Patrick R. Laughlin

Demonstrability and social combination processes on mathematical intellective tasks.

Abstract Research on social combination models of group problem solving and decision making indicates that the number of group members that is necessary and sufficient for a collective decision is inversely proportional to the demonstrability of a proposed group response. Mathematics is the preemenent domain of demonstrability. Accordingly, a truth wins social combination process, in which a single correct group member is necessary and sufficient for a correct group response, was predicted for five-person groups on 10 mathematical problems. After taking the problems as individuals, college students took them again as five-person groups or control individuals. They then took the same problems a third time as individuals. Groups performed better than individuals on the second administration, and individuals who had been in groups performed better on the third administration than individuals who had not been in groups. As predicted, the best-fitting social combination model was truth wins. We propose that demonstrability requires four conditions, and that the social combination process on a given task corresponds to the degree to which these four conditions are fulfilled.

Groups Perform Better Than the Best Individuals on Letters-to-Numbers Problems: Effects of Group Size

Individuals and groups of 2, 3, 4, or 5 people solved 2 letters-to-numbers problems that required participants, on each trial, to identify the coding of 10 letters to 10 numbers by proposing an equation in letters, receiving the answer in letters, proposing a hypothesis, and receiving feedback on the correctness of the hypothesis. Groups of 3, 4, and 5 people proposed more complex equations and had fewer trials to solution than the best of an equivalent number of individuals. Groups of 3, 4, and 5 people had fewer trials to solution than 2-person groups but did not differ from each other. These results suggest that 3-person groups are necessary and sufficient to perform better than the best individuals on highly intellective problems.

Groups perform better than the best individuals on Letters-to-Numbers problems

Individuals and groups of 2, 3, 4, or 5 people solved 2 letters-to-numbers problems that required participants, on each trial, to identify the coding of 10 letters to 10 numbers by proposing an equation in letters, receiving the answer in letters, proposing a hypothesis, and receiving feedback on the correctness of the hypothesis. Groups of 3, 4, and 5 people proposed more complex equations and had fewer trials to solution than the best of an equivalent number of individuals. Groups of 3, 4, and 5 people had fewer trials to solution than 2-person groups but did not differ from each other. These results suggest that 3-person groups are necessary and sufficient to perform better than the best individuals on highly intellective problems.

Collective versus individual induction: Recognition of truth, rejection of error, and collective information processing.

Four-person groups and 4 independent individuals solved rule induction problems under 4 levels of potential information. Groups performed at the level of the 2nd-best individuals for correct hypotheses (recognition of truth) and at the level of the best individuals for nonplausible hypotheses (rejection of error)

Groups perform better than the best individuals on letters-to-numbers problems: informative equations and effective strategies.

One-hundred 3-person groups and 300 individuals solved 2 letters-to-numbers problems, requiring identification of the coding of 10 letters to 10 numbers by proposing an equation in letters, receiving the answer in letters, proposing a hypothesis, and receiving feedback on the hypothesis on each trial. There were 5 instruction conditions: (a). standard, (b). use at least 3 letters on all equations, (c). use at least 4 letters on all equations, (d). number 1 known before beginning problem, and (e). number 9 known before beginning problem. The groups had fewer trials to solution, proposed more complex equations, and identified more letters per equation than the best individuals. Performance was best under instructions to use at least 4 letters and with the number 9 known.

Individual versus tetradic performance on a complementary task as a function of initial ability level

Abstract In a test of a model of the relationship of ability to group problem solving on a complementary task, 1008 college students were administered the Terman Concept Mastery Test. After being trichotomized as High (H), medium (M), or low (L) ability, they retook the test working with three partners in one of the 15 possible ability combinations of tetrads HHHH, HHHM,…, LLLL. Control H, M, and L individuals retook the test alone. The predicted order of improvement scores from the first to the second test for the three ability levels was largely supported, as was the predicted order of absolute second-test performance for the 15 groups. It is proposed that, on a difficult complementary task, group problem solving performance increasingly exceeds the performance of the same individuals working, independently as the ability level of the individuals comprising the group increases. The failures of prediction of the model are interpreted as indicating that low and/or medium-ability members may hinder the performance of high-ability members of a problem-solving group.

Social decision schemes of the same four-person groups on two different intellective tasks.

501 female high school students took the Remote Associates Test (RAT) and the Otis Quick-Scoring Mental Ability Test first as individuals and then were assigned to cooperative groups or control individual conditions for a 2nd test administration. 10 social decision scheme models were tested at each of 3 ability levels for each task as theories of the underlying group process. As predicted, the best-fitting social decision scheme on the RAT represented a truth-wins process, while the best-fitting social decision scheme on the Otis test represented a complex combination of a truth-supported-wins process when 3 or 4 members knew the correct answer, an increment from grouping when 2 members knew the answer or no members knew the answer, and strong conformity pressures against a single correct member. Results extend previous research in which the group task and group members have been confounded to a demonstration of different social decision schemes for the same groups on different group tasks.

Collective Versus Individual Induction With Single Versus Multiple Hypotheses

Four-person cooperative groups and 4 independent individuals solved rule induction problems by proposing 1, 2, or 4 hypotheses per trial while selecting the same amount of evidence per trial. Groups performed at the level of the best individuals and better than the 2nd-best, 3rd-best, and 4th-best individuals for both correct hypotheses and nonplausible hypotheses. Increasing the number of proposed hypotheses from 1 to 2 to 4 did not increase correct hypotheses but increased nonplausible hypotheses. Transition probabilities from hypotheses on trial t to t + 1 indicated superior performance for the groups and best individuals for each of positive and negative hypothesis tests followed by examples and nonexamples; once the groups and best individuals proposed the correct hypothesis, they were more likely to continue to propose it than the other individuals.

Collective induction: Mutual group and individual influence by exchange of hypotheses and evidence☆

Abstract Yoked four-person groups and individuals induced a rule under four conditions of information exchange. The yoked groups and individuals exchanged both hypotheses and evidence on each trial, hypotheses only, evidence only, or neither. Both the exchange of hypotheses and the exchange of evidence improved the aggregate performance of the yoked group and individual. Group performance was superior to individual performance. Significant three-way interactions indicated that this superiority was greatest when evidence, but not hypotheses, was exchanged. Alternatively, the interactions indicated that exchange of evidence had relatively more effect than exchange of hypotheses for groups, whereas exchange of hypotheses and exchange of evidence had comparable effects for individuals. The patterns of same and different individual and group hypotheses on trials t and t + 1 indicated more group influence on the individual than individual influence on the group. Social combination analyses of the group hypotheses for distributions of member hypotheses indicated that the same basic social combination process applied in all four conditions. Sequential transition analyses of the transition probabilities from distributions of member hypotheses on trial t to distributions on trial t + 1 indicated that once the correct hypothesis was proposed by one or more group members it was highly likely to be proposed again by one or more members on the subsequent trial. We propose that the inductive task and yoking methodology will be useful for research on majority and minority influence.

Group-to-Individual Problem-Solving Transfer

Many scientific, educational, business, military, and political groups assume that people who solve problems in groups and teams will solve subsequent problems better as individuals than people without previous group problem-solving experience. In order to assess such group-to-individual transfer, sets of three people solved four letters-to-numbers decoding problems as groups (G) or individuals (I) in five conditions: GGGG, GGGI, GGII, GIII, or IIII. Results supported four hypotheses: (a) groups performed better than individuals, (b) positive group-to-individual transfer occurred, (c) one group experience was sufficient for transfer, (d) transfer was at the level of group performance (complete) on problems 2 and 3 but incomplete on problem 4, due to exceptional performance in the GGGG condition.