Abweichungen in Prognosepanels mit mehreren Agenten untersuchen

# 06_multi_agent_research.py


```py
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# %% [markdown]
# # Multi-Agent Research
#
# **Docker image**: `ml4t`
#
# One research agent gives one answer with no way to tell a considered probability from a
# lucky search. Running several is the cheapest available check, and it only works if they
# disagree: three agents returning the same number are one agent charged for three times.
#
# This notebook runs three copies of the agent from
# [`04_research_agent`](04_research_agent.ipynb) on one question, in parallel, and looks at
# what came back. Nothing distinguishes the three except their identifiers, which is the point:
# no roles, no settings, nothing assigned to make them differ. Two things can still make them
# differ anyway - the model samples its replies, and each agent's searches return different
# documents - and this run separates neither.
#
# **What this run establishes, and what it does not.** The numbers below are one live capture
# (`claude-sonnet-4`, Tavily search) taken on 2026-06-09 and replayed by default, so the
# figures are the same whenever the notebook runs. One capture on one question is a
# demonstration that a panel of identical agents is not degenerate. It is not an experiment:
# nothing here varies temperature, retrieval, or question wording independently, so the spread
# cannot be attributed to any of them. And the market's own probability was in every prompt,
# which rules out reading the agents' closeness to the market as skill.
#
# **Learning Objectives**:
# - Run several agents concurrently and keep each one's conversation separately attributable
# - Read a panel's timelines to tell genuine disagreement from one agent run three times
# - Exclude agents that never produced a forecast before aggregating
# - Show how far the assumed correlation moves an aggregate, relative to how far the agents
#   are apart
# - Say what a single dated capture of a multi-agent run does and does not establish
#
# **Book Reference**: Chapter 24, Section 24.7 (Multi-Agent Forecasting Systems -
# Agent Ensemble)
#
# **Prerequisites**: [`04_research_agent`](04_research_agent.ipynb) (the agent),
# [`05_aggregation_math`](05_aggregation_math.ipynb) (the aggregation rules).

# %%
"""Multi-Agent Research - parallel agents on one shared question."""

from concurrent.futures import ThreadPoolExecutor, as_completed
from datetime import date, datetime

import matplotlib.pyplot as plt
import polars as pl
from agent_fixtures import get_chapter_clear_question
from agent_observability import (
    TRACES_DIR,
    RunTrace,
    merge_calls,
    replay_llm_calls,
    show_agents,
    trace_llm,
)
from agent_pipeline import neyman_extremize, neyman_extremize_weighted
from agent_providers import TokenUsage, create_llm_client
from agent_research import ResearchAgent, format_agent_summary
from agent_schemas import AgentForecastArtifact
from agent_tools import create_search_client
from IPython.display import Markdown, display

from utils.style import COLORS, add_message_title, format_pct_axis, show_with_alt

