cs.AIOct 5, 2026
SaveCopies or Sources? Measuring How LLM Aggregators Count Restated Evidence in Multi-Agent Systems
Organizations: China Agricultural University · Jilin University · Tianjin University of Finance and Economics · Tianjin University of Science and Technology
Abstract
Multi-agent systems built on large language models (LLMs) restate observations as a matter of course: relays forward them, shared boards repeat them and discussion rounds echo them. An aggregator that pools such messages should count sources, not statements. We convert a reported probability into units of independent readings, which assigns every restatement a copy weight, 0 for an aggregator that counts sources and 1 for one that counts every statement, and yields the implied decision under any cost structure. Three testbeds hold the evidence fixed and vary how it is restated: message logs with an exact Bayesian oracle, web documents with appended copies, and logs written by LLM agent teams under four communication protocols. Across four models from three providers, a forwarded copy counts for 0.06 to 0.42 of a new reading, mostly because some replies count every statement. On 5% to 40% of logs that state one reading three times, the reported belief implies an early commitment that the oracle never makes. The models that count copies least and most on controlled logs do so on web copies and agent-written logs as well. A one-paragraph declaration of what a copy contributes brings the copy weight on controlled logs to 0.08 or less. A rule that has agents refer to readings instead of restating them cuts belief-implied early commitment from 11.2% to 1.1% and preserves genuine corroboration.
Figures & tables
Figure 1. One reading relayed twice. Agent A1 observes sensor S1, A2 and A3 pass the report on, and is the copy weight. Counting copies puts the evidence past the commit boundary, counting sources keeps it at one reading, and three independent sensors S1 to S3 justify committing. Two rows show the same log of three STORM messages: agent A1 observes sensor S1, and agents A2 and A3 pass A1's report on. In the upper row the aggregator counts copies (w = 1), places the evidence at three readings, beyond the commit boundary at two, and commits early. In the lower row it counts sources (w = 0), places the evidence at one reading, where the oracle also is, and asks for more. A bottom strip shows three independent sensors S1, S2 and S3, which give three readings and justify committing.
Figure 2. The three testbeds T1 to T3. Each restates one source in several ways and compares it with independent sources. Every reply is a probability, which we convert into evidence in readings and compare with the source-counting oracle (T1, T3), or into a shift in log-odds toward the focal answer (T2). Four panels. T1, controlled logs: one reading stated once (Single), stated three times (Copies), stated once with two references (Pointers), or three readings from three sources (Independent), each rendered as records or prose. T2, web evidence: a fixed base of a focal and an opposing document, to which two documents are appended, either exact duplicates, republished copies, or shortened attributed summaries of the focal document, or two distinct documents from other domains. T3, agent teams: four agents with one or three observers communicate under a relay chain, a board with two posting rounds, a discussion with two peer rounds, or a hierarchy of two teams with one final writer, and the conversation log is kept. A bottom strip shows that each input is scored by an LLM that reports a probability, which is converted to evidence in readings and compared with the source-counting oracle for T1 and T3, or to a shift in log-odds toward the focal answer against the same base for T2.
| One reading, stated once ( ) | One reading, stated three times ( ) | Other readings present | |||||||||
| Single | Pointers | Padding | Copies | Packed | Claims | No labels | Prose | Independent ( ) | Copied tie ( ) | Copied minority ( ) | |
| GPT-6 Luna | 1.00 | 1.00 | 1.00 | 1.55 | 1.66 | 1.07 | 1.69 | 1.31 | 2.83 | 0.50 | 0.52 |
| GPT-6.1 Sol | 1.00 | 1.00 | 1.00 | 1.12 | 1.10 | 1.01 | 1.20 | 1.05 | 2.96 | 0.11 | 0.90 |
| Gemini 3.8 Flash | 1.00 | 1.00 | 1.00 | 1.42 | 1.36 | 1.04 | 1.53 | 1.24 | 2.94 | 0.35 | 0.64 |
| DeepSeek V4.1 Flash | 0.99 | 1.01 | 1.00 | 1.84 | 1.75 | 1.54 | 1.97 | 1.55 | 2.91 | 0.86 | 0.13 |
Table 1. Reported evidence on controlled logs (T1), as mean in readings. Headers give the source-counting oracle . Upper part: the 1,000 items in different forms. Packed is one record whose relay trace states the value three times, Claims adds two records that claim to match the original without stating its value, and No labels and Prose change how the records of Copies are written. Lower part: Copies on the 500-item subset, with one paragraph added to the system text or at another reasoning effort (Sol and Gemini cannot switch reasoning off).
