A paper I'm reading (Davis-Stober et al, 2014) contains the following statement:

A crowd is wise if a linear aggregate, for example a mean, of its members’ judgments is closer to the target value than a randomly, but not necessarily uniformly, sampled member of the crowd. (p79)

When I googled "linear aggregate" I didn't find any definitions or Wikipedia pages devoted to this concept.

It would be helpful if in addition to a definition the answerer could provide some more examples of linear aggregates, and some examples of nonlinear aggregates.

Davis-Stober, C. P., Budescu, D. V., Dana, J., & Broomell, S. B. (2014). When is a crowd wise?. Decision, 1(2), 79-101.

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    $\begingroup$ I would say that is is an 'aggregate' that is defined as a linear function, e.g. a sum $x_1+x_2+\dots x_n$ or an average$\frac{x_1+x_2+\dots x_n}{n}$ are both linear aggregates, a weighted average is another example. $\endgroup$
    – user83346
    Aug 30, 2015 at 13:26
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    $\begingroup$ "Linear combination" is a standard term. In the context it might be intended that the coefficients sum to unity and possibly even be non-negative, which would make it a weighted arithmetic mean. $\endgroup$
    – whuber
    Apr 1 at 15:36

1 Answer 1


It's not a technical term. fcop's comment summarizes my thoughts: it's any linear function that aggregates the data.

Without getting too technical, a "linear function" is any function $f$ with the following two properties: $$ f(x + y) = f(x) + f(y) \\ f(ax) = af(x) $$ There's a lot more detail on Wikipedia about what this definition implies.

For our purposes, it encompasses all functions that aggregate data points additively. The mean, $\frac{\sum x}{n}$, is probably the most famous and most useful such function. It shouldn't be hard for you to convince yourself that it is in fact a linear function (with respect to each data point) as per the above definition.

To be honest, I'm not aware of any useful "linear aggregates" exist apart from the mean. There are, however, several useful nonlinear aggregates; The median and standard deviation both fall into this category.

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    $\begingroup$ Hello. I took the liberty of submitting an edit and writing $\frac{\sum x}{n}$ instead of $\frac{n}{\sum x}$, since that looked like a typo. $\endgroup$
    – Stef
    Apr 1 at 13:39

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