Discussion 1: Problem Solving
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ExpertiseinGroupProblemSolvingRecognitionSocialCombinationandPerformance..pdf
Expertise in Group Problem Solving: Recognition, Social Combination, and Performance
Bryan L. Bonner University of Utah
This laboratory study assessed how recognition of expertise affects group decision making and performance. Three-person groups and independent individuals solved 4 intellective problem-solving tasks in 3 experimental conditions: 4 individual tasks, 1 individual task followed by 2 group tasks followed by 1 individual task, or 1 individual task followed by 2 group tasks (with intragroup rankings) followed by 1 individual task. Findings indicate that (a) both groups with ranking information and groups without are fairly well calibrated with respect to expertise, (b) group decisions were best approx- imated by “expert-weighted” decision schemes in which the highest performing mem- ber of the group has twice the influence of other group members, and (c) groups performed at the level of the best of an equivalent number of individuals.
Many of the most important decisions made in our world are arrived at not by individuals working in isolation but by collectives working in unison. In areas as diverse as courtroom justice, advertising, education, and large-scale acquisitions, groups of problem solvers are fre- quently called upon to “put their heads to- gether” and determine the best courses of ac- tion. For these groups to operate as effectively and efficiently as possible, they must coordinate and utilize their resources to their fullest extent (Steiner, 1972). Access to abundant intragroup resources (e.g., member expertise) will not aid the group if it fails to use those resources wisely (Hackman, 1987). Because groups are typically composed of members with variable levels of expertise and often work to solve problems that require them to combine their input and form some type of aggregate product or decision, achieving a better understanding of how groups
combine member input to reach consensus is of great importance.
A recent study (Bonner, Baumann, & Dalal, 2002) examined the effects of performance feedback on subsequent decision making and performance in three-person groups working on the logic problem Mastermind (described in Knuth, 1976 –1977). This study found that groups gave more weight to the input of their highest performing members, with the group decision-making process being best approxi- mated by post hoc “expert-weighted” social de- cision schemes. These weighted models attrib- uted twice as much influence to the highest performing group member relative to other members when veridical expertise rankings (based on prior performance) were made avail- able to the group. This study also found that groups performed at the level of the best of an equivalent number of individuals regardless of whether they had access to explicit performance rankings.
The current study seeks to expand on Bonner et al.’s (2002) findings in several areas. First, whereas in the previous study the expert- weighted models were derived after the fact to fit the data, in the present study these decision schemes were tested a priori against an inde- pendent data set. Thus, the prior and current studies follow a model-fitting/model-testing se- quence in which decision schemes derived from one set of data are tested on another (Kerr, Stasser, & Davis, 1979). Second, the previous
This article is based on a study that was submitted in partial fulfillment of the requirements for the degree of doctor of philosophy in psychology in the Graduate College of the University of Illinois at Urbana–Champaign. I would like to thank Patrick Laughlin, David Budescu, Peter Carnevale, Incheol Choi, and Andrea Hollingshead for their invaluable input on this study. I would also like to thank Michael Baumann for his comments on a draft of this article.
Correspondence concerning this article should be addressed to Bryan L. Bonner, David Eccles School of Business, University of Utah, 1645 East Campus Center Drive, Salt Lake City, UT 84112. E-mail: [email protected]
Group Dynamics: Theory, Research, and Practice Copyright 2004 by the Educational Publishing Foundation 2004, Vol. 8, No. 4, 277–290 1089-2699/04/$12.00 DOI: 10.1037/1089-2699.8.4.277
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study constrained the problem-solving groups to choose their collective decisions only from the options advocated by group members (i.e., the groups could not generate emergent re- sponses). In the current study this restriction was lifted, and the expert-weighted models were modified to account for possible emergent group responses. Third, in the previous study, groups solved only one collective problem over the course of 1 hr. In the current study, groups were given 2 hr to solve two group problems (in addition to individual problems). This increased level of interaction may have allowed group members to better assess intragroup expertise. Fourth, the Mastermind task used in the previ- ous study allows problem solvers to make only one type of task-related decision (i.e., they choose a proposed solution to test against the actual problem solution on every trial until they are correct or they exhaust their trials). In the current experiment, Mastermind was replaced by the letters-to-numbers task (Laughlin & Bonner, 1999). In the letters-to-numbers task, problem solvers make three different decisions on every problem trial: (a) what evidence to gather, (b) what hypothesis to test, and (c) what solution to propose. The greater complexity of the problem type and the increased opportuni- ties for problem solvers to make decisions pro- vides a more interaction-rich task environment. Thus, the current study seeks to assess how the availability of information on member expertise affects both group decision-making patterns and subsequent group performance in the context of the interaction-rich letters-to-numbers problem.
