First a study by Jenness, in 1932. The aim of the study was to investigate the effect of group discussion on the accuracy of individual judgements. Individually, participants were asked to estimate the number of jellybeans in a jar. They then discussed their estimates in a large group or in several small groups. During this time, they learnt that their estimates varied wildly. Within their groups, they were asked to give a second estimate, this time working together to produce a number. Finally, participants were asked for a second individual estimate. The study found that the second estimates tended to be much nearer the group estimate than the individual's first guess. This change of opinion was greater among females. As a result, the study concluded that individual judgments are affected by majority influence, especially in an ambiguous situation. The psychology that's believed to be behind this is based around informational social influence. Individuals have a basic need to be right- in a situation where the right answer is unclear (such as in this case), they look to see what others think. This type of conformity is called internalisation- the individual changes both their private and public views. Ergo, you have the convergence seen.
Secondly is Asch's study into conformity. The aim was to investigate the extent to which individuals will conform to a majority who give obviously wrong answers. 132 male American students volunteered to take part, with each individual participating on their own. They believed that what they'd volunteered for was a study into visual perception. The participant was placed with seven to nine other people, who were introduced as other participants but who were actually confederates. Their task was to say which line (A, B or C) was the same as a stimulus line.