# %% [markdown]
# ## Settings
#
# `RUN_LIVE` left at `False` replays the pinned capture named below and makes no API calls.
# Setting it to `True` forecasts a current question against live search and live models, which
# costs money and will not reproduce these numbers; a prediction-market question moves under
# you, and once it resolves it has to be swapped for a current one of the same kind.
#
# `N_AGENTS` is how many copies to run on the live path. Three is enough for a spread to be
# visible and small enough to be cheap; the replay uses however many the capture holds.
#
# `MAX_STEPS` and `MAX_SEARCH_RESULTS` are the per-agent turn budget and search width from
# [`04_research_agent`](04_research_agent.ipynb). Open models tend to search more before
# committing, so raise `MAX_STEPS` if agents start hitting the budget without forecasting.
#
# `NEYMAN_CORRELATION` is the pairwise correlation assumed when the panel is aggregated. It is
# the input nothing here measures, and the sensitivity section further down is what says how
# much rests on it.
#
# `LLM_PROVIDER` is empty so the factory picks the first provider whose key is set; the cell
# below reports which provider the capture used. Setting it to `"openrouter"` with
# `OPENROUTER_MODEL="deepseek/deepseek-v4-pro"` drives an open model instead. `"mock"` returns
# a constant forecast and is a smoke test, not a reproduction of this run.

# %% tags=["parameters"]
RUN_LIVE = False
PINNED_TRACE = "06_multi_agent_research_20260609T141413Z_9fc4a2655471.json"
LLM_PROVIDER = ""
N_AGENTS = 3
MAX_STEPS = 5
MAX_SEARCH_RESULTS = 5
NEYMAN_CORRELATION = 0.3

# %% [markdown]
# ## Setup
#
# All three agents share one model client and one search client. Each gets a distinct
# `agent_id` and nothing else: the same prompt, the same tools, the same sampling temperature.
# Nothing is built in to make them disagree. Two channels remain open: the model's own
# sampling, and the different documents each agent's searches return. The timelines below show
# the second; nothing here separates the two.
#
# The question is `CHAPTER_CLEAR_QUESTION` from `agent_fixtures.py`, *"Will the US enter a
# recession by the end of 2026?"*, carrying the prediction-market probability recorded on
# 2026-06-09.
#
# **That market probability was included in every prompt.** It is passed to `agent.run` as
# `market_price` below, so each agent saw the market's answer before it searched. That makes
# the comparison between the agents and the market circular, and it is why the market line in
# the chart further down is labelled as context rather than as a benchmark. A run designed to
# test the agents against the market would withhold it, as
# [`04_research_agent`](04_research_agent.ipynb) does.

# %%
if RUN_LIVE:
    llm = create_llm_client(LLM_PROVIDER)
    search = create_search_client(LLM_PROVIDER)
    question = get_chapter_clear_question()
    provider_name = llm.model_name
    n_agents = N_AGENTS
    captured_on = date.today().isoformat()
else:
    pinned_run = RunTrace.load(TRACES_DIR / PINNED_TRACE)
    question = pinned_run.question_obj()
    provider_name = pinned_run.provider
    n_agents = len(pinned_run.agents)
    captured_on = datetime.fromisoformat(pinned_run.created_at).date().isoformat()

mode = "live" if RUN_LIVE else f"replay of a capture recorded {captured_on}"
print(f"Mode:         {mode}")
print(f"Provider:     {provider_name}")
print(f"Question:     {question.question}")
print(f"Market p_yes: {question.current_market_price}")
print(f"Agents:       {n_agents}")

# %% [markdown]
# ## Running the Agents in Parallel
#
# Each agent spends most of its time waiting on a network call, so running them one after
# another wastes the whole panel's latency. A `ThreadPoolExecutor` gives each its own thread;
# they share the model client and the search client, so both have to be safe under concurrent
# calls. Anthropic's and Tavily's clients are. A provider whose client is not would need
# construction inside the worker rather than outside it.
#
# Each agent gets its own tracer wrapping the shared client. That is what keeps the captured
# conversations attributable: one tracer across three threads would interleave three agents'
# prompts into one log with no way to separate them afterwards. The per-agent logs are merged
# once the pool has drained.


# %%
def run_agent(agent_id: str):
    """Run one research agent under its own tracer, returning both."""
    tracer = trace_llm(llm, label=agent_id)
    agent = ResearchAgent(
        llm=tracer,
        search=search,
        agent_id=agent_id,
        max_steps=MAX_STEPS,
        max_search_results=MAX_SEARCH_RESULTS,
    )
    return agent.run(question, market_price=question.current_market_price), tracer


# %% [markdown]
# The live path submits one task per agent. The replay path rehydrates the three saved
# artifacts and their conversations instead, and every display cell below reads the same
# objects either way.

# %%
artifacts: list[AgentForecastArtifact] = []

if RUN_LIVE:
    tracers = []
    with ThreadPoolExecutor(max_workers=N_AGENTS) as pool:
        futures = {pool.submit(run_agent, f"agent_{i}"): i for i in range(N_AGENTS)}
        for future in as_completed(futures):
            artifact, tracer = future.result()
            artifacts.append(artifact)
            tracers.append(tracer)
    llm_calls = merge_calls(*tracers)
else:
    artifacts = pinned_run.agent_artifacts()
    llm_calls = pinned_run.call_log()

# Threads finish in whatever order they finish; sort so the display is stable.
artifacts.sort(key=lambda a: a.agent_id)

# The replay is a fixed record. These fail closed if the named trace changes underneath.
if not RUN_LIVE:
    assert [a.p_yes for a in artifacts] == [0.12, 0.22, 0.22]
    assert len(llm_calls) == 12

