An application of the matching law to social dynamics - Eric

AN APPLICATION OF THE MATCHING LAW TO SOCIAL DYNAMICS

JOHN C. BORRERO, STEPHANY S. CRISOLO, QIUCHEN TU, WESTON A. RIELAND,NOEL A. ROSS, MONICA T. FRANCISCO, AND KENNY Y. YAMAMOTO

UNIVERSITY OF THE PACIFIC

Using a procedure similar to the one described by Conger and Killeen (1974), we evaluatedlevels of attending for 25 college students who participated in either a 20-min (n 5 12) or 30-min (n 5 13) discussion on juvenile delinquency. Confederates delivered statements ofagreement (e.g., ‘‘I agree with that point’’) according to independent variable-interval schedules.Pooled results were evaluated using three generalized formulations of the matching law, andshowed that matching was more likely during the first 5 min of the discussion than during thelast 5 min. Individual data for 7 of 9 participants were better described by the generalizedresponse-rate matching equation than by the generalized time-allocation matching equationwhen response allocation was characterized in terms of frequency rather than duration.

DESCRIPTORS: choice, matching law, social dynamics, conversation, agreement, verbalbehavior

_______________________________________________________________________________

Response allocation under concurrent sched-ules of reinforcement has been the subject ofappreciable basic and applied behavior-analyticresearch (Fisher & Mazur, 1997). This may bedue in part to the ubiquitous nature ofconcurrent schedules in the natural environ-ment. As suggested by McDowell (1988, 1989)and others, at any moment, organisms havethe opportunity to engage in one of severalconcurrently available responses (e.g., reada newspaper, mow the lawn, or go for a run).Similarly, a pigeon may peck one of twoconcurrently available keys, or engage ingrooming, and so on. Which one of two ormore available alternatives is selected describeschoice (Catania, 1998), and by observing choiceand subsequent preference, we look next to thevariables that control response allocation.

Behavior-analytic research on choice hasshown that there are a number of factors thatmay contribute to response allocation (e.g.,reinforcer quality, reinforcer magnitude), per-haps the most widely studied of which isreinforcer rate. Given two concurrently availableresponse alternatives (all other variables beingequal), response allocation has been shown to bea function of relative reinforcer rates associatedwith each alternative. This frequently observedlinear relation between relative response rate andrelative reinforcer rate is known as the matchinglaw, and was first described by Herrnstein(1961). Herrnstein assessed the responding ofpigeons when key pecking was exposed to a seriesof concurrent variable-interval (VI) schedules.For example, one pair of schedules arrangedreinforcers on the left key according to a VI 75-sschedule while reinforcers on the right key werearranged according to a VI 270-s schedule.Across all pairs of concurrent-schedule arrange-ments, relative response allocation occurred inlinear relation to relative reinforcer rates, whenthe appropriate changeover delay was included aspart of the procedure. These results were assessedin terms of the following equation:

R1

R1 z R2

~r1

r1 z r2

; ð1Þ

This experiment was completed as a senior project bythe second and third authors under the supervision of thefirst. We thank Andrew Samaha for his assistance insoftware development. We also thank Pauline Cabales andHong Nguyen for their assistance in completing thisproject. Portions of this research were presented at the25th meeting of the California Association for BehaviorAnalysis in Burlingame. Monica Francisco is now at theUniversity of Kansas.

Direct correspondence to John C. Borrero, who is nowat the Department of Psychology, University of MarylandBaltimore County, 1000 Hilltop Circle, Baltimore,Maryland 21250 (e-mail: [email protected]).

doi: 10.1901/jaba.2007.589–601

JOURNAL OF APPLIED BEHAVIOR ANALYSIS 2007, 40, 589–601 NUMBER 4 (WINTER 2007)

589

where R1 and R2 represent the rate of respondingto the left and right keys, respectively, and r1 andr2 represent the rate of reinforcement forresponses to the left and right keys, respectively.Equation 1 is often referred to as the pro-portional matching equation or the strictmatching equation.

