Are birds smarter than mathematicians? Pigeons (Columba livia) perform optimally on a version of the Monty Hall Dilemma

Abstract

The "Monty Hall Dilemma" (MHD) is a well known probability puzzle in which a player tries to guess which of three doors conceals a desirable prize. After an initial choice is made, one of the remaining doors is opened, revealing no prize. The player is then given the option of staying with their initial guess or switching to the other unopened door. Most people opt to stay with their initial guess, despite the fact that switching doubles the probability of winning. A series of experiments investigated whether pigeons (Columba livia), like most humans, would fail to maximize their expected winnings in a version of the MHD. Birds completed multiple trials of a standard MHD, with the three response keys in an operant chamber serving as the three doors and access to mixed grain as the prize. Across experiments, the probability of gaining reinforcement for switching and staying was manipulated, and birds adjusted their probability of switching and staying to approximate the optimal strategy. Replication of the procedure with human participants showed that humans failed to adopt optimal strategies, even with extensive training.

Figure 1

Proportion of switching (left bars) and staying (right bars) responses, averaged across all birds in Experiment 1. The top panel represents the first day of training, and the bottom panel represents the 30th day of training. Error bars represent 95% confidence intervals.

Figure 2

Percent of reinforced trials on Day 1 (left bar) and Day 30 (right bar) averaged across all birds in Experiment 1. Reference lines show the expected performance for a strategy of always switching (67%), guessing randomly (50%), and always staying (33%). Error bars represent 95% confidence intervals.

Figure 3

Proportion of switching (left bars) and staying (right bars) responses, averaged across all birds in Experiment 2. The top panel represents the first day of training, and the bottom panel represents the 15th day of training. Error bars represent 95% confidence intervals.

Figure 4

Proportion of switching (left bars) and staying (right bars) responses, averaged across all human participants in Condition 1 of Experiment 3. The top panel represents the first 50 trials, and the bottom panel represents the final 50 trials. Error bars represent 95% confidence intervals. Reference lines show the probability of switching by pigeons during the first (top panel) and final (bottom panel) days of training in Experiment 1.

Figure 5

Proportion of switching (left bars) and staying (right bars) responses, averaged across all human participants in Condition 2 of Experiment 3. The top panel represents the first 50 trials, and the bottom panel represents the final 50 trials. Error bars represent 95% confidence intervals. Reference lines show the probability of switching by pigeons during the first (top panel) and final (bottom panel) days of training in Experiment 2.

Figure 6

Probability of switching in both conditions of Experiment 4 across trials. Each data point represents the average of 10 consecutive trials. Error bars represent one standard error.

Figure 7

Proportion of switching (left bars) and staying (right bars) responses, averaged across all birds in Experiment 4. The top panel represents the first day of training, and the bottom panel represents the 30th day of training. Error bars represent 95% confidence intervals.

Figure 8

Daily probability of switching for three individual birds (birds 10, 11, and 12) in Experiment 4.

Figure 9

Percent of reinforcers earned for staying, for all six birds in Experiment 4. Left (dark) bars represent the first five days of training. Middle (light) bars represent the second five days of training. Right (medium) bars represent the 30th and final day of training.