Recognition of Expertise
One of the greatest resources available to a problem-solving group is the expertise of its members (McGrath, 1984). Research in small group behavior has repeatedly shown that a group’s ability to accurately assess the expertise of its members can be vital to the group’s suc- cess (Baumann & Bonner, 2004; Bottger & Yetton, 1988; Einhorn, Hogarth, & Klempner, 1977; Libby, Trotman, & Zimmer, 1987; Yetton & Bottger, 1982). The literature in this area has, however, provided somewhat mixed results concerning the actual ability of groups to iden- tify their best members. Whereas some studies have found groups to be at least somewhat proficient at expertise identification under cer-
tain conditions (Henry, Strickland, Yorges, & Ladd, 1996; Libby et al., 1987; Yetton & Bott- ger, 1982), others have found groups to be less effective in this regard (Littlepage, Schmidt, Whisler, & Frost, 1995; Miner, 1984; Trotman, Yetton, & Zimmer, 1983).
Bonner et al. (2002) suggested that the lack of agreement in the expertise identification lit- erature is a function of the tasks performed by the groups and the conditions under which the group problem-solving experiments are con- ducted. They defined two primary characteris- tics that a task should possess in order for group members to recognize and use intragroup ex- pertise. First, group members must have access to accurate, diagnostic information on the rela- tive competencies, knowledge, or performance of the group members (Henry et al., 1996; Stasser, Stewart, & Wittenbaum, 1995). One way that groups may assess the relative exper- tise of group members is through the use of explicit performance feedback (Littlepage, Ro- bison, & Reddington, 1997). Explicit perfor- mance feedback leads group members to under- take a social comparison process with other group members (O’Leary-Kelly, 1998). This al- lows them to develop perceptions of the perfor- mance-level rankings within the group. Alter- natively, this ranking information, if available, may be explicitly provided to group members. Second, the task must have a level of difficulty that allows for substantial variation in perfor- mance in order for members to identify the differences in ability levels among group mem- bers (Baumann & Bonner, 2004; Libby et al., 1987). If the task is too easy or difficult, with the result that all group members perform at a similar level (ceiling and floor effects, respec- tively), members will have little information with which to assess expertise. Additionally, in such situations the value of identifying the high- est performer in the group may be of limited practical value.
The letters-to-numbers task used in the cur- rent study is well suited toward satisfying the two criteria for expertise identification. First, it is relatively transparent in terms of perfor- mance. That is, success in the task is demon- strable and readily apparent to those under- standing rudimentary mathematics and logic. Thus intragroup performance variability may be assessed without performance feedback. Pro- viding veridical performance feedback should
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reinforce these accurate perceptions of member expertise. Second, this task has an established level of difficulty that promotes substantial vari- ance in performance (Laughlin & Bonner, 1999; Laughlin, Bonner, & Miner, 2002; Laughlin, Zander, Knievel, & Tiong, 2003). These points lead to the first two hypotheses of the current study:
Hypothesis 1: Group members will be well calibrated in their perceptions of intra- group expertise (i.e., actual and perceived expertise rankings will be positively correlated).
Hypothesis 2: Members of groups pro- vided with performance rankings will be better calibrated with respect to intragroup expertise than members of groups lacking this information.
Social Permutations: Expert-Weighted Models
Identifying expertise is only the first step in utilizing this valuable resource. The next step involves how groups use the information. Spe- cifically, this is a question of how groups weigh the input of expert group members relative to other members of the group. This weighting procedure can be framed in the context of the social combination approach to studying group interaction. This approach has played an impor- tant role in the study of group behavior for decades. The social combination method con- ceptualizes the processes of cooperative prob- lem solving in the form of social decision schemes (e.g., Davis, 1973; Lorge & Solomon, 1955; Smoke & Zajonc, 1962; Thomas & Fink, 1961). Given a set of mutually exclusive and exhaustive response alternatives, group mem- bers may initially prefer different alternatives. The task of the group is to map this distribution of preferences to a collective decision. This mapping process is tested against models drawn from theoretical expectations as to what would occur given certain assumptions about the pro- cesses underlying group decision making.
Traditional social combination approaches typically treat group members as being inter- changeable and indistinguishable from one an- other and are therefore not suited to dealing with questions involving individual differences within groups. A method of social combination
termed social permutation (Bonner, 2000) ex- pands on the traditional approach by treating individual group members as consistent entities across trials. This method is amenable to deci- sion schemes capable of predicting unequal in- fluence between group members on the basis of known individual differences. This allows for the development of models that differentially weight member influence on the basis of such factors as extroversion (Bonner, 2000) or exper- tise (Bonner et al., 2002).
Recent research involving social permutation analysis of groups working on the Mastermind task found that expert-weighted social decision schemes, where the highest performing member of the group wields twice as much influence as other group members, provided a very good a posteriori fit to the obtained data (Bonner et al., 2002). The model that was found to have the best fit was majority, otherwise weighted pro- portionality, with experts receiving 2/(N � 1) proportion of group influence and all other group members receiving 1/(N � 1) proportion of influence (in this and all following social decision schemes, N represents the number of group members). Although the model fit well with the data in that case, it is limited in that it cannot, in its current form, account for emergent group responses.
