Telephone Game With Functions

In the old telephone game each person would pass on a phrase to the next person in the chain; the final phrase might little resemble the first.  An interesting variation appeared in the Phil. Trans. Royal Society last November:

Here each row is a chain of people passing along a function relating X to Y.  Each person first guesses and is corrected on 50 (X,Y) cases, then just guesses on 100 more cases.  The final guesses of the last person become data for the next person.  The final relations are all basically lines, 7/8 with a positive slope, 1/8 with a negative slope.

The lesson?  When we are mainly rewarded for predicting what others will say on a topic, rather than predicting a more basic reality, our answers become dominated by typical prior expectations; reality has little influence.  HT to Jef Allbright. More from that paper:

In situations in which each person’s response is used to determine the data seen by the next person, people converge on concepts consistent with their inductive biases irrespective of the information seen by the first member of the chain. …

In this experiment, each generation of par ticipants received 50 trials of training on a single function. On each trial, the value of the stimulus was presented as a visual magnitude, being the width of a horizontal bar on a computer screen.  Participants responded by adjusting the height of a vertical bar and then received corrective feedback. … After training, participants responded to 100 stimuli that covered the entire possible range of magnitudes without receiving feedback. …

Participants were arranged into eight families of nine generations, for each of four conditions. The conditions differed with respect to the function used to generate the training data seen by the ﬁrst generation of participants: those initial values were drawn either from a positive linear, negative linear or quadratic function, or entirely at random. … The responses of each participant on 50 of the test trials were taken as the data used to train the participant in the next generation of that family. …

Across generations all of the initial functions gradually disappeared and transited into only one of two stable functions: positive linear (28 out of 32 families) and negative linear (4 out of 32), both with approximately unit slope.

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