Exercises 3.71 to 3.73 consider the question (using fish) of whether
uncommitted members of a group make it more democratic. It has been argued
that individuals with weak preferences are particularly vulnerable to a vocal
opinionated minority. However, recent studies, including computer simulations,
observational studies with humans, and experiments with fish, all suggest that
adding uncommitted members to a