Laughlin and Hollingshead (1995) have shown that taking emergent responses into ac- count substantially improves model fit for col- lective induction problems. They found the best fitting model to be majority, otherwise propor- tionality with a 1/(N � 1) possibility of emer- gent responses. Incorporating a proportionate possibility of an emergent group response into the expert-weighted model yields majority, oth- erwise a weighted proportionality in which the expert receives a 2/(N � 2) proportion of the influence and all other group members receive a 1/(N � 2) proportion of influence, with a 1/(N � 2) possibility of an emergent response. This leads to the third hypothesis of this study:
Hypothesis 3: Group choices will be best approximated by the decision scheme ma- jority, otherwise a weighted proportional- ity in which the expert receives a 2/(N � 2) proportion of the influence and all other group members receive a 1/(N � 2) pro- portion of influence, with a 1/(N � 2) possibility of an emergent response.
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Group Performance Relative to Individuals
If group members are able to recognize ex- pertise and this knowledge influences their de- cision-making processes, the next question deals with how performance will be affected. A growing body of literature suggests that on in- tellective tasks (i.e., tasks possessing demon- strably correct answers), groups tend to outper- form the average individual (Hastie, 1986; Hill, 1982; Kelly & Thibaut, 1969) and to perform at the level of the best of an equivalent number of individuals (Bonner et al., 2002; Laughlin, Bon- ner, & Altermatt, 1998; Laughlin, VanderStoep, & Hollingshead, 1991, Experiment 2). In two recent experiments, groups were found to out- perform even the best comparison individuals (Laughlin et al., 2002, 2003). Superior group performance has been attributed to groups’ su- perior processing ability on information-rich problems (Laughlin et al., 1998), an interpreta- tion consistent with the emerging notion of groups as information processors (Hinsz, Tin- dale, & Vollrath, 1997).
The current experiment assessed group ver- sus individual performance on the letters-to- numbers task. As no previous studies involving tasks of this type have taken group decision processes or member expertise into account, the current study is in a unique position to frame performance differences in the context of both of these potentially influential factors. Thus, the final hypothesis of the study:
Hypothesis 4: Groups will perform at the level of the best of an equivalent number of independent individuals and better than other comparison individuals.
Method
Participants
The participants were 162 students enrolled in introductory psychology courses at the Uni- versity of Illinois at Urbana–Champaign who received course credit for their participation in this 2-hr experiment.
The Letters-to-Numbers Task
The goal of the letters-to-numbers task (Laughlin & Bonner, 1999) is to decode a series
of numbers (0 –9) that have been randomly coded, without replacement, into a series of letters (A–J). Problem solvers go through a se- quence of 10 trials. On each trial, they first ask for information about the series of letters in the form of an addition or subtraction equation. The experimenter then solves their equation in letter form. Problem solvers then propose a hypothe- sis as to the letter-to-number mapping of one of the characters. The experimenter then labels the hypothesis as correct or incorrect. Finally the problem solvers attempt to solve the entire se- quence by providing the complete code (the solution to the problem). The instructions and examples given to participants are provided in the Appendix.
Design
Participants were randomly assigned to one of three possible conditions: group not given explicit ranking feedback, group given explicit ranking feedback, or individual. Of the 162 participants, 108 were assigned to one of the two group conditions. Fifty-four of these partic- ipants were assigned to the no-feedback condi- tion and 54 to the feedback condition. All par- ticipants in the group conditions completed the letters-to-numbers task first individually, twice more as part of the same three-person group, and once more individually. The remaining 54 participants were assigned to the individual condition and completed the letters-to-numbers task four times individually.
This study used a randomized block design with session as the blocking variable. Partici- pants came to the laboratory in groups of 9 on one of 18 sessions and were randomly assigned to one of the three experimental conditions. Each set of 9 participants solved the same set of four random letters-to-numbers codes; a differ- ent set of four codes was used for each of the 18 sessions. Groups of 9 participants were obtained by overbooking participants for the sessions and randomly selecting 9 participants from those who attended. Participants not chosen to partic- ipate in this study participated in a questionnaire study instead.
Group members were ranked from first (high- est performance on the first individual adminis- tration of the task) to third based on trials to solution. Ties were broken by summing the number of correct mappings of the problem
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solvers’ codes across trials, with the participant having the higher sum winning the tie (Laughlin et al., 2002). Groups were assembled immedi- ately after the initial individual administration of the task was scored. In the no-feedback con- dition, the ranking information was not commu- nicated to the participants. In the feedback con- dition, the rankings of all group members were verbally communicated to the assembled groups by the experimenter immediately prior to the group administrations of the task.
