Evaluate GEO across the whole conversation, not one answer.

Abstract in brief

GEO has mostly been evaluated one answer at a time: for a fixed query, an evaluator measures how visible a source is in a single response. That procedure assumes queries are exogenous, supplied independently of the system, and that turns are independent of each other.

In a real conversation, the agent’s answer changes what the user believes and therefore what they ask next. When GEO tilts an answer toward a source, the bias carries into later turns through a machine-side channel, retrieval and generation conditioned on dialogue history, and a human-side channel, follow-up questions steered toward that source. The paper names this conversational capture. Crucially, the persistence can be decoupled from how relevant the source is to the user’s current need.

The paper does not propose a new GEO method or benchmark. It is a theory paper that questions the unit of evaluation itself. No human annotations were collected, and every number it reports is computed from the model.

Method: modeling the conversation as a closed loop

The conversation is modeled as a two-layer closed-loop system, a user layer that updates information needs and asks questions and an agent layer that retrieves and answers, and the paper defines constructs that can be computed across the whole trajectory.

1. Cumulative conversational visibility (CCV): Per-turn visibility summed over the conversation. Existing GEO metrics, such as position-adjusted word count or an LLM-judged impression score, can be reused turn by turn.
2. Direct and feedback terms: Trajectory gain is split into a direct term, which a single-turn evaluator can extrapolate, and a feedback term that only arises when the loop is closed. The feedback term is identically zero under single-turn evaluation.
3. Machine-side M1 and human-side M2: A nested counterfactual splits the feedback term into re-citation through dialogue history (M1) and the drift of the user’s questions (M2). M1 needs no user model and can be measured by comparing a history-conditioned engine with a stateless one on identical queries.
4. Capture coefficient, compounding ratio and misranking diagnostic: Defines how much a previous citation raises the next citation probability (capture coefficient κ), the ratio of realized gain to the single-turn extrapolation (compounding ratio ρ), and the agreement between single-turn and trajectory rankings of GEO methods (Kendall’s τ).
5. Theoretical analysis: Using Pólya-urn reinforcement-process theory, the paper proves path dependence (non-ergodicity), where early turns decide the long-run outcome, and that cumulative GEO gain grows superlinearly with conversation length while capture develops.

Model-derived illustration: decomposing gain at 10 turns

Key findings

• In the model-derived illustration, the direct term that single-turn evaluation can see was 1.20 of a 2.68 trajectory gain over ten turns; the feedback term from the closed loop (1.48) was larger.
• The compounding ratio reached 2.23 at ten turns, more than twice the single-turn extrapolation. Underestimation widens as conversations get longer before levelling off at a ceiling (about 4.17 in this example).
• In a comparison of five GEO methods, the single-turn winner ranked only third by trajectory gain, and the two rankings agreed weakly (Kendall’s τ = 0.4).
• Across 50,000 random five-method sets, the rankings disagreed in 90% of draws, and in 48% the single-turn winner was not the trajectory winner.
• If users answer a captured response with corrective follow-ups such as “is this independently confirmed?” that steer toward competitors, the human channel turns negative and single-turn evaluation overestimates GEO. Either way, the single-turn estimate is biased.

What it means for GEO and LLMO work

How VeReach reads the theory for practice. These are hypotheses: the paper itself has not yet measured effect sizes in deployed engines.

Limitations

• This is theory and modeling. No deployed AI search engine or real users were measured, and every reported figure is computed from the model.
• The M1/M2 split (0.35 / 0.25) is illustrative; real values must be estimated empirically.
• The model centers on competition between one GEO-optimized source and an aggregate competitor. Competition among several optimized sources is out of scope.
• As a next step, the paper describes an empirical protocol using conversational QA corpora such as TopiOCQA, QReCC and ORConvQA.

Frequently asked questions

What is conversational capture?

It is the phenomenon in multi-turn conversations with generative AI where a source cited in early turns becomes more likely to be cited in later ones. It works through retrieval conditioned on dialogue history (machine side) and follow-up questions steered by the answer (human side), and it can persist regardless of whether the source still fits the user’s current need.

Why is single-turn GEO evaluation not enough?

Single-turn evaluation assumes queries come from outside and turns are independent, so the closed-loop effect of an answer changing the next question, the feedback term, is always treated as zero. In the paper’s model-derived illustration, the part that is missed was larger than the part that is seen, and rankings of GEO methods diverged.

Where was the paper published?

It appears in HAI ’26, the 14th ACM International Conference on Human-Agent Interaction (November 16–19, 2026, Osaka), and was posted to arXiv (2609.40069) on September 30, 2026. Its DOI is 10.1145/3841580.3841626.

What should change in GEO and LLMO work?

Do not judge tactics on single-turn citation rate alone, check important topics across conversations that include follow-ups, and aim to be a reliable source cited in the first answer. Effect sizes in deployed engines have not yet been measured, including by the paper.