The Matching Law. Definitions. Herrnstein (1961) 20/03/15. Erik Arntzen HiOA Mars, 2015

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1 The Matching Law Erik Arntzen HiOA Mars, Definitions The Matching Law states that responses are allocated to the richest reinforcement schedules. The Matching Law has been shown in both nonhumans and humans. 2 Herrnstein (1961) Concurrent VI VI schedules of reinforcement. 1.5 s COD (Change over delay) 3 1

2 The Matching Law Let ra be four reinforcers per min rb be one reinforcer per min What will the pigeon do? Switching between the schedules at random? Spending all the time at A? The matching law predicts RA/RB= ra/rb = 4/1 =4. The pigeon should make Response A four times more than the Response B 4 Why this is important Prediction of behavior is one purpose for behavior analysis Therefore, it is important to study functional relationships between environmental events and behavior Rate of reinforcement is such an event Matching Law is a functional relationship in which the environmental event is related to behavior The Matching Law suggests that if we can accurately assess rates of reinforcement, then we may also be able to predict rates of response or behavioral likelihood To the extent that this functional relationship holds, it also gives us an explanation of the behaviors involved Such functional relationships (or explanations) provide practical interpretations of other, more complex behavior 5 Another example Let ra = 4 reinforcers per minute (e.g., VI 15 ) rb = 1 reinforcer per 2 minute (e.g., VI 2min) =.5 reinforcer per minute* *Note: ra and rb must be expressed in same units of measure, in this case, reinforcers per minute P(RA) = RA/(RA+ RB) = ra/(ra+ rb) = 4/(4 +.5) = 4/4.5 =.89 = P(RA) 6 2

3 Ulike formler B = Behavior R = reinforcers B = Behavior r = reinforcers R = responses r = reinforcers

4 Ulike mønstre ved matching Matching Proporsjonen av responser matcher eller er lik proporsjonen av forsterkere. Undermatching Proporsjonen av responser er lavere en proporsjonen av forsterkere. Overmatching Proporsjonen av responser er høyere en proporsjonen av forsterkere 10 Extension of the Matching Law Baum (1974) a= slope k= intercept 11 Pierce and Cheney (2013)

5 13 From Barrero and Vollmer (2002) They are studying severe behavior problems in 4 individuals with varying degrees of developmental disabilities Linda, a 14-year-old girl showing aggression and disruption. Mandy, a 24-year-old woman with Sticklers syndrom showing selfinjurious behavior as head banging, nose punching, chin punching, and head hitting. Max, a 7-year-old boy diagnosed with autism. He was showing aggression, consisting of hitting, slapping, and pulling hear of others. Dan, a 9-year-old boy showing aggression and disrupting behavior which consisted of hitting and kicking others, bangig against walls, throwing materialism and property destruction. 14 From Barrero and Vollmer (2002) 15 5

6 Vollmer and Bouret (2000) They studied basketball and two- and three-point shots. The results showed that players allocated responding in accordance with relative reinforcement rate for two-and three-point shots Conger and Killeen (1976) 19 6

7 20 21 Questions about choice Discuss the small and immediate and large and long term (delayed) consequences To study for the MALKA212 exam or watching soap on TV. To go jogging or watching a soccer match on TV. To get up when the alarm clock rings or sleep in 22 7

8 Introduction The matching law suggests that response rate will be proportional to the amount/duration of positive reinforcement delivered. Foxall (1999) gave the first theoretical attempt to apply Herrnstein s matching law on consumer behavior. Foxall proposes that the proportion of money spent for a product match the proportion of reinforcers earned. Consumer behavioral studies by Foxall and colleagues (Foxall & James, 2002, 2003; Foxall & Schrezenmaier, 2003; Foxall et al.,2004) have accumulated comprehensive knowledge about consumers choice pattern based on Herrnstein s Matching law. 2 Purpose We wanted to employ an experiment by arranging a simulated on-line purchase situation with different schedules of reinforcement for two groups of participants. Furthermore, we wanted to compare the allocation of responses on the two alternatives between the two groups, that is, VR4 and VR8 for Group 1 and VR4 and VR16 for Group 2. In addition, we wanted to expand the knowledge in choice situations by comparing switching within and switching between alternatives, and average choice time. Method Participants Group 1: Twenty male students. Group 2: Sixteen males and 4 females. All participants had purchased on-line previously. Apparatus and Setting Two web shops were made in Macromedia Dreamweaver. MediaLab was used to present the tasks. 8

9 Procedure The participants were instructed to buy 116 products in a simulated web shop. They could buy either from a blue web shop or from an orange web shop. Free shipment was presumed to be a reinforcing stimulus, and was presented after the participant had chosen and confirmed the order. FR1 was arranged for the first 4 choices. VR4 and VR8 were arranged for the next 112 choices. 5 Step 1 Step 2 Step 3 Step 4 Post-experimental interview When all 116 products had been bought, the participants were asked two debriefing questions: What influenced your choice of web shop? Were there any differences between the two web shops? 9

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11 Matching 8 Undermatching 6 Color sensitive 2 Extinction 4 N = 20 11

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13 Matching 10 No matching 1 Undermatching 3 Color sensitive 5 Extinction 1 N = 20 13

14 Discussion We found that participants responded in according to four different patterns, that is, matching, undermatching, color sensitivity or extinction. This distinctions of patterns is relevant to Baum s (1974) expansion of the matching equation by including bias and under-matching. Most participants (33 out of 40) switched between the web shops. This support studies by Ehrenberg (1988), who found that only a few consumers are loyal to one alternative. Hence, most consumers purchase several alternatives over a sequence of purchases. con t Moreover, we found matching in 18 out of 40 participants. Hence, not as frequently as in the correlational studies by Foxall and colleagues (e.g., Foxall & James, 2001). However, the frequency of undermatching is higher when the difference in density of reinforcement between the reinforcement schedules is smaller (in Group 1 there were 6 occurrences of undermatching while 3 in Group 2). This finding is supported by Baum (1974) who claims that poor discrimination between alternatives might produce more cases of undermatching. Finally, we have identified cases, such as Participant 6 and 8 in Group 1 and Participant 3 and 17 in Group 2, that from a simple calculation based on Herrnstein s (1961) equation would be misclassified as matching. Further Research Replicate the present study with VI/VI schedules. Arrange more measurement points within one group so that it is possible to do calculation based on Baum s generalized Matching Law. Increase number of responses. Increase change over delay (COD) to see if this reduce cases with undermatching. Include tokens instead of free shipping. 14

15 Conclusion The experiment showed response patterns indicating matching, undermatching, color sensitivity, or extinction. The present study represents one out of few attempts to apply matching theory in the analysis of consumer decision behavior by observing individual behavior. Information about individual behavior is important for the complementarity of comprehension and precision, which is vital to our understanding and explanation of consumers choice. Self-control