law of large numbers

Posted: January 4th, 2007 | Author: Alex | Filed under: perception | No Comments »

The law of large numbers is interesting and useful:

For example, the average weight of 10 apples taken from a barrel of 100 apples is probably closer to the “real” average weight of all 100 apples than the average weight of 3 apples taken from that same barrel. This is because the sample of 10 is a larger number than the sample of only 3 and better represents the whole group. If you took a sample of 99 apples out of 100 apples, the average would be almost exactly the same as the average for all 100 apples.

This is not just logical, but it also appears so intuitive as to be self-evident.

And yet: Looking at product ratings, it is often easy to give preference to a product with a 5-star rating to one with a lower 4-star rating. Of course, the rating itself really loses much of its meaning without knowing the number of people who would agree with it. Maybe a product that received 100 4-star ratings (and no others) is of higher quality than a product that received 10 5-star ratings (and no others).

Yes, these ratings, especially in a context of collaborative filtering are subjective. Just because someone enjoyed a product (show, etc.) does not mean that you will, too. But that exactly is the power of large numbers: The more people enjoy a product the higher the probability that that will be the case for you, too.

However: It frequently and indeed subtlely appears to be intuitive to accept  certains claims as true, even though they would – upon further investigation – seem improbable. Often, we like to look for conclusions that can confirm just exactly what we want to believe. I suspect this is true in those cases as well – at least to some degree.

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