Based on certain deviations from strictmatching as described by Herrnstein (1961),Baum (1974) proposed what is now known asthe generalized matching equation, or moreformally,

logR1

R2

� �~s log

r1

r2

� �z log b; ð2Þ

where R1, R2, r1, and r2 represent the samefeatures of the environment described inEquation 1. The s parameter describes sensitiv-ity (the slope), and the b parameter describesresponse bias (the intercept). The generalizedmatching equation takes into account perfor-mance sensitivity (s) given a one-unit change inthe relative reinforcer ratio. For example, if aninitial reinforcer ratio of 2:1 (e.g., VI 30 s VI60 s; twice as much reinforcer availability onResponse Alternative 1) were altered to a ratioof 3:1 (e.g., VI 30 s VI 90 s; three times asmuch reinforcer availability on Response Alter-native 1), one would expect a concomitant one-unit change in relative response allocation.Although an s parameter equal to unity (orlog 1 5 0) occurs infrequently in the publishedliterature, s values of less than 1 are the mostfrequently reported in the literature and aretermed undermatching (a less than one-unitincrease in relative response ratios given a one-unit increase in relative reinforcer ratios; e.g.,Madden, Peden, & Yamaguchi, 2002). Mea-sures of s that exceed 1 (e.g., Aparicio, 2001) areless frequently reported and are termed over-matching (a greater than one-unit change inrelative response ratios given a one-unit changein relative reinforcer ratios). For example, in thestudy by Aparicio, overmatching was associatedwith increased response effort (e.g., climbing

obstructions). The b parameter describes altera-tions in response allocation that are notaccounted for by differences in relative re-inforcer rates. In both nonhuman and humanlaboratories, bias may result from qualitativelydifferent stimuli (e.g., food vs. water), differ-ences in effort associated with the two responsealternatives (e.g., difficult math problems vs.mastery level math problems), and seeminglyimmutable preferences for one alternativerelative to the others (e.g., a strong preferencefor the color green; Baum; Neef, Shade, &Miller, 1994).

In some instances, behavior may be moreappropriately captured in terms of its duration.For example, Baum and Rachlin (1969)assessed the behavior of pigeons in terms oftime spent on one side or another of a modifiedoperant chamber as a function of relativereinforcer rates. Baum and Rachlin assessedmatching using the following equation:

logT1

T2

� �~s log

r1

r2


where T1 and T2 represent time allocated toResponse Alternatives 1 and 2, respectively, andr1 and r2 are as described in Equations 1 and 2.In general, relative time allocation matchedrelative reinforcer rates; however, considerablebias was observed.

Oliver, Hall, and Nixon (1999) assessed theaggressive and communicative behavior exhib-ited by a young boy in terms of its duration asa function of the relative duration of reinforceraccess associated with the two response alter-natives (aggression and communication) usingthe following equation:

logT1

T2

� �~s log

t1

t2


where T1 and T2 are as described in Equation 3,and t1 and t2 represent duration of reinforce-ment associated with Response Alternatives 1and 2, respectively. This seems to have been

590 JOHN C. BORRERO et al.

a particularly appropriate model because ag-gression was shown to be sensitive to negativereinforcement in the form of escape frominstructional demands. It is likely that theduration of escape would be a more relevantreinforcement parameter than its rate. Alsonoteworthy is that the data used to assess thematching relation were gathered in the partic-ipant’s natural classroom environment duringinteractions with his teacher. The resultsreported by Oliver et al. were consistent withmatching and illustrated how the phenomenoncould be modeled using parameters of re-inforcement other than rate, as well as quanti-fications of behavior in terms other than rate.

Equation 1 and its proportional variationshave been applied infrequently in more recentexperimental research (relative to Equations 2,3, and 4), in part because of the increasedexplanatory utility of the latter equations.Specifically, the generalized matching equationsdescribe whether, and to what extent, behaviordeviates from perfect matching. Further, thegeneralized equations describe potential sourcesof these deviations (e.g., bias to one alternativeor insensitivity to reinforcer rates).