# %% [markdown]
# ## What Each Agent Returned
#
# Probability, confidence, sentiment, and how much evidence each one gathered getting there.
# The last two columns are worth as much as the first: two agents landing on the same
# probability after two searches and after six searches did not do the same thing.

# %%
total_tokens = TokenUsage()
for a in artifacts:
    total_tokens = total_tokens + a.token_usage

panel_df = pl.DataFrame(
    [
        {
            "agent_id": a.agent_id,
            "p_yes": round(a.p_yes, 3),
            "confidence": round(a.confidence, 3),
            "sentiment": a.sentiment.value,
            "queries": a.search_queries_made,
            "sources": a.sources_consulted,
        }
        for a in artifacts
    ]
)
print(f"Market price shown to the agents: {question.current_market_price:.1%}")
print(f"Total tokens across the panel:    {total_tokens.total_tokens:,}\n")
panel_df

# %% [markdown]
# The market line is drawn as context rather than as a benchmark, for the reason given above:
# every agent was shown it.

# %%
probabilities = panel_df["p_yes"].to_list()
probability_range = max(probabilities) - min(probabilities)

fig, ax = plt.subplots()
bars = ax.bar(
    panel_df["agent_id"].to_list(),
    probabilities,
    color=COLORS["blue"],
    width=0.6,
)
ax.axhline(
    question.current_market_price,
    color=COLORS["amber"],
    linestyle="--",
    linewidth=1.5,
    label="Market price, shown to every agent",
)
ax.bar_label(bars, labels=[f"{value:.0%}" for value in probabilities], padding=3)
ax.set_xlabel("Research agent")
ax.set_ylabel("Probability of recession")
ax.set_ylim(0, max(probabilities) + 0.08)
format_pct_axis(ax)
add_message_title(
    ax,
    "Probability of recession, by research agent",
    subtitle=f"Same prompt, tools and temperature; capture recorded {captured_on}",
)
ax.legend(loc="upper left")
show_with_alt(
    fig,
    "Bar chart with one bar per research agent, each labelled with the probability that agent "
    "returned, and a dashed horizontal line at the market price every agent was shown. Two of "
    "the bars are the same height and sit just above the market line; the third is much "
    "shorter and sits well below it.",
)

# %% [markdown]
# ## Reading the Agents, Not the Aggregate
#
# The table gives each agent's answer and none of its reasoning. `show_agents` renders the full
# captured timeline for all three: every query, the documents it returned with title, date, URL
# and a snippet, and the untruncated rationale, key findings and uncertainties. Each artifact
# carries this in its `traces`, the `AgentTrace` records built in
# [`04_research_agent`](04_research_agent.ipynb).
#
# Read side by side, the timelines answer the question the bar chart cannot. Three agents
# reaching similar numbers by different search paths is three observations. Three agents
# pulling the same documents and reasoning in step is one observation printed three times, and
# aggregating it produces confidence that nothing earned. The second case is what a panel of
# identical agents drifts toward, and it is worth checking before any aggregation is trusted.

# %%
print(show_agents(artifacts))

# %%
probability_text = ", ".join(f"{value:.2f}" for value in probabilities)
display(
    Markdown(
        f"**This run**: the three agents returned {probability_text}, a range of "
        f"{probability_range:.2f} on a question where the market stood at "
        f"{question.current_market_price:.1%}. That range is one observation from one capture. "
        "It says the panel is not degenerate; it does not say how large the spread would be on "
        "another question, another day, or with a different model."
    )
)