On every trial of the group administrations of the task, the members of the group first, without discussion, recorded the equation that they wished the experimenter to solve. The group then engaged in free discussion and proposed one equation (e.g., A � B � __), which the experimenter solved for them (e.g., A � B � G). Next, each member of the group, without discussion, recorded the hypothesis that they wished the experimenter to answer. The group then engaged in free discussion and selected one hypothesis (e.g., A � 2), which the experi- menter identified as being true or false (e.g., A � 2 is true). Then the group members, again without discussion, recorded their proposed so- lutions to the letters-to-numbers problem (i.e., the complete code). The group again engaged in free discussion and proposed one solution. If the group’s proposed solution was correct, the group was told this and the problem ended. If the proposed solution was not correct, then the group continued on to the next trial and repeated the process. This continued for 10 trials or until the group solved the problem. Groups were not constrained to adopt the equations, hypotheses, or codes proposed by group members (i.e., emergent responses were allowed). In the group conditions, after the final group problem was solved (the third administration of the task, overall), group members were separated and each group member ranked all members, in- cluding themselves, in terms of expertise on the letters-to-numbers task.
Participants assigned to the individual condi- tion completed the task individually four times, proposing equations, hypotheses, and codes in a manner similar to that of participants in the group condition, with the exception that no col- laboration was called for. The primary proce- dural distinction between group and individual conditions was that individuals were able to
move at their own pace because they did not have to wait for others to generate responses.
Results
Recognition of Expertise
Recognition of expertise was evaluated by comparing the participants’ actual obtained rankings to their perceived rankings. Actual ob- tained ranks were based on the relative perfor- mance of problem solvers on the initial (indi- vidual) administration of the task. Perceived rankings were obtained by aggregating all member-generated rankings of a given group member across the group (i.e., rankings were based on the mean of the three rankings as- signed to each member including the self-rank- ing). Ties in perceived rankings were broken randomly. Because recognition of expertise was expected to vary as a consequence of the pres- ence or absence of explicit ranking information, analyses were computed separately for both conditions. Figure 1 shows the proportion of actual obtained ranks by perceived ranks as- signed by the group for both feedback condi- tions. Chi-square tests indicated a lack of inde- pendence between actual and perceived ranks in both the no-explicit-feedback condition and the explicit feedback condition, �2(4, N � 51) � 15.52, p � .01, and �2(4, N � 54) � 32.67, p � .01, respectively. Correlations between actual and perceived rankings also in- dicated that group members were significantly calibrated in both the no-explicit-feedback con- dition, rs(51) � .53, p � .05, and the explicit feedback condition, rs(54) � .64, p � .01. These results support Hypothesis 1.
It was predicted that group members would be significantly better calibrated in the explicit feedback condition than in the no-explicit-feed- back condition. A Fisher’s r-to-z test was used to compare the magnitudes of the two correla- tions in the previous analysis. The difference between the correlations was not significant (z � .84, p � .05). Similarly, a test comparing the proportions of correct perceived rankings between the no-explicit-feedback condition (in which 54.90% of group-assigned rankings were accurate) and the explicit feedback condition (in which 62.96% of group-assigned rank- ings were accurate) was also nonsignificant, t(102) � 0.84, p � .05. These findings failed to
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support Hypothesis 2.1 As explicit feedback did not significantly affect recognition of expertise, these two conditions were combined for the analysis of social combination patterns.
Group Decision Models
For the purpose of this analysis, each group is represented by a series of three letters. The first (highest performing) member is represented by the leftmost letter, the second (median) member is represented by the middle letter, and the third (lowest performing) member is represented by the rightmost letter. Correct responses are la- beled as C, and noncorrect responses are labeled as A, B, or D. Emergent group responses are labeled as E. Different letters denote different individual responses. For example, if codes were being examined, the label “CAB” would represent a member distribution in which the
1 Another method of evaluating the accuracy of expertise assessment involves comparing actual rankings to self-rank- ings only. Self-rankings and aggregated group rankings correlated very highly in both the no-feedback and feedback conditions, rs(51) � .75, p � .01, and rs(54) � .80, p � .01, respectively. In a three-person group there is only 1 degree of freedom remaining in ranking the entire group after a self-assessment is made. Thus, it is not surprising that the two methods provided very similar results. Tests indicated a lack of independence between actual and self-ranks in both the no-feedback condition and the feedback condition, �2(4, N � 51) � 8.06, p � .05, and �2(4, N � 54) � 28.06, p � .01, respectively. Correlations between actual and self-rank- ings were also significant in both conditions, rs(51) � .34, p � .05, and rs(54) � .57, p � .01, respectively. The difference between the correlations was not significant, Z � 1.44, p � .05. A comparison of the proportions of correct self-rankings between the no-feedback condition (50.98% accurate) and the feedback condition (59.30% ac- curate) was also nonsignificant, t(102) � 0.86, p � .05.
