Why Splitting 12 Options into 3 Groups of 4 Actually Helps
Under Hick's Law, decision time scales with the number of choices — but why does splitting 12 flat options into 3 groups of 4 measurably reduce decision time, rather than just feeling less busy?
The correct answer is "The relationship is logarithmic, so two smaller log2 decisions beat one larger one."
Hick's Law's formal relationship is logarithmic: decision time scales with log2(n) for n roughly-equally-likely choices, not linearly. Splitting 12 flat options into 3 groups of 4 turns one log2(12) decision into a log2(3) decision followed by a log2(4) decision, and the sum of those two smaller logs is meaningfully less than the one larger log — grouping reduces the effective branching factor of the decision, not just the visual clutter.
The distractors misstate the mechanism: the relationship isn't linear, so "12 minus 5 grouped choices equals 7" isn't how the cost actually works; grouping doesn't remove any items from consideration — all 12 remain reachable, it just reorganizes how they're decided among; and Hick's Law does apply here — the whole point of the example is that grouping measurably helps because of the logarithmic relationship, not that the law is inapplicable.
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