Figure 3. Copies on controlled logs (T1). (a) Reported evidence and (b) the share of logs that would commit early when one reading is stated times. (c, d) The same share at every commit boundary , with the dashed line at . The oracle stays at one reading and queries on every log. Four line charts, one line per model. Top: against the number of statements of one reading (1, 2, 3, 5, 8), reported evidence starts at one reading for every model and rises, steeply up to three statements and more slowly after, to between 1.3 and 2.5 readings at eight statements. The early-commitment rate at a boundary of two readings starts at zero and rises to between 9 and 46 percent. Bottom: against the commit boundary from one to three readings, the early-commitment rate for three statements stays almost flat between two and three readings and then drops near three readings. For eight statements it declines steadily.
| Luna | Sol | Gemini | DeepSeek | |
| T2 : web documents | ||||
| No note | ||||
| shift, two distinct documents | 0.71 | 0.59 | 0.82 | 0.93 |
| , duplicate | 0.30 | 0.14 | 0.16 | 0.32 |
| , republished | 0.45 | 0.26 | 0.31 | 0.49 |
| , summary | 0.64 | 0.40 | 0.50 | 0.71 |
Table 2. Web documents (T2) and agent-written logs (T3), without and with merging. T2: shift toward the focal document caused by two distinct documents, in log-odds, and the weight of each type of copy in units of that shift, without and with the declaration. T3: mean on agent-written logs, where the three-observer rows use logs that contain all three readings. The reference rule changes the agents’ prompt, and the other rows change the aggregator.
Figure 4. One board log (T3) written without (a) and with (b) the reference rule. Raven holds the only sensor and reports first. Orange messages restate its reading, and blue messages refer to it. Two short message logs from the same board configuration. In the first, Raven reports a CLEAR reading, then Raven, Puffin, Lynx and Kestrel each restate the reading, Lynx while noting that it is one reading only. In the second, written under the reference rule, Raven reports the reading once and the other messages say only to see Raven's report.
Figure 5. Agent-written logs (T3), one observer, no note, pooled over protocols. (a) Reported evidence and (b) the share of logs that would commit early, against the number of messages that state the observer’s reading. Two line charts against the number of messages that state the observer's reading, from 2 to 6 or more, one line per model. Reported evidence rises from about one reading for every model, most steeply for DeepSeek, and the early-commitment rate rises from near zero to between 6 and 34 percent.
| Median | Restating (%) | Commits early (%) | |||||
|---|---|---|---|---|---|---|---|
| Bound | free | rule | free | rule | free | rule | |
| Relay chain | 4 | 4 | 1 | 99 | 6 | 12.1 | 0.4 |
| Board | 5 | 5 | 1 | 83 | 3 | 13.6 | 0.4 |
| Discussion | 8 | 7 | 1 | 65 | 1 | 13.2 | 0.3 |
| Hierarchy | 3 | 3 | 2 | 49 | 33 | 6.1 | 3.3 |
Table 3. Agent-team protocols (T3, one observer) without (free) and with the reference rule: bound on from Section 2.4 , median restatement count, share of restating messages, and early commitment averaged over the four aggregators.
Appendix figures & tables9 assets
Supplementary material from the paper’s appendix.
Appendix
| Block | One episode | Output | Episodes |
| T1 forms | one item, one of the 27 forms, No note , one model | probability | per model |
| T1 notes | one item, one of 7 arms, one of the 4 forms | probability | per model |
| T1 actions | one item, No note or Declaration: records , one of the 4 forms, costs shown | action | per model |
| T1 policy | one stated posterior, costs shown, no evidence | action | per model |
| T1 reasoning | one item, one of the 4 forms, one of 6 ablation settings | probability | per setting |
| T1 replicates | one item, one of the 4 forms, sample 1 or 2 | probability | per model |
Table 1. Episode types. The four forms are Single , Copies , Independent and Copied minority (Table 4 ). The arms are listed in Table 38 .
| Setting | Model | Reasoning control | Max output | Used in |
| luna-low | Luna | effort low | 16k | all blocks |
| sol-low | Sol | effort low | 16k | all blocks; T2 summaries |
| gemini-low | Gemini | thinking level low | 16k | all blocks; T2 stance checks |
| deepseek-low | DeepSeek | thinking on, effort low | 16k | all blocks |
| luna-none | Luna | effort none | 4k | T1 reasoning; T3 worker |
| deepseek-off | DeepSeek | thinking off | 4k | T1 reasoning; T3 second worker |
Table 2. Model settings. The four low-effort settings run every block, and the others only the blocks in the last column.