Figure 1. Actual versus perceived rankings for no-feedback and feedback conditions. 1st Gn � first group member, no-feedback condition; 1st Gf � first group member, feedback condition; 2nd Gn � second group member, no-feedback condition; 2nd Gf � second group member, feedback condition; 3rd Gn � third group member, no-feedback condition; 3rd Gf � third group member, feedback condition.
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first member selected the correct code and the second and third members selected two differ- ent noncorrect codes.
Note that correct responses (C) apply only to accurate problem solutions (i.e., correct codes), not to information gathered toward the solution of the problem (i.e., equations and hypotheses). For codes, a correct choice represents the true solution to the puzzle. Equations, however, are neither correct nor incorrect. They are simply questions asked by group members about math- ematical relationships between coded letters. Hypotheses may be used positively (i.e., with the expectation that the hypothesis will be con- firmed) or negatively (i.e., with the expectation that the hypothesis will not be confirmed) to gain information about the problem (Klayman & Ha, 1987, 1989; Laughlin, Bonner, & Alter- matt, 1999; Wason, 1960). Because hypotheses may be used strategically in this way, it would be inappropriate to treat them as meaningfully correct for the purposes of this study. Thus, for equations and hypotheses, only responses A, B, and D are appropriate, whereas for codes, all four response alternatives (i.e., C, A, B, and D) are applicable. This results in 5 member distri- butions for equations and hypotheses (AAA, AAB, ABA, ABB, and ABD) and 15 member distributions for codes (CCC, CCA, CAC, ACC, CAA, ACA, AAC, CAB, ACB, ABC, AAA, AAB, ABA, ABB, and ABD).
Row labels indicate the distribution of mem- ber preferences prior to the group discussion. Column labels indicate the group decision. An “x” indicates an impossible group decision for a given member distribution. To illustrate, con- sider the following example trial. The first member chooses the equation, “I � J � ?” (i.e., “What letter represents the sum of I and J?”) as her individual selection, and the second and third members both choose the equation, “J � J � ?” as their individual selections. This group preference distribution would be represented as “ABB” (row). If this group chooses “I � J � ?” as its response, then the group choice would be an “A” (column). If this group chooses “J � J � ?,” then the group choice would be a “B.” If the group chooses anything other than these two solutions, then the group response would be coded as an “E.”
Analyses revealed no appreciable differences between Time 2 and Time 3 choice patterns for equations, hypotheses, or codes. The patterns of
model fit and the cumulative difference statis- tics between theoretical and obtained choice distributions (D) for all tested models at Time 2 paralleled those obtained at Time 3. For the sake of brevity, only the results for the com- bined times are presented. It should be noted that combining across time in this manner also results in a more demanding D statistic and thus a more conservative model test. Tables 1, 2, and 3 provide the obtained probabilities for equa- tions, hypotheses, and codes, respectively.
Equations and hypotheses. A model testing procedure using Kolmogorov–Smirnov one- sample tests was conducted independently for equations and hypotheses. Four different aggre- gate-level models describing the social combi- nation process were tested against the obtained results. The first of these models accounted for neither emergent responses nor expert weight- ing (majority, otherwise proportionality), the next accounted for emergent responses but not expert weighting (majority, otherwise propor- tionality with a proportionate probability of an emergent response), the third accounted for ex- pert weighting but not emergent responses (ma- jority, otherwise expert-weighted proportional- ity), and the fourth accounted for both expert weighting and emergent responses (majority, otherwise expert-weighted proportionality with a proportionate probability of an emergent re- sponse). An alpha level of .20 was used for all tests. This alpha criterion is the standard for model-testing procedures of this type. Smaller D statistics represent better model fit. As Table 4 illustrates, the predicted model, which took into account both expert weighting and the pos- sibility of emergent group solutions, provided the best fit to the obtained data for both equa- tions and hypotheses. Further, this was the only
Table 1 Obtained Probability of Group Choices by Member Distributions for Equations
Member distribution
Group choice
SumA B D E
AAA 1.00 x x .00 64 AAB .86 .14 x .00 37 ABA .97 .03 x .00 37 ABB .08 .92 x .00 37 ABD .39 .29 .21 .11 256
Note. n � 431.
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model tested that could not be rejected in either analysis. These findings support Hypothesis 3.
Codes. When an objectively true solution exists, as in the case of codes, “truth wins” models may be tested. Under a “truth wins” decision scheme, if a correct solution is pro- posed by any group member, then the group will adopt that option. Thus, for the model tests involving codes, four additional “truth wins” models were tested in addition to the four mod- els listed above: (a) Truth wins, otherwise ma- jority, otherwise proportionality; (b) truth wins, otherwise majority, otherwise proportionality with emergents; (c) truth wins, otherwise ma- jority, otherwise expert-weighted proportional- ity; and (d) truth wins, otherwise majority, oth- erwise expert-weighted proportionality with emergents. As Table 5 indicates, all models tested were rejected for fit with the obtained codes data, including the predicted model. Pos- sible explanations for this unexpected lack of fit are addressed in the Discussion section.
