Source
Handfield, Garcia, Hilbe and Yeo (2025), arXiv:2504.06485, LIT-966, read in full in NOTE-795: §§2.4–2.6, Table 1, Fig 5, and SI C and D.3.
What was actually shown
- The setting.
- Two debaters hold truth assignments to n = 3 atomic propositions.
- Valid two-premise arguments eliminate positions.
- A refuted debater moves to the nearest tenable position.
- Each picks one of 16 premise × conclusion rules, or Exit.
- The debate continues with probability δ after each argument.
- Payoffs are u = w·v − d, with v the number of true beliefs at the end and d the total revisions, computed exactly by Markov chain.
- The dilemma (Table 1, δ = 0.8).
- At truth weight 2.5 there is a prisoner’s dilemma.
- At 3.5, a stag hunt and a snowdrift.
- At 4.5, a snowdrift.
- At 9.5, none.
- The cooperative action in each pair is the more epistemically productive one.
- The free-riding equilibrium (§2.6.3). At moderate truth weight or in longer debates, the best reply to the bold S+S− is a compromise strategy such as S+O+. That strategy forces a change of mind only on propositions where the two disagree. The result is an asymmetric equilibrium with “a modest loss of collective accuracy”.
- Disengagement.
- At low w, (Exit, Exit) is the selected equilibrium, an “agreement to disagree”.
- With error (α = 0.1, 0.3), Exit takes over much of the space.
- Non-monotonicity (§2.6.5, Fig 5, Fig 9). At α = 0 and 0.1 there is a borderline band with no pure equilibrium. There, in the mixed equilibrium, a player who cares more about truth faces an opponent who must more often play strategies that frustrate it, so collective accuracy dips as w rises. The dip survives a utilitarian equilibrium-selection rule.
What could have come out otherwise: mutual boldness could have been an equilibrium wherever truth is valued, as it is at high w in short debates. Accuracy could have risen monotonically in w.
What this does not say
- Not that a group settles on a belief no member reasoned to. The outcome measured is collective accuracy, the mean of two individual accuracies. Consensus is tracked separately and is not the result.
- Not about communities. There are two debaters. Whether the snowdrift becomes a many-player public-goods problem is untested.
- Not that truth-seeking motives backfire in general. The dip is local, small and confined to a band of mixed equilibria. At high truth weight in short debates the unique equilibrium is truth-optimal.
- Not about debaters with pure epistemic motives. Obstinacy is built into the utility. The paper argues informally (§3) that obstinacy is rational under deductive refutation. The result holds for agents who pay a cost to revise.
- Not robust to the strategy space, as far as shown. Strategies are fixed, memoryless rules over current positions. The targeted “ideal cooperative debater” lies outside them, and so does any learning.
- Not independent of equilibrium selection. (Exit, Exit) is an equilibrium everywhere. The regimes describe the truth-optimal equilibrium among those left after removing weakly dominated strategies.
Connections
- QUESTION-047. A named mechanism by which individually rational
inquirers produce a worse collective epistemic state: the costs of
being refuted are private and the benefits shared. It bears on the
question’s “which mechanisms”, for a pair. No
answers:relation is declared, because the paper does not show a belief that the pair settles on. - THEORY-148 (transient diversity). Both concern how much disagreement a group should sustain. There, too little lasting diversity loses the better option. Here, refusal to bear revision costs leaves disagreement standing where mutual boldness would have removed it. The paper cites Zollman for “why expert communities sometimes maintain mistaken consensus” without modelling it.
Note of 2026-10-19: what the narrowing keeps and why
The promotion audit reviewed this entry in batch 041. Its title is a model result, not an argument: “argument” there names what the debaters exchange. It is not a theorem either. The paper proves nothing, and checking it by hand would mean recomputing a 2,816-state Markov chain over a 17 × 17 payoff table. So it was judged as one study under ADR-047 v3, on the precedent of THEORY-178.
- Kept: the snowdrift equilibrium (§2.6.3, Table 1 at δ = 0.8, Fig 5) and the dip in accuracy as the truth weight rises, which Fig 5 shows and NOTE-795 viewed as a rendered page. The dip is small and lies in the band without a pure equilibrium, and the title now says where it lies.
- Dropped: the unqualified “debaters”. Every exact result is for two players and n = 3, and the strategy space excludes the targeted “ideal cooperative debater”. Those extensions are QUESTION-173.
- Still carried by the body: the dependence on equilibrium selection. (Exit, Exit) is always an equilibrium, and the regimes describe the most truth-conducive equilibrium left after removing weakly dominated strategies.