Although the response alternatives describedby Herrnstein (1961) and Baum (1974) in-volved key pecks exhibited by pigeons, the workof Oliver et al. (1999) and Borrero and Vollmer(2002) have demonstrated that relative mea-sures of communication and problem behaviorexhibited by individuals with developmentaldisabilities can also be expressed in terms of thematching relation. Other applications of thematching law (see Davison & McCarthy, 1988,for an extensive review) have involved assess-ments of academic responding of individualswith and without developmental disabilities(Mace, McCurdy, & Quigley, 1990) andcollegiate (Vollmer & Bourret, 2000) andprofessional (Reed, Critchfield, & Martens,2006) sports performance. Thus, the matchinglaw is not limited by conceptualizations ofresponse alternatives (e.g., key pecks or com-

municative responses). Rather, the limits of thematching law remain a subject of ongoingbehavior-analytic research.

Although there have been numerous demon-strations of the matching relation with nonhu-mans (responding for primary reinforcers),there have been considerably fewer studiesinvolving humans and attention as reinforce-ment (e.g., Pierce & Epling, 1983). Like the keypecks of pigeons or the academic engagementof students, communicative exchanges duringconversation (i.e., verbal behavior, Skinner,1957) should also be amenable to evaluationsof matching. In one such study Snyder andPatterson (1995) evaluated interactions betweensocially aggressive boys and their mothers aswell as boys who were not socially aggressiveand their mothers. The researchers accumulated10 hr of interactions for each mother–childdyad and then conceptualized maternal termi-nation of the conflicts as the reinforcer forselection of various tactics (e.g., positive verbal,negative verbal) adopted by their children.These data were then evaluated in terms ofthe matching relation; results suggested that thelikelihood of a particular tactic was in partdetermined by the likelihood of reinforcementassociated with each of those tactics, a conclu-sion consistent with the matching law.

In a similar study, Dishion, Spracklen,Andrews, and Patterson (1996) evaluated theinteractions of adolescent boys while focusingon the content of these discussions (e.g.,discussion of illegal behavior, discussions offamily and school that did not involve in-appropriate activities, termed rule breaking andnormative, respectively) and the responses ofthe listener (e.g., laughing or pausing). Data for181 dyads were assessed using Equation 1, andthe researchers found that relative rates of rulebreaking were well accounted for by relativerates of laughing. Stated differently, Dishion etal. suggested that the content of naturallyoccurring conversations between adolescentswas a function of the extent to which listeners

MATCHING AND SOCIAL DYNAMICS 591

reinforced (laughed at) the conversation con-tent.

The studies by Synder and Patterson (1995)and Dishion et al. (1996) are particularlyimportant because they speak to the durabilityof the matching phenomenon (in terms of socialdynamics) when reinforcer rates are not exper-imentally manipulated. However, these analysesinvolved between-groups comparisons; thus,conclusions regarding matching at the level ofthe individual cannot be discerned from theseresults. However, the extent to which adultsdifferentially attend to, or engage with, othersin social exchanges has also been evaluatedwhen reinforcer rates were experimentallyprogrammed (Beardsley & McDowell, 1992).

Conger and Killeen (1974) evaluated levels ofattending for 5 college students who wereinvited to participate in a 30-min discussion.According to independently programmed con-current VI schedules, confederates deliveredstatements of agreement (e.g., ‘‘I agree with thatpoint’’) following a participant’s comments.Data for the first and last 5 min of each sessionwere then evaluated using a variation ofEquation 1 (a classic iteration of the matchingequation) and pooled for all participants.Results showed that during the relatively briefdiscussions, participants’ relative response allo-cation (between each of the confederates) waswell described by relative rates of agreementduring the last 5 min of the session. During thefirst 5 min of the discussion, however, no linearrelation was observed. These data seemed tosupport the notion that matching is a steady-state phenomenon (e.g., Baum, 1974) thatrequires some exposure to experimental con-tingencies before it occurs.

