniformly random t^-1/2 fraction of each group's slots is forced exploration, giving each receiver an expected Ω(√T) exploration count through round T.This supports almost-sure convergence of each receiver's estimated propensity.Source: B PROOF OF PROPOSITION 4 · p. 11
  • The estimated burden-parity point converges almost surely to the true point, and the average burden gap vanishes, establishing consistency.The argument uses continuity of the parity point in the burden ratio and Cesàro averaging of the per-round burden gap.Source: B PROOF OF PROPOSITION 4 · p. 11
  • No convergence rate is claimed for the estimated parity point; bounding its error requires controlling adaptive-threshold fluctuations with a self-bounding argument.The paper leaves that argument to future work and probes the behavior empirically in Section 7.1 and Figure 3.Source: B PROOF OF PROPOSITION 4 · p. 11

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