Performance
Performance was defined as trials to solution. Problem solvers who did not solve the task within the allotted 10 trials were assigned a trials-to-solution score of 11. The percentages of nonsolving participants in the individual con- dition for Time 1, Time 2, Time 3, and Time 4 were 24%, 11%, 15%, and 9%, respectively. The percentages of nonsolving participants in the group conditions for Time 1, Time 2, Time 3, and Time 4 were 19%, 0%, 3%, and 11%, respectively, where Time 1 and Time 4 represent group members working individually and Time 2 and Time 3 represent groups work- ing interactively.
Although it was shown that members of groups provided with explicit ranking feedback were not significantly more likely to recognize intragroup expertise than were members of groups without this information, a direct com- parison of the two group conditions was con- ducted to assess whether they differed in terms of performance. A randomized blocks multivar- iate analysis of variance (with session as the blocking variable) compared performance for the two group conditions at Time 2 and at Time 3. The effect of feedback was nonsignif- icant, F(2, 16) � 1, Wilks’ lambda � 0.93, p � .05. Because the two group conditions did not significantly differ in terms of performance, these conditions were collapsed into one overall group condition in subsequent analyses. Fig- ure 2 shows the performance levels of groups, group members, and ranked independent indi- viduals at Times 1, 2, 3, and 4.
A randomized blocks analysis of variance was performed to assess the performance of the groups relative to the independent individuals for Time 2 and Time 3. For Time 2, the effect of problem solver was found to be significant, F(3, 90) � 19.03, p � .001, MSE � 2.10. Tukey post hoc comparisons revealed that the group did not perform significantly better than the best inde- pendent individual ( p � .05) but did perform significantly better than the second and third
Table 2 Obtained Probability of Group Choices by Member Distributions for Hypotheses
Member distribution
Group choice
SumA B D E
AAA .98 x x .02 61 AAB .88 .09 x .04 57 ABA .91 .07 x .02 45 ABB .23 .74 x .02 43 ABD .41 .23 .16 .20 225
Note. n � 431.
Table 3 Obtained Probability of Group Choices by Member Distributions for Codes
Member distribution
Group choice
SumC A B D E
CCC .96 x x x .04 27 CCA .83 .00 x x .17 12 CAC .92 .00 x x .08 12 ACC .50 .50 x x .00 2 CAA 1.00 .00 x x .00 2 ACA .33 .67 x x .00 6 AAC .00 1.00 x x .00 2 CAB .77 .08 .00 x .15 13 ACB .33 .33 .00 x .33 3 ABC .60 .00 .20 x .20 5 AAA .17 .83 x x .00 12 AAB .10 .70 .00 x .20 10 ABA .00 .78 .00 x .22 9 ABB .00 .25 .56 x .19 16 ABD .00 .20 .15 .14 .51 300
Note. n � 431.
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independent individuals (both p � .05). The same pattern was found for Time 3. The effect of problem solver was again significant, F(3, 89) � 40.37, p � .001, MSE � 1.38, and post hoc comparisons again indicated that the group did not outperform the first individual ( p � .05) but did outperform the second and third inde- pendent individuals (both p � .001). Together, these results support Hypothesis 4.
Discussion
Expertise Identification
The first hypothesis of this study predicted that group members would be generally well calibrated in their rankings of expertise. This prediction was supported. Group members, re- gardless of whether they were provided with explicit feedback, were relatively accurate with respect to their assessments of intragroup ex- pertise. However, the second hypothesis, pre- dicting that groups provided with explicit feed- back would be more accurate than groups not provided with this feedback, was not supported. Hypothesis 2 was based on previous research
suggesting the necessity of explicit feedback. In the current experiment, explicit feedback was not required. This may be due to the fact that the letters-to-numbers task exceeded expectations in satisfying the requirements of expertise iden- tification. Participants were fairly accurate re- gardless of their feedback conditions, and feed- back did not significantly contribute to accuracy in identifying expertise. This finding furthers our understanding of expertise in groups by demonstrating that explicit feedback is not al- ways necessary for the problem solvers to rec- ognize expertise within their group if the task is sufficiently intellective.