Pierce, Epling, and Greer (1981) extendedthe work described by Conger and Killeen(1974) by using Equations 2 and 3 (morecontemporary models of the matching relation)and by conducting more extended experimentalsessions. Using procedures similar to those ofConger and Killeen, the response allocation of 6

participants was assessed during seven 1-hrsessions. For 2 of 6 participants, matching wasobserved during the last 30 min of experimentalsessions (coefficients of determination rangedfrom .45 to .69). Also noteworthy was theobservation that 3 of 6 participants allocatedrelatively more verbal behavior and time to theconfederate who provided relatively less agree-ment.

Taken together, the results reported byConger and Killeen (1974) and Pierce et al.(1981) leave the matter of matching duringcommunicative exchanges unresolved when dataare evaluated at the level of the individual. Thepresent study was designed to replicate theprocedures reported by Conger and Killeen, andlater by Pierce et al., by evaluating levels ofattending, given concurrent schedules of agree-ment, for a larger sample of college students,using contemporary (Equations 2, 3, and 4)variations of the matching equation (McDow-ell, 2005).

METHOD

Participants and Setting

Participants were 25 undergraduate collegestudents who were enrolled in a small privateuniversity and had completed no more than twocollege-level psychology courses. The mean ageof participants was 20.2 years, and each hadcompleted a mean of 3 years of college-levelcourse work. Forty-eight percent of participantswere female. Prior to the experimental session,participants were asked to sign an informedconsent form (approved by the universityinstitutional review board) in a room near theexperimental session room. Participants weretold that contingent on their consent, theywould participate in a discussion to assesscollege students’ understanding of the factorscontributing to juvenile delinquency. Twoconfederates also completed the informedconsent process. Next, participants were re-minded that the discussion would be videotaped(also included in the informed consent form).


After the consent form was signed, an experi-menter directed the participant and the twoconfederates into the session room. Sessionswere conducted in a laboratory that measuredapproximately 5 m by 5 m. Materials includeda desk, four chairs (one for the participant, onefor each confederate, and one for a moderatorresponsible for evoking discussion), and posterson the walls (included to evoke discussion).Only 1 participant at a time was involved ina discussion session. The participant wasstrategically seated with his or her back toa one-way mirror, with each confederate seatedapproximately 1.5 m to either side of theparticipant. The moderator was seated directlyacross from the participant (approximately 1 m)and facilitated conversation (described in moredetail below).

Response Measurement andInterobserver Agreement

Data were collected on comments made bythe participants (any vocal responses in refer-ence to the topic); attending, defined as eyecontact between the participant and eitherconfederate or the moderator; and orientationof the body toward either confederate or themoderator. Data were collected separately forattending to Confederate 1, Confederate 2, andthe moderator. Data were also collected onstatements of approval delivered by eachconfederate (e.g., ‘‘I think you are right’’). Bothfrequency and duration data were collected onhandheld computers for each of the aforemen-tioned measures by both primary and secondaryobservers for 88% of all sessions. Duration ofparticipant responses was scored given aninstance of attending and ended the momentattending to either confederate or the moder-ator ceased. Agreement coefficients were calcu-lated by dividing the smaller frequency (orduration in seconds) by the larger frequency (orduration in seconds) in each 10-s interval andmultiplying by 100%. Mean agreement coeffi-cients for all measures exceeded 80% (range,81% to 94%).

Procedure and Data Analysis

While seated in the experimental setting, themoderator read the following instructions to theparticipants at the beginning of the discussion:

Before this session begins, we ask that you do notdisclose any personal information about yourselfregarding any of the topics to be discussed. Tofurther control for this, we also ask that allexperiences shared be in third person such as ‘‘Iknow this person who …’’ This is to further insureyour confidentiality. Thank you.

Participants were asked not to disclose anypersonal information regarding any of thetopics to be discussed. After the instructions,the moderator began the experimental sessionwith the question, ‘‘What do you think aresome factors that influence juvenile delinquen-cy?’’ or a similarly phrased question.