# %% [markdown]
# ## Aggregating the Panel
#
# Three ways to turn three probabilities into one, from
# [`05_aggregation_math`](05_aggregation_math.ipynb):
#
# | Method | What it assumes |
# |---|---|
# | Simple mean | Nothing beyond the forecasts themselves |
# | Neyman | A pairwise correlation, supplied rather than estimated |
# | Weighted Neyman | That correlation, plus that the confidence values mean something |
#
# Only artifacts that actually produced a forecast may enter any of the three. An agent that
# exhausted its step budget carries the loop's fallback probability, and averaging that in
# would pull the panel toward even odds on the strength of an agent that never answered.

# %%
answered = [a for a in artifacts if a.forecast_produced]
if not answered:
    raise RuntimeError("no agent produced a forecast; there is nothing to aggregate")

panel_probabilities = [a.p_yes for a in answered]
panel_confidences = [a.confidence for a in answered]

simple_mean = sum(panel_probabilities) / len(panel_probabilities)
result_neyman = neyman_extremize(panel_probabilities, base=0.5, correlation=NEYMAN_CORRELATION)
result_weighted = neyman_extremize_weighted(
    panel_probabilities, panel_confidences, base=0.5, correlation=NEYMAN_CORRELATION
)

print(f"Agents that produced a forecast: {len(answered)} of {len(artifacts)}")

pl.DataFrame(
    [
        {
            "method": "Simple mean",
            "aggregate": round(simple_mean, 3),
            "d": None,
            "n_eff": None,
        },
        {
            "method": "Neyman",
            "aggregate": round(result_neyman.extremized_probability, 3),
            "d": round(result_neyman.extremization_factor, 3),
            "n_eff": round(result_neyman.effective_n, 2),
        },
        {
            "method": "Weighted Neyman",
            "aggregate": round(result_weighted.extremized_probability, 3),
            "d": round(result_weighted.extremization_factor, 3),
            "n_eff": round(result_weighted.effective_n, 2),
        },
    ]
)

# %% [markdown]
# Both Neyman variants sit further from the base rate than the mean, which is what
# extremization does. The gap between them is the whole contribution of the confidence
# weights, and those weights are a function of how far each probability sits from even odds
# rather than of anything measured, so the two lines being close is not reassurance.

# %% [markdown]
# ## How Much the Correlation Assumption Decides
#
# $\rho$ is the one input to Neyman extremization that nothing in this run measures, and it is
# the input the answer is most sensitive to. Sweeping it over the same three forecasts shows
# how much of the aggregate is evidence and how much is assumption.

# %%
correlation_rows = []
for rho in [0.0, 0.1, 0.3, 0.5, 0.7, 0.9]:
    r = neyman_extremize(panel_probabilities, base=0.5, correlation=rho)
    rw = neyman_extremize_weighted(
        panel_probabilities, panel_confidences, base=0.5, correlation=rho
    )
    # The reported aggregate is clamped into [0.01, 0.99]. Recovering the value before the
    # clamp from the same result - the mean, the base rate and the diversity factor it used -
    # is what shows when the clamp is carrying the answer.
    unclamped = 0.5 + r.extremization_factor * (r.raw_probability - 0.5)
    correlation_rows.append(
        {
            "correlation": rho,
            "neyman": round(r.extremized_probability, 3),
            "before the clamp": round(unclamped, 3),
            "weighted_neyman": round(rw.extremized_probability, 3),
            "shift_from_mean": round((r.extremized_probability or 0) - simple_mean, 3),
        }
    )
correlation_df = pl.DataFrame(correlation_rows)
correlation_df

# %% [markdown]
# The `before the clamp` column is the one to read first. This panel sits far enough below the
# base rate that the formula, credited with three near-independent observations, returns a
# **negative** probability, and `neyman_extremize` floors it. Where the two columns differ, the
# reported aggregate is the floor rather than the method's answer, and the sensitivity curve
# below is flat there for that reason and no other.

# %%
rho_values = correlation_df["correlation"].to_list()

unclamped_values = correlation_df["before the clamp"].to_list()

fig, ax = plt.subplots()
ax.plot(
    rho_values,
    unclamped_values,
    ":",
    color=COLORS["negative"],
    linewidth=1.5,
    label="Neyman before the clamp",
)
ax.plot(
    rho_values,
    correlation_df["neyman"].to_list(),
    "o-",
    color=COLORS["blue"],
    linewidth=2,
    label="Neyman as reported",
)
ax.plot(
    rho_values,
    correlation_df["weighted_neyman"].to_list(),
    "s--",
    color=COLORS["copper"],
    linewidth=1.5,
    label="Confidence-weighted Neyman",
)
ax.axhline(
    simple_mean,
    color=COLORS["neutral"],
    linestyle="-.",
    linewidth=1.5,
    label="Simple mean",
)
ax.set_xlabel(r"Assumed pairwise correlation ($\rho$)")
ax.set_ylabel("Aggregate probability")
ax.set_xlim(0, 0.9)
ax.set_ylim(min(unclamped_values) - 0.02, simple_mean + 0.04)
format_pct_axis(ax)
add_message_title(
    ax,
    "Aggregate probability against the assumed correlation",
    subtitle="Same three forecasts throughout; the mean is the unextremized baseline",
)
ax.legend(loc="lower right")
show_with_alt(
    fig,
    "Line chart of the aggregate probability against the assumed pairwise correlation, from "
    "independent to nearly identical. Both reported series rise steadily toward the horizontal "
    "line marking the unextremized mean, and both run flat at the independent end. The dotted "
    "line showing the value before the clamp keeps falling there, below zero, which is what "
    "the flat section is hiding.",
)

