the simulation of individual prediction in an 'alone' - and 'group' - condition

summary: 30 subjects had to predict a stimulus persons reactions to the itmes of a value test. they were given 5 answers of the s-person among which each of the five assumed dimensions of the unnormed test was represented. then 10 additional answershad to be predicted. after each prediction the true answer of the s-person was announced (by the experimenter) or could be found in an envelope. the same 30 subjects were run with the same value test but 2 different s-persons (one constructed, the other a modified empirical person) first in an "alone condition" where the prediction was given without interaction and then in a "group condition" where the 5 members first fixed an individual prediction each and then discussed these and derived a group prediction item by item. in the group condition the amount of individual interaction seemed to have no influence on the immediate outcome of the group decision (almost without exception - 56 out of 60 cases - the median of the individual predictions was chosen). it therefore was supposed that the interaction might have some influence on the group members individual solution process for the subsequent trials. to prove this assumption some models to simulate the individual prediction process were constructed. in the alone condition a variety of programs which assumed that for the first trials "projection" will take place (i.e. predict one's private opinions for the s-persons) and that then a learning process, which leads to a preference for the most often heard category of the s-persons answers, will take over, were the models with the best fit (119 maximal correct predictions out of 300) . these models did very bad in the group condition. in this situation models which assumed the summation of reaction tendencies and the realization of the biggest one were much more appropriate. the most important summands of the reaction potential were the "content structure" of the test itself (the face validity of the items presumably) and some preferences for not too extreme but yet information-conveying response categories (maximal success achieved was 136 correct predictions out of 300). the prior answers of the s-person were important only for the first trials and then ones own and the partner's priors predictions became predominately important. also the projection mechanism or one's private opinion to the items was much less important in the group than in the alone condition. the dissimilarities between the solution process in the alone-condition and the group-condition are exhibited by the simulation models which best describe each of the two situations. to obtain more perfect fit in both situations the consideration of personality variables and information on the test items and of verbal content of interaction in the group situation seems quite inevitable. only the second of the three kinds of information necessary was used to a small extent in our models, the primary goal of the investigation being to exploit the redundancies in both situations considered.

Beweis eines Theorems in der Graphentheorie: Eine Ungleichung für den maximal möglichen Grad der Unbalanciertheit eines vollständigen exklusiven Bigraphen

zusammenfassung (gekuerzt): abelson und rosenberg geben eine ungleichung fuer den maximal moeglichen grad der unbalanciertheit eines vollstaendigen exklusiven bigraphen zu n punkten an. der beweis dieser ungleichung konnte seit der aeusserung dieservermutung 1958 nicht gefunden werden. hier soll dieser beweis gegeben werden, indem zunaechst das problem geloest wird, um wieviel der grad der unbalanciertheit eines vollstaendigen exklusiven bigraphen zu n punkten maximal anwachsen kann, wenn ein weiterer, n plus 1ter punkt hinzugefuegt wird. daraus ergibt sich im naechsten schritt eine formel zur direkten berechnung des maximal moeglichen unbalanciertheitsgrades eines vollstaendigen exklusiven bigraphen zu n punkten.

beweis eines theorems in der graphentheorie: eine ungleichung fuer den maximal moeglichen grad der unbalanciertheit eines vollstaendigen exklusiven bigraphen

zusammenfassung (gekuerzt): abelson und rosenberg geben eine ungleichung fuer den maximal moeglichen grad der unbalanciertheit eines vollstaendigen exklusiven bigraphen zu n punkten an. der beweis dieser ungleichung konnte seit der aeusserung dieservermutung 1958 nicht gefunden werden. hier soll dieser beweis gegeben werden, indem zunaechst das problem geloest wird, um wieviel der grad der unbalanciertheit eines vollstaendigen exklusiven bigraphen zu n punkten maximal anwachsen kann, wenn ein weiterer, n plus 1ter punkt hinzugefuegt wird. daraus ergibt sich im naechsten schritt eine formel zur direkten berechnung des maximal moeglichen unbalanciertheitsgrades eines vollstaendigen exklusiven bigraphen zu n punkten.

Nonparametric IRT: Testing the bi-isotonicity of isotonic probabilistic models (ISOP)

instrumental pair comparison systems, weak subject independence, weak item independence, multidimensional coordinatewise partial order, sample-free estimates, index of association and of isotonicity,

computer simulation of small group decisions

summary: in a test of three computer models to simulate group decisions, data were used from 31 american and austrian groups on a total of 307 trials. the task for each group was to predict a series of answers of an unknown subject on a value-orientation questionnaire after being given a sample of his typical responses. the first model which used the mean of the individual opinions as a simulation of the group judgment simulated exactly over half of the trials. the simulation was improved in model two, which also used the mean, when individual opinions were weighted according to their total participation in the discussion and "learning" was added. this was especially true when the cutting points were changed so that the mean would represent more extreme opinions. the best simulation occured with model three which used the median of the individual opinions as the best simulation of the group decisions. using this model over 75 percent of the trials were accurately simulated.