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- W90840747 abstract "Questions involving (re)aggregating parts into wholes are fundamental to all branches of scientific inquiry Saari (2001). After discussing two very general insights we derive from the aggregation literature, we look at how wholes may sometimes be reconstructed from their parts when we weight the parts appropriately, and we show that the notion of weighted averages can be used to make sense of seeming paradoxes: including how family income can go down even though per capita income is going up; how standardized test scores can go down even though the scores of every racial and ethnic group taking the test is going up; why most people think that roads are crowded even though most of the time there may be hardly any cars on the road; why teachers can teach mostly small classes, yet students can take mostly large ones; why George Bush could have won the Electoral College in 2000 even though he loses the popular vote; and why your friends can be expected to have more friends than you do. Questions involving aggregating parts into wholes are fundamental to all branches of scientific inquiry. Saari (2001). For example, there is huge literature on aggregation issues in social choice theory (see reviews in Saari (1994), Saari (1995); Nurmi(1999), and another one in statistics with statistical applications ranging from demography to brain imaging (see e.g., King (1997) to information pooling (see e.g., Grofman (1986). After a brief review of some insights from this literature we will focus on the implications of the simple idea of a “weighted” average, and show that understanding the properties of weighted averages allows us to understand some seeming paradoxes and puzzles involving composition effects. We conclude this essay with a few brief observations about other important types of averages most notably the geometric mean and the harmonic mean." @default.
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- W90840747 date "2010-01-01" @default.
- W90840747 modified "2023-10-16" @default.
- W90840747 title "Puzzles and Paradoxes Involving Averages: An Intuitive Approach" @default.
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- W90840747 doi "https://doi.org/10.1007/978-3-642-02865-6_10" @default.
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