# %% [markdown]
# At the dependent end the panel is credited with barely more than one observation and the
# aggregate settles onto the mean. At the independent end it is credited with three, the
# formula pushes so far below the base rate that it leaves the unit interval, and what the
# chart shows there is the floor. The agents' own forecasts never move along any of these
# curves. Everything that does move is the assumption.
#
# A clamp that carries the answer is worth naming rather than tolerating. It is not part of
# the theory: it exists so the function always returns something a downstream consumer can
# treat as a probability, and where it binds, the method has failed on this panel rather than
# answered it. The reading to take from the left of this chart is that a three-agent panel this
# far from even odds, under an independence assumption, is mapped outside the unit interval by
# this formula, which therefore has no answer to give: not that the aggregate is whatever the
# floor happens to be set to, and not that these three agents are in fact correlated.
#
# Nothing in this run estimates $\rho$, and the confidence values feeding the weighted variant
# are the extremity heuristic from [`04_research_agent`](04_research_agent.ipynb) rather than
# measured skill. So the mean is the number to report, and the curve is what says how much
# would be at stake in estimating the correlation properly.

# %% [markdown]
# ## What the Next Stages Receive
#
# Debate and supervisor reconciliation do not read the artifacts directly. They read this
# summary: the agent's id, its probability and confidence, the opening of its rationale, and,
# where the model enumerated any, its first few key findings. None of these three rationales
# enumerates anything - all three are continuous prose - so no findings block appears below,
# which is what [`04_research_agent`](04_research_agent.ipynb) means when it says the field
# records how the model chose to present its reasons. Everything else - the full search trail,
# the evidence, the uncertainties - stays in the record and out of the next prompt, which is a
# context budget decision as much as a design one.

# %%
all_summaries = "\n\n---\n\n".join(format_agent_summary(a) for a in artifacts)
print(all_summaries)

# %% [markdown]
# ## Search Execution Audit
#
# Rolling every agent's search steps into one table shows the panel's evidence-gathering at a
# glance: who asked what, and how much came back. Queries appearing in more than one agent's
# rows are shared retrieval, which is one of the two things that could explain agreement; the
# table shows the overlap and does not, on its own, attribute the spread to it.

# %%
audit_df = pl.DataFrame(
    [
        {
            "agent_id": a.agent_id,
            "step": t.step,
            "query": t.query,
            "results": len(t.results),
        }
        for a in artifacts
        for t in a.traces
        if t.action == "search"
    ]
)
audit_df

# %% [markdown]
# Two properties of the record are worth measuring rather than assuming, and the cell below
# measures both. How many of the saved prompts carried the market's own probability, and how
# many retrieved results carry a publication date.

# %%
search_results = [
    result for artifact in artifacts for trace in artifact.traces for result in trace.results
]
dated_sources = sum(result.published is not None for result in search_results)
market_mentions = sum(f"{question.current_market_price:.3f}" in str(call) for call in llm_calls)

display(
    Markdown(
        f"**Replay audit**: {market_mentions} of {len(llm_calls)} saved model calls include "
        f"the market probability; {dated_sources} of {len(search_results)} retrieved results "
        "record a publication date."
