A token-budget method predicts when debate groups help

When a language-model group reads one another’s answers, does the extra information improve accuracy enough to repay the reasoning space those messages use? This matters when reading and generating compete for the same fixed token window, where adding members can shrink each member’s room to reason.

TB-MAD uses single-agent tests and early answers to estimate vote accuracy, then chooses a debate group size without calibrating through debate.

TB-MAD measures how one agent’s accuracy changes as its generation allowance changes, and uses initial answers to estimate how agents’ errors relate. It combines these measurements to predict vote accuracy and choose a group size without running debate during calibration.

Across five open models and four reasoning tasks, TB-MAD’s average held-out accuracy gap from each model-task pair’s best configuration was 1.40 percentage points, versus 1.58 for the closest probe-calibrated method. The result supports its selection rule at the tested calibration spends.

These conclusions apply to the paper’s shared-window setup and its tested models and tasks. The group-accuracy model is an approximation, and the debate comparison includes one revision round whose effect is not covered by the initial-round theory.