In Tree of Thought, how does value prompting differ from vote prompting?

## Why partial states need scoring Tree of Thought treats reasoning as search. Once candidate next steps exist, something must decide which partial states to expand and which to abandon. That decision is the state-evaluation step, and it is what separates a useful tree from an expensive random walk: if the evaluator carries no signal, branching only multiplies cost. A state is a *partial* solution — two steps of a synthesis route, half an outline, an unfinished program. Nothing has been verified because nothing is finished, so evaluation is always a prediction about a future that has not happened yet: how likely is it that continuing from here reaches a good answer? Two prompting shapes dominate. ## Value prompting: an independent verdict per state Value prompting hands the model one state and asks for a judgement about that state alone. The output can be a number on a fixed scale, a probability-like score, or a small ordinal vocabulary. Coarse labels usually behave better than fine-grained numbers, because a model asked for "7.3 out of 10" is inventing precision it does not have. The original Tree of Thoughts formulation used three buckets — sure, likely, impossible — and mapped them to numeric values. Because each judgement stands alone, the scores mean roughly the same thing everywhere in the tree. That has two consequences. First, you can compare states at different depths and on different branches. Second, you can set an absolute cutoff and prune anything beneath it, which is impossible with a purely relative signal. The price is variance and calibration. A single sample of a value prompt is noisy, so practitioners sample the evaluation several times and average, which multiplies the call count. Worse, absolute scores drift with depth: a model often rates a longer, more elaborated state higher simply because it looks more finished, not because it is more likely to succeed. Consider a retrosynthesis planner working backwards from a target molecule. Each state is a proposed intermediate compound, and the value prompt asks whether that intermediate is reachable from reagents on the shelf — sure, likely, or impossible. "Impossible" is the cheap, high-value verdict: it kills a whole subtree in one call. ## Vote prompting: rank the siblings against each other Vote prompting inverts the framing. All candidate states from one expansion go into a single prompt, and the model is asked which one is most promising, with a short justification. That comparison is sampled repeatedly — five or so times is common — and the state with the most votes wins. Comparative judgement is generally easier for a model than absolute judgement, in the same way a human reviewer ranks three drafts more reliably than they assign each a number out of ten. Suppose the task is a grant proposal and three partial outlines exist; asking five sampled comparisons which outline best fits the funder's stated criteria produces a more stable ordering than three independent scores would. Voting also amortizes cost. One prompt covers every sibling, so a five-sample vote over four candidates is five calls total rather than the twenty a five-sample value prompt would need. The limitation is that votes are ordinal and local. You learn which sibling is best, not whether any of them is good. If every candidate at a node is hopeless, voting still elects a winner and the search happily walks into the dead end. Vote prompts are also sensitive to how options are presented; shuffling the order across samples is a cheap defence against the model favouring a fixed position. ## Choosing between them Use value prompting when you need an absolute cutoff, when states must be compared across branches or depths, or when the task has a natural feasibility verdict that can kill a subtree outright. Use vote prompting when the task is open-ended and quality is inherently comparative — writing, planning, design — or when the call budget is tight relative to the branching factor. The two also compose. A common arrangement uses a cheap value pass to eliminate clearly dead states, then a vote among the survivors to pick what to expand. That keeps the absolute floor while spending the more expensive comparative judgement only where it changes the outcome. ## What goes wrong The recurring failures are the same in both shapes. Single-sample evaluation is too noisy to trust. Scores that look precise are not necessarily calibrated, so a threshold picked by intuition can silently discard correct solutions. And if the evaluator carries no real signal for the task, it degrades to random selection — at which point the tree costs many times a single linear pass and returns no more accuracy. Before scaling a tree, it is worth checking that the evaluator can distinguish states you already know are good from states you know are bad.