    )
)

# %% [markdown]
# Both counts bound what this run can be used for. Every prompt carried the market price, so
# the agents were told the answer the market had reached before they searched, and their
# closeness to it says nothing about their skill. No result carries a publication date, so
# nothing establishes that a document was available before the question was asked; the trace
# reproduces what the agents saw and cannot date it.

# %% [markdown]
# ## Persisting the Full Run Trace
#
# Auditing an agent means being able to reconstruct exactly what it saw and
# said. `RunTrace.capture` bundles the question, the parameters, every agent's
# structured artifact, the aggregation result, and the complete raw model
# conversation (`llm_calls` - every prompt sent and every response received,
# captured by the per-agent `TracingLLMClient`s above) into one object, and
# `save()` writes it to `forecast_traces/` as JSON. That saved file is exactly
# what the replay path above reloads: it is the durable record of this
# point-in-time run, which a reviewer can reopen long after the live market and
# web evidence have moved on. A live run (`RUN_LIVE = True`) writes a fresh trace
# here; the default replay run reports the pinned trace it loaded instead of
# overwriting it.

# %%
if RUN_LIVE:
    run = RunTrace.capture(
        notebook="06_multi_agent_research",
        provider=provider_name,
        question=question,
        params={
            "n_agents": N_AGENTS,
            "max_steps": MAX_STEPS,
            "max_search_results": MAX_SEARCH_RESULTS,
        },
        agents=artifacts,
        aggregation=result_neyman,
        final_probability=result_neyman.extremized_probability,
        notes="Parallel research agents on one pinned, market-aware question.",
        llm_calls=llm_calls,
    )
    trace_path = run.save()
    print(
        f"Saved {len(run.llm_calls)} model calls "
        f"({run.total_tokens():,} tokens) → {trace_path.relative_to(trace_path.parents[1])}"
    )
else:
    # Replay: report the pinned trace we loaded rather than writing a new file.
    run = pinned_run
    trace_path = TRACES_DIR / PINNED_TRACE
    print(
        f"Replayed {len(run.llm_calls)} model calls "
        f"({run.total_tokens():,} tokens) from {trace_path.name}"
    )

# %% [markdown]
# ## The Raw Conversation
#
# The timeline above is the parsed trace. This is what the model actually received and sent.
# For the first agent, `replay_llm_calls` prints each message in order - the system prompt, the
# question, and every tool result fed back in - beside the untruncated JSON returned at each
# step.
#
# This is where an audit ends up when a forecast looks wrong. The parsed rationale, the search
# queries and the probability are all derived from these responses, so a disagreement between
# the summary and the source is settled here. Pass `content_chars=None` for the complete
# payloads.

# %%
agent_0_calls = [c for c in llm_calls if c.label == "agent_0"]
print(replay_llm_calls(agent_0_calls, content_chars=600))

# %% [markdown]
# ## Key Takeaways
#
# 1. **Identical agents diverge, and that is the panel's entire value.** Nothing distinguishes
#    these three: same prompt, same tools, same client, same sampling temperature. Three
#    different answers come out anyway, from the model's sampling and from what each agent's
#    searches returned, in proportions this run does not separate.
# 2. **A panel is only worth aggregating if its members are worth aggregating separately.**
#    Read the timelines before the aggregate. Agents converging by different routes is evidence;
#    agents pulling identical documents and reasoning in step is one agent run three times, and
#    the aggregate will report false confidence.
# 3. **Extremization moves the answer more than the panel does.** Sweeping the correlation
#    assumption over the same three forecasts moves the aggregate further than the forecasts
#    themselves are apart. With no estimate of that correlation, the mean is the number to
#    report and the Neyman values are a sensitivity analysis around it.
# 4. **An agent handed the market's own probability is not an independent check on it.** This
#    capture put the market price in every prompt, so the agents' proximity to it is not
#    evidence about their skill.
# 5. **Parallelism is a thread pool and a per-agent tracer.** Agents share the model client and
#    the search client, so both have to be safe under concurrent calls; each gets its own
#    tracer, which is what keeps the captured conversations correctly attributed.
#
# **Known limitations of what is built here.** One capture, one question, three agents: the
# spread has no error bar and nothing establishes it would recur. The confidence values feeding
# the weighted aggregate are the extremity heuristic from
# [`04_research_agent`](04_research_agent.ipynb), not measured skill. No retrieved result
# carries a publication date, so nothing here can be scored as a point-in-time forecast. And
# the agents differ only by sampling: a panel built to be diverse would vary the model, the
# search index, or the framing of the question.
#
# **Next**: [`07_adversarial_debate`](07_adversarial_debate.ipynb) takes a panel that disagrees
# and makes the disagreement do work, by having the agents argue the two sides.
#
# **Book**: Section 24.7 presents multi-agent forecasting systems.

```