During the discussion, confederates emittedinfrequent verbal responses that were not inresponse to a statement made by the partici-pant. Given an extended lull in the conversation(e.g., 30 s), the moderator attempted to evokediscussion using the following list of discussiontopics:

Factor 1: Drug and alcohol useFactor 2: Peers and cliquesFactor 3: Quality of school system or school

environmentFactor 4: Unfavorable home environmentFactor 5: Subculture participation

Confederates participated in the conversation(directed to the participant) (a) followinga verbal response from a participant that (b)occurred after the VI interval associated witheach confederate elapsed. Confederates weresignaled by colored flashlights operated byexperimenters on the opposite side of the one-way mirror. For example, Confederate 1 wassignaled by a blue light, and Confederate 2 wassignaled by a yellow light. The signal indicatedthat a VI schedule for one confederate hadelapsed, and that a statement of agreementcould be delivered after a participant’s currentor next response. The lights were not visible tothe participant. It was possible to have a signal


delivered at a time when the opportunity todeliver an agreeable statement was not available.For example, a VI interval might have elapsedduring a period in which the participant wasnot talking. Thus, the confederate delayeddelivery of an agreeable statement until a par-ticipant’s next response. For this reason,programmed and obtained reinforcer rates werenot identical. Confederates were instructed notto attend (look at, orient toward, or speak) tothe participant under any other circumstances.Between reinforcer deliveries, the confederateseither looked down, at each other, or at themoderator.

Statements of agreement were deliveredaccording to independent VI schedules (i.e.,VI 120 s VI 300 s for 20-min discussions, andVI 30 s VI 120 s for 30-min discussions).Distributions of the VI schedules were de-termined using the method described byFleshler and Hoffman (1962). The fidelity withwhich confederates delivered statements ofagreement was not assessed and cannot bediscerned. Data were reported in either 5-mincomponents or for the entire session. For the20-min discussions, the confederate who ini-tially delivered statements of agreement accord-ing to the VI 120-s schedule switched to the VI300-s schedule after 10 min, and the confederatewho initially delivered statements of agreementaccording to the VI 300-s schedule providedstatements of agreement according to the VI120-s schedule. During the 30-min sessions,confederates switched schedules after 10 min. Atthe conclusion of the session, the participant wasdebriefed and was awarded extra credit ina required seminar for his or her participation.

Data for all participants were then evaluatedusing Equations 2, 3, and 4. Data wereexpressed in several ways. First, data werepooled for all participants and plotted duringthe first 5 min of the discussion, during the last5 min of the discussion, and during the entire20- or 30-min discussion. Second, for partici-pants who completed the 30-min discussion, we

also evaluated response allocation in terms ofEquations 2 and 3 in an attempt to determinewhether duration of response allocation or rateof response allocation would be better describedby relative rates of statements of agreement.

RESULTS

Figure 1 depicts the results of the matchinganalyses using Equations 2, 3, and 4. The leftcolumn depicts results of the analyses duringthe first 5 min of the discussion for allparticipants. The middle column depicts dataaccording to each equation during the last5 min of the discussion for all participants. Theright column depicts data according to eachequation during the entire 20- or 30-mindiscussion for all participants.

When evaluated as pooled data (across allparticipants) using Equation 2, results illustrateundermatching (i.e., s , 1), with no notewor-thy b values. Results using Equations 3 and 4also were generally similar, in that coefficientsof determination were modest, but were largerin all cases during the first 5 min of thediscussion than in the last 5 min. One analysis(Equation 3, from the first 5 min of thediscussion) produced a slope greater than 1and considerable bias (b 5 20.372).