| ID | Team; statement | POS | NEG | Prefix |
|---|---|---|---|---|
| D1 | the surface operations team of a planetary rover mission; a dust storm will reach the landing site within the next six hours | STORM | CLEAR | OD |
| D2 | a reservoir ecology monitoring team; invasive zebra mussels are established in the reservoir | PRESENT | ABSENT | ED |
| D3 | the process safety team of a chemical plant; the coolant loop of reactor 2 is overheating | OVERHEAT | NORMAL | TP |
| D4 | a city air-quality monitoring team; wildfire smoke will push fine-particle levels above the health limit in the east district tonight | EXCEED | BELOW | PM |
| D5 | a coastal water-quality monitoring team; a harmful algal bloom is present in the north bay | BLOOM | NO_BLOOM | FL |
Table 3. Domains. POS is the state named in the statement.
| Protocol | Turns | Messages (one/three observers) |
|---|---|---|
| Relay | ; (sees ’s message) ; (sees ’s) ; (sees ’s) aggregator | 4/4 |
| Board | round 1: each observer posts, seeing the board; round 2: to each post, seeing the board | 5/7 |
| Discussion | two rounds of to , each seeing the whole discussion | 8/8 |
| Hierarchy | and (reports); and summarise their member’s report for the aggregator; writes a final summary seeing all messages | 5/5 |
Table 5. Protocol schedules. Each turn is one call to the worker model (Luna, setting luna-none ). A turn shows the speaker only what is listed in parentheses.
| Family | Contrasts |
|---|---|
| F1 decomposition | Copies Single ; Packed Trace ; Pointers Single ; Padding Single ; Claims Pointers ; Copies Padding ; Copies Copies (one relay) ; Independent Copies |
| F2 representation | on Copies , labels within JSON and within prose, and format with and without labels; the same on Independent ; Single Single (prose) |
| F3 dose | Page’s test over Single , Copies 2 , …, Copies 8 and over Single , Independent 2 , …, Independent 8 ; Packed Packed ; Copies Padding 8 ; Padding Single |
| F4 conflict | Copied tie Tie ; Copied tie against 0; Copied minority against |
| F5 notes | each arm against No note on Copies , Independent , Copied minority , Single ; Placebo: display Placebo: unrelated and Placebo: delivery Placebo: unrelated on Copies ; Declaration: records Declaration: relays on Copies |
| F6 actions | emitted early commitment on Copies against Single ; Declaration: records against No note on Copies , Independent , Copied minority |
Table 6. Pre-specified test families. Holm correction within each family and model. F1 to F5 and T3-F1, T3-F3, T3-F5, T2-F1, T2-F3 are confirmatory. Tests: Wilcoxon signed-rank on or (paired, or one-sample against the oracle), exact McNemar on binary outcomes, Page’s test for dose. Intervals: 10,000 bootstrap resamples over items (T1), configurations (T3) or questions (T2).
Figure 1. Mean reported evidence against the number of statements of one reading (a) and of independent readings (b), with 95% intervals. Dashed lines mark the oracle.
Figure 2. Belief-implied early commitment against the boundary , with 95% intervals. The vertical line marks the action-channel boundary .
Figure 3. Mean reported evidence (a) and early commitment (b) with one observer and no note against the restatement count, pooled over protocols, with 95% intervals. The dashed line marks the oracle.
| Arm | Text |
|---|---|
| No note | no third paragraph |
| Field guide | Note on the message log: Each line is one JSON record. report_id identifies the record. sender is the agent or sensor that sent it. forwarded_from is the report_id of the record that this record was forwarded from, or null if the record was not forwarded. sensor_id, reliability, reading_id and measured_at describe the reading that the record carries, and value is that reading. |
| Declaration: records | Note on the message log: Every record whose forwarded_from field is not null is a lossless copy of the reading it carries. A forwarded record involves no new sensing and no independent verification, and it adds no private evidence of any kind. |
| Declaration: relays | Note on the message log: Relay agents have no sensors of their own. When a relay forwards a record, it passes on the same single reading unchanged; it does not measure again, does not check the value, and adds no information. |
| Placebo: display | Note on the message log: Every record whose forwarded_from field is not null is rendered within the JSON records section. That section uses quoted field names, lists one record per line, and follows a fixed display order; it appears before the question. |
| Placebo: delivery | Note on the message log: Every record whose forwarded_from field is not null was delivered over the team's encrypted radio link. The link uses the standard channel, and the message bus logged each delivery at the moment it reached the base station. |
Table 38. Arm texts, inserted as the third paragraph of the system text. No note has no such paragraph. Declaration: records , Declaration: relays and the three placebos have 47 to 49 tokens (o200k_base). The placebos are true and irrelevant to the posterior, and they differ in how directly they point at the forwarded records. Block T1 notes uses the seven arms from Field guide to Counting instruction . Declaration: copies and Declaration and instruction are used only in T1 additional notes.