Group Decision Models
The third hypothesis stated that group deci- sion making would be best approximated by the model majority, otherwise expert-weighted pro- portionality with a proportionate probability of an emergent response. This prediction was sup- ported through an analysis of the decision pat- terns within groups. The predicted scheme was the only model that could not be rejected for equations and hypotheses. Although the pre-
Table 4 Kolmogorov–Smirnov Model Tests for Equations and Hypotheses
Model tests
Dmax
Equations Hypotheses
Majority, otherwise proportionality .06729 .11369 Majority, otherwise proportionality with emergents .10673 .07831 Majority, otherwise expert-weighted proportionality .07193 .11369 Majority, otherwise expert-weighted proportionality with emergents .05151a .00929a
Note. Dcrit � .05154. a Fail to reject at � � .20.
Table 5 Kolmogorov–Smirnov Model Tests for Codes
Model tests Dmax
Truth wins, otherwise majority, otherwise proportionality .38979 Truth wins, otherwise majority, otherwise proportionality with emergents .21578 Truth wins, otherwise majority, otherwise expert-weighted proportionality .38888 Truth wins, otherwise majority, otherwise expert-weighted proportionality
with emergents .25058 Majority, otherwise proportionality .38979 Majority, otherwise proportionality with emergents .20186 Majority, otherwise expert-weighted proportionality .38979 Majority, otherwise expert-weighted proportionality with emergents .23944
Note. Dcrit � .05154.
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dicted model was rejected for codes, it should be noted that all other models tested were sim- ilarly dismissed. An examination of Table 3 suggests a possible explanation for this lack of model fit. Deviation from the predicted model (and all other tested models) seems to be due to the extraordinarily high frequency of emergent group decisions for codes. Whereas emergent group decisions were selected 7% of the time for equations and 11% of the time for hypoth- eses, emergent decisions accounted for 39% of group codes.
Observations of the interacting groups sug- gested that the relative abundance of emergent codes was due in part to the problem solvers’ perceptions of the general improbability of pro- posing a correct code during the early trials of the experiment. Participants seemed to believe that whereas equations and hypotheses were useful on early and late trials alike, codes were considerably more valuable on later trials, when sufficient information had been gathered to nar- row down the potential answers. This percep- tion has a strong basis in reality, as the odds against choosing the correct code without having identified any of the 10 numbers is
3,628,800 to 1. Because it is futile to speculate on the code until information has been gathered, many groups simply opted to choose a haphaz- ard selection for the group code on the early trials rather than waste time discussing the is- sue. In fact, examination of the frequency of emergent code proposals by trials reveals that 65% of the emergent code proposals were made within the first three trials of the problem.
A second possible explanation for the abun- dance of emergent proposals for codes lies in the nature of the code variable as opposed to the equation and hypothesis variables. When form- ing equations and hypotheses, participants are called upon to formulate simple requests for information, which, depending on the complex- ity of the strategy being used by the problem solver, may require only a very basic under- standing of the state of knowledge relative to the problem (see Laughlin et al., 2003, for a discussion of strategies for solving the letters- to-numbers problem). When formulating codes, however, participants are called upon to inte- grate all of the information available to them from previous equations, hypotheses, and pro- posed codes. Whereas individual equations and
Figure 2. Performance of groups, group members, and ranked independent individuals. T1 � Time 1; T2 � Time 2; T3 � Time 3; T4 � Time 4; GM � group members working individually (aggregated across members); G � interactive group; I1 � first independent individual; I2 � second independent individual; I3 � third independent individual.
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hypotheses are not easily meaningfully com- bined, codes are much more amenable to com- bination. It may be the case that group code proposals were more likely to be generated in- tegratively, borrowing elements from different members’ understandings of the solution to the problem. Thus, the integrative nature of codes may have contributed to the large number of group proposals that were not directly adopted from individual group member inputs.
It should be noted that the two possible ex- planations offered are not mutually exclusive but could be operating in tandem. The first explanation, dealing with the intractability of the problem given sparse information, is an explanation more relevant to the early trials of the problem, when information is relatively scarce. The second explanation, dealing with the integration and combination of different members’ inputs, is an explanation more rele- vant to later trials, when information has accu- mulated to the point where meaningful specu- lation as to the correct code can take place.
Group Versus Individual Performance
The fourth hypothesis predicted that groups would perform at the level of the best of an equivalent number of individuals. This predic- tion was supported by the performance findings at both Time 2 and Time 3 (i.e., both group interactions). Groups performed at the level of the best of an equivalent number of individuals at both times. This finding supports a growing literature on group performance relative to in- dividuals on problem-solving tasks and extends the existing literature by comparing intact groups with the same individuals on two con- secutive task administrations. As indicated by Tables 2, 3, and 4, it is clear that the high level of group performance relative to independent individuals in the current experiment was not due to chronic acquiescence to the groups’ best members. If this were the case, the highest performing members in the groups (represented by the leftmost letters in the member distribu- tions) would determine the group choices re- gardless of the distribution of group preferences (e.g., situations involving majorities), whereas the data indicate otherwise. It seems likely that the high level of performance of groups in the current study was due to group-level processes such as error correction (e.g., Hill, 1982; Laugh-
lin et al., 1991) and not, in this case, to the adoption of a best member strategy (e.g., Henry, 1995; Yetton & Bottger, 1982). This specula- tion is also consistent with the notion that the groups in this study used an integrative method to construct their group codes, as discussed earlier.