Figure 2 depicts data for 4 participants whocompleted the 30-min discussion, in 5-minintervals. Data for individuals who completedthe 30-min discussion were selected for furtheranalysis if there were at least five data points toevaluate (i.e., the numerator or denominatorwas nonzero for at least five 5-min intervalsbecause the logarithm of zero is undefined).Data depicted in each row reflect analyses forindividual participants. The left column depictsresults according to Equation 2, and the rightcolumn depicts results according to Equation 3.Equations 2 and 3 were selected to compare thetime-allocation and response-rate variations ofthe generalized matching equation during socialinteraction. For Participants 15, 18, 20, and 17,Equation 2 produced relatively larger s param-


eters (indicating that they were more sensitive tochanges in relative reinforcer ratios whenstatements made by the participants wereexpressed in terms of relative rate of occur-rence), smaller b parameters (indicating thatfactors not captured by relative reinforcer ratioshad a negligible impact on relative responseallocation), and larger coefficients of determi-nation. Participants 20 and 17 produced perfectmatching when expressed using Equation 2.Note that three data points for Participant 20are plotted in coordinates (0, 0), and thus, onlythree data points are visible.

Figure 3 depicts results for the remaining 5participants who completed the 30-min discus-sion, in 5-min intervals. Results are similar tothose depicted in Figure 2, with two notableexceptions. First, Participants 26 and 27exhibited considerable bias to one of the twoconfederates (b 5 20.648, 20.560, and b 5

0.286, 0.193, respectively, for Equations 2 and3 and Participants 26 and 27). Based on theavailable data, we cannot determine why these 2participants might have demonstrated such bias.Second, Participants 27 and 14 were the 2participants for whom Equation 3 produced

Figure 1. The left column depicts pooled data for all participants during the first 5 min of the discussion accordingto Equations 2, 3, and 4 (from top to bottom). The middle column depicts pooled data for all participants during the last5 min of the discussion according to Equations 2, 3, and 4 (from top to bottom). The right column depicts pooled datafor all participants during the entire 20- or 30-min discussion according to Equations 2, 3, and 4 (from top to bottom).Dashed diagonal lines represent perfect matching, and solid lines represent best fit lines.


larger coefficients of determination (relative toEquation 2); however, the difference observedfor Participant 14 was rather small. ForParticipant 27, these differences may be betterexplained in terms of the spread in relativereinforcer ratios. That is, relative reinforcerratios were highly concentrated such thatevaluations of matching might be limited based

on the limited range of relative reinforcer ratesand not based on the model assessed.

For 7 of 9 participants who completed the30-min discussion, Equation 2 provided a betteraccount of response allocation than did Equa-tion 3, suggesting that characterizations ofresponse allocation in terms of relative rate orduration may influence summaries based on

Figure 2. Data depicted according to Equations 2 and 3 for 4 participants whose data were selected for furtheranalysis. All data are for participants who completed the 30-min discussion. Dashed diagonal lines represent perfectmatching, and solid lines represent best fit lines.


Figure 3. Data depicted according to Equations 2 and 3 for 5 participants whose data were selected for furtheranalysis. All data are for participants who completed the 30-min discussion. Dashed diagonal lines represent perfectmatching, and solid lines represent best fit lines.


relative reinforcer rates. In other words, notonly is selection of an appropriate modelimportant, but the way in which responding ischaracterized may also contribute to findings insupport of the matching relation.

DISCUSSION

The matching relation was assessed duringexperimentally arranged conversations amongcollege students. To extend the classic work ofConger and Killeen (1974) and Pierce et al.(1981), three iterations of the matching equa-tion were assessed at the between-subjects level.Each equation was applied to capture relevantfeatures of social dynamics (i.e., relative dura-tions of response allocation, relative rates ofresponse allocation, relative durations of agree-ment, and relative rates of agreement). At thebetween-subjects level, positive correlationsbetween relative response allocation and relativereinforcer rates were obtained, despite the wayin which behavior and statements of agreementwere expressed. This general finding is consis-tent with those reported by Conger and Killeen.In addition to the between-subjects analyses, thematching relation was also assessed at the levelof the individual, using Equations 2 and 3.These two models were selected to determinewhether rate or duration of response allocationwas better accounted for by relative rates ofagreement. Results of these analyses wereindicative of matching using one or both ofthe models for all participants. These results arealso consistent with those reported by Pierce etal., although matching was observed forrelatively more participants in the currentinvestigation than in the study by Pierce et al.

