ESR221 Fall 2002

Heuristic: Recognition

Part A: You can rank pairs of items from a long list suprising effectively if you can remember only the top several items.

For example if you know the ranking of the top five cities out of a list of a number of cites, you will be able to determine which city is bigger in many pairs.

The table below illustrates all of the possible pairings between the different cities. Since you don't compare a city with itself and the order of comparison doesn't matter, the number of comparisons is limited.

R = know directly
k = know because you know that one is one of the top ranked cities
u = you don't know the answer

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1

 R R R R k k k k k k k k k k
2 R R R k k k k k k k k k k
3 R R k k k k k k k k k k
4 R k k k k k k k k k k
5 k k k k k k k k k k
6 u u u u u u u u u
7 u u u u u u u u
8 u u u u u u u
9 u u u u u u
10 u u u u u
11 u u u u
12 u u u
13 u u
14 u
15

This leads to the following %known comparisons.

number of cities % known
6 100%
7 95%
8 89%
9 83%
10 78%
15 57%
20 45%
25 37%
30 31%
35 27%
40 24%

 

 

Part B: Even if you only recognize the top five ranked items, but can't rank them, this will still give you the ability to rank pairs pretty effectively.

F = fuzzy recognition, know it's one of the top five but you don't know the order.
k = know because you know that one is one of the top ranked cities
u = you don't know the answer

The number of correctly ranked pairs would come from comparing the top 5 to the unrecognized, but presumably smaller cities. This example shows that value of not knowing anything about these cities.

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1

 F F F F k k k k k k k k k k
2 F F F k k k k k k k k k k
3 F F k k k k k k k k k k
4 F k k k k k k k k k k
5 k k k k k k k k k k
6 u u u u u u u u u
7 u u u u u u u u
8 u u u u u u u
9 u u u u u u
10 u u u u u
11 u u u u
12 u u u
13 u u
14 u
15

 

cities ratio % known
6 5/15 33%
7 10/21 48%
8 15/28 53%
9 20/36 56%
10 25/45 56%
11 30/55 55%
12 35/66 53%
13 40/78 51%
14 45/91 49%
15 50/105 48%

 

 

 

Daniel Goldstein and Gerd Gigerenzer (1999) The Recognition Heuristic: How Ignorance Makes Us Smart. Chapter 2. In:Simple Heuristics That Make Us Smart. Gerd Gigerenzer, Peter M. Todd and the ABC Research Group. Oxford University Press, Oxford. pp 37-58.

John Rueter
ESR221
January 8, 2002