Two recent studies (Laughlin et al., 2002, 2003) using large numbers of participants have found evidence of group superiority to the best comparison individuals. As Figure 2 indicates, in the current study, groups performed at the level of, or even nonsignificantly better than, the best individuals. At Time 2, interactive groups took nonsignificantly fewer trials to solve the problem than did the best individual problem solvers (M � 6.11 vs. M � 6.50). At Time 3, interactive groups and the best individuals per- formed at the same level (both Ms � 5.89). Thus, the current study does not contradict the findings of Laughlin and colleagues but does suggest that a fairly substantial level of statisti- cal power may be necessary to capture the group superiority effect.
Future Research
Future research in this area should focus on expanding our understanding of how individu- al-differences variables can influence group be- havior, performance, and problem-solving strat- egies across tasks of various types. Factors hy- pothesized to affect the influence of group members should be closely examined in a for- mat that will allow the tracking of individual member influence over the course of the prob- lem-solving experience. Possible factors in- clude gender (Karakowsky & Siegel, 1999; Knight & Saal, 1984), status (Kirchler & Davis, 1986), extroversion (Bonner, 2000), knowledge (a form of expertise; Hollingshead, 1998, 2000; Stewart & Stasser, 1995, 1998), and expertise as defined in the current experiment.
It should be noted that although participants in the no-feedback condition of the current study did not receive the explicit ranking infor- mation that was made available to the other group participants, other potentially valuable information was available to them. For exam- ple, all participants had access to task-related information (e.g., the solutions to proposed equations), and all group participants had access to other information in the form of social cues,
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verbal cues, perceptions of confidence, and so forth. An examination of how individual differ- ences, task-related information, and perceptual cues can lead to accurate (or inaccurate) exper- tise identification warrants further investigation.
Conclusions
Groups make choices that impact all levels of society. The current study contributes to our understanding of the effects of expertise in such groups. Experts were found to wield far more influence than other group members even when no explicit performance feedback was provided. This adds to our understanding of groups as potentially effective and resourceful informa- tion-processing systems.
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(Appendix follows)
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Appendix
Instructions Given to Participants for Letters-to-Numbers Task
This is an experiment in problem solving. The objective is to figure out a Code in as few trials as possible. The numbers 0 –9 have been coded as the letters A–J in some random order. You will be trying to find out which letter corresponds to which number. It is important to remember that all we are doing is changing the characters used to represent the numbers. We are not changing the way that the number system works. That is, we are still using the same decimal number system you have been using all of your life. Here is an example of a random Code: [A � 3, B � 5, C � 8, D � 2, E � 1, F � 6, G � 4, H � 7, I � 4, J � 9]. Since we are still using the same number system, we can write any number using our Code. For example, the number “846” could be written as “CGF.” The number “negative seven” could be written as “�H”, etc. You will use a three-step process to solve the Code. In the first step you will come up with addition or subtraction Equations using the letters A–J that will be solved by the experimenter who will give you the answer in letter form. Then you will form a Hypothesis as to what one of the letters represents. The experimenter will tell you if your Hypothesis is correct or incorrect. Finally you will guess what the entire Letters-to- Numbers Code actually is. When you have figured out the
entire Letters-to-Numbers Code you will have solved the problem. You will continue this process for ten trials or until you solve the problem. Here are four example trials using the random Code above. [Note that underlined characters represent experimenter responses.]
In the first trial the problem solver chooses the equation “A � B � ” and the experimenter tells the problem solver that the solution to this Equation is “C.” This is because A � 3 and B � 5 which sums to 8, the number represented by C. The problem solver then Hypothesizes that A repre- sents the number 1 and the experimenter indicates that this is not the case. The problem solver then guesses the entire Code and is incorrect. On the second trial the problem solver asks the solution to the Equation, “B � C � ” and is told that the answer is “EA.” This is because B � 5 and C � 8 which sums to 13 or E(1)A(3). Note that on the third trial this problem solver chooses to add three num- bers together. You may use as many numbers as you desire in your Equations. Note that in the fourth trial the problem solver chooses to use a subtraction Equation. You may use either addition or subtraction Equations as you see fit.
Received February 5, 2004 Revision received July 31, 2004
Accepted August 20, 2004 �
Trial Equation Hypothesis Feedback Code 1 A � B � C A � 1 False A � , B � , C � , . . .J � 2 B � C � EA A � 8 False A � , B � , C � , . . .J � 3 F � A � D � EE E � 1 True A � , B � , C � , . . .J � 4 H � J � �D I � 0 True A � , B � , C � , . . .J �
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