The present findings also differ from thosereported in prior work. For example, when datawere pooled, Conger and Killeen (1974) foundthat closer approximations to matching wereobserved during the last 5 min of the 30-mindiscussion than in the first 5 min. Results of thepresent investigation found just the opposite(i.e., closer approximations to matching during

the first 5 min than in the last 5 min of thediscussion), suggesting that participants in thecurrent investigation were immediately sensitiveto reinforcer rates. As noted previously, Congerand Killeen applied a variation of Equation 1 (aproportional equation), which has been shownto be of less explanatory utility. Thus, if datareported by Conger and Killeen were reex-pressed using generalized matching equations,the findings may not be commensurate. Asecond discrepancy lies in the rather lowcoefficients of determination obtained in thecurrent study (at the between-subjects level)relative to those reported by Conger andKilleen. However, this discrepancy may not beunique to these two studies. Consider anexperiment in which 13 pigeons respond ona pair of five VI schedules, during which eachpair of VI schedules is presented for 5 min. Ifone were to assume stable responding and thenselect (at random) pairs of schedules and plotthe data across subjects, low coefficients ofdetermination would be expected. However,when those data are reexpressed at the level ofthe individual subject, considerably highercoefficients of determination would likely beobtained. Differences of this sort may even beexpected given differences in terms of sensitivityand bias (as reflected in Figures 2 and 3).Therefore, although low coefficients of de-termination were obtained at the between-subjects level in the current investigation (whichmight be expected), improvements were ob-served at the level of the individual (which alsomight be expected).

It is also possible that the 20-min discussionsin the current investigation did not allowsufficient time for participants’ behavior tocome under the control of the programmedschedules, and thus, influenced the utility of theequations in describing the pooled data.Matching is a steady-state phenomenon. Infact, analyses conducted for the 20-min partic-ipants and the 30-min participants separatelyshowed that more of the variance was accounted


for among 30-min participants (r2 5 .79) than20-min participants (r2 5 .06) using Equation2 (data not depicted). However, considerablyfewer data points were available for comparisonin the 20-min discussion; thus, this conclusionshould be interpreted cautiously.

The present findings also differed from thosereported by Pierce et al. (1981) in that positivecorrelations were observed for all 9 participants(using one or both models) whose data wereassessed at the level of the individual, whereasPierce et al. observed matching in only 2 of 6cases. This apparent discrepancy may be theresult of procedural differences and differencesat the level of data analysis. Specifically,participants in the study by Pierce et al. wereexposed to 7 hr of discussion, and data from thefirst and last 30 min of each discussion wereaggregated. Discussions in the current investi-gation were considerably shorter (20 or30 min), and the unit of analysis was consid-erably smaller in the present investigation(5 min vs. 30 min). With such a lengthyexperiment (seven 1-hr discussions), partici-pants may have become suspicious of theexperimental procedure (reported for 1 partic-ipant in Pierce et al.), and as a result engaged inbehavior that was antithetical to the matchingrelation (Sidman, 2000). Although possible,this represents nothing more than conjecturethat can be addressed only by experimentation.If procedural differences were responsible forthese findings, these discrepancies may beelucidated by employing similar proceduresand may warrant future research.

The current investigation should be inter-preted in light of at least three potentiallimitations. First, a single pair of VI scheduleswas evaluated. Current evaluations of thematching relation in the nonhuman experimen-tal laboratory typically involve several pairs ofschedules. Had a greater number of scheduleparameters been evaluated, or schedule param-eters that were either more or less disparate beenevaluated, the results of the current investiga-

tion might have differed. Second, the integritywith which confederates delivered statements ofagreement cannot be extracted from the data. Itis possible that poor integrity might haveinfluenced these results, however, confederatesreceived extensive training in mock sessionsbefore initiating the experiment. Finally, pro-grammed rates of reinforcement were notequivalent to obtained rates. As noted by Baum(1974) and others (e.g., Herrnstein, 1970), thematching law applies only to obtained re-inforcement. However, this was in part a resultof the procedure. Rather than interruptinga participant’s comment, confederates waiteduntil the participant completed a comment.This sometimes delayed the availability of thenext reinforcer on the same schedule. Similarly,reinforcer availability occurred independent ofthe participant’s comments. Therefore, theabsence of responding also drove down the rateof obtained statements of agreement.

