Cooperative Dilemmas in Rational Debate

TL;DR

We address how rational debate can fail to maximize truth due to cooperative dilemmas between truth-seeking and obstinacy. A two-debater framework is introduced where each agent occupies a binary vector over $n$ propositions; arguments deductively prune tenable positions, and a continuation probability $\\delta$ together with an error rate $\\alpha$ shape dynamics. The study identifies regimes and equilibria (e.g., bold, conservative, refusenik, compromising) and shows that higher truth-motivation can paradoxically reduce collective accuracy in longer debates. These results illuminate the social dynamics of knowledge production and have implications for fostering productive cooperation and mitigating polarization in public discourse.

Abstract

As an epistemic activity, rational debate and discussion requires cooperation, yet involves a tension between collective and individual interests. While all participants benefit from collective outcomes like reaching consensus on true beliefs, individuals face personal costs when changing their minds. This creates an incentive for each debater to let others bear the cognitive burden of exploring alternative perspectives. We present a model to examine the strategic dynamics between debaters motivated by two competing goals: discovering truth and minimizing belief revisions. Our model demonstrates that this tension creates social dilemmas where strategies that are optimal for individuals systematically undermine the collective pursuit of truth. Paradoxically, our analysis reveals that increasing debaters' motivation to seek truth can sometimes produce equilibria with worse outcomes for collective truth discovery. These findings illuminate why rational debate can fail to achieve optimal epistemic outcomes, even when participants genuinely value truth.

Figures (9)

• Figure 1: Evolution of a debate over three propositions. The debater positions are indicated by the red and blue nodes, while the truth is the yellow node (A). Red introduces an argument which forces Blue to adopt a new position (B). Blue produces an argument which affects an unoccupied position (C). At the end of the debate, Red has 2 true beliefs and Blue has one true belief (D).
• Figure 2: Expected collective accuracy over debate length, for all strategy profiles grouped by type. A:$\geq 1$ bold strategy B: both conservative C: both refusenik D:$\geq 1$ compromising, none bold. $n = 3$.
• Figure 3: Expected collective accuracy over debate length, for varying levels of $\alpha$. Profiles from Table 1 are identified in the legend. At $\alpha = 0$, the strategy profile (S+S--,S+S--) is truth maximizing for all levels of $\delta$, but at non-zero $\alpha$, other, less argumentative strategies, fare better in long debates.
• Figure 4: Harmony/conflict index (rank correlation of players' payoffs) across parameter space. To focus the analysis on the most relevant payoff differences, we have first removed dominated strategies. In white areas, the conflict index is undefined, because there is only one dominant strategy.
• Figure 5: Upper panels: overview of equilibrium types at various levels of $\alpha$. Lower panels: Collective accuracy of beliefs (normalized) as a function of debaters' truth-weight in the utility function, at various levels of $\alpha, \delta$.

Theorems & Definitions (2)

• Example 1
• Example 2