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aggregation

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    Paradox & Proof Entry #0157

    Why a growing company can have shrinking margins on every sale

    Total profit and profit per unit are separate quantities that can move in opposite directions. Growth is reported in one of them and health is assumed in both.

    Novice
    The hidden part #0157

    A total is a rate times a volume. Growth in the product says nothing about the direction of either factor.

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    Paradox & Proof Entry #0156

    The reason improving every hospital can worsen the statistics

    Every department improved. The overall figure got worse. Both statements are true at once, and the reason is one of the most useful traps in data.

    Master
    The hidden part #0156

    A total is not a neutral summary of its parts. It is the result of a grouping decision, and that decision can point the conclusion in either direction.

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    Statistical Illusions Entry #0429

    The reason two true statistics can contradict each other

    One batter can have a higher average than another in every single season and a lower average across both. Neither figure is wrong; the weighting differs.

    Adept
    The hidden part #0429

    A combined average is weighted by attempt counts. Change the weights and the comparison can reverse without any figure being wrong.

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    Paradox & Proof Entry #0165

    Why a market can be efficient and wrong at once

    Efficiency means a price has absorbed the available information. It says nothing about whether that information was complete, and the two are often confused.

    Master
    The hidden part #0165

    Efficiency describes how fast information reaches a price. It makes no claim about how good that information was.

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    Paradox & Proof Entry #0171

    Why voting can produce a result nobody wanted

    Individual preferences can be perfectly consistent while the group preference formed from them is not. The cycle is a property of aggregation.

    Novice
    The hidden part #0171

    Transitivity does not survive aggregation. Where a cycle exists the agenda order picks the winner, through a rule that looks purely procedural.

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