Naturally occurring interactions may beunder multiple sources of control. Althoughresponding was well described by relativereinforcer rates in the current study (at thelevel of the individual), future research mayassess relative measures of response allocationusing concatenated versions of the matchinglaw. For example, it may be the case thatindividuals allocate their responding in betteraccordance with the matching law whenmagnitude (duration) of agreement and rateare assessed. Similarly, qualitative aspects ofagreeable statements may also exert control overresponse allocation. In the present experiment,confederates were specifically instructed toprovide approximately equivalent forms ofagreement; however, this is clearly not howreinforcers are distributed during social inter-actions in everyday conversation. Concatenatedequations of this sort have been applied to thebehavior of nonhumans (e.g., Miller, 1976) andhumans (e.g., Vollmer & Bourret, 2000), andmay affect evaluations of matching duringcomplex social interactions.


Statements of agreement are also not the onlytype of response encountered during typicalconversational exchanges. In some instances, thecontent of verbal behavior may be punished,producing either a decrease in the specificsource of content, a decrease in the overall levelof communicative exchanges, or both. Futureresearch may assess relative response allocationwhen concurrently available alternatives areassociated with asymmetrical outcomes. Forexample, using procedures similar to those inthe current study, one confederate might emitwhat are procedurally punitive responses whileanother delivers what are procedurally reinfor-cing responses (like those delivered in thepresent study), followed by a switch inassociated outcomes. One might expect to seedifferences based on the specific models evalu-ated in such an arrangement. For example,punitive statements may result in greaterdurations of engagement directed toward thesource of the statement but a decrease in therelative rate of those interactions.

Some implications for a variety of appliedsocial contexts may also be extracted from thepresent experiment. First, unacceptably low (orhigh) levels of classroom participation may beeasily altered based on programmed schedulesof agreement or teacher approval. For example,relatively dense rates of teacher approval may bearranged for students exhibiting relatively lowlevels of vocal participation (and vice versa).Similarly, the relentless and repetitious verbalbehavior (e.g., speaking without permission) ofyoung school-aged children might be assessedunder nonexperimental conditions (e.g., Bor-rero & Vollmer, 2002) and then subsequentlyevaluated experimentally (using schedule valuesderived from descriptive observations). Al-though a matching analysis may not benecessary to draw this conclusion, it doesprovide a parsimonious account of the variablesthat control behavior, and may provide a morequantitative description of sensitivity to con-current-schedules arrangements than those of-

fered in other disciplines (e.g., developmentaland stage theorists). Second, and related to theprior point, results of the current study andthose reported by Conger and Killeen (1974)illustrate that changes in attending can beobserved in a relatively short period of time atthe level of the individual. Thus, if the initiallylow participatory behavior of 1 student quicklybecomes unacceptably high, changes in levels ofparticipation can be controlled just as easily. Assuggested previously, this (e.g., comparisons ofbehavioral sensitivity both within and acrossstudents of various ages) might allow behavioralresearch on what are commonly areas of childdevelopmental research.

These results add to the generality of thematching law and were based on the socialinteractions of adults. These findings reiteratethe contention that verbal behavior is subject tothe contingencies of reinforcement that are alsoresponsible for nonverbal behavior. However, asnoted by Skinner (1957), verbal behavior isfrequently a function of more than one variable.The present experiment was designed to assessthe frequency and duration of verbal behaviorbased on known parameters of reinforcement,using a durable model of behavior (thematching law). There remain, however, multi-ple factors that may contribute to relativeresponse allocation in social dynamics, all ofwhich can benefit from additional research.

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Received July 20, 2006Final acceptance April 9, 2007Action Editor, Kenneth Silverman


An application of the matching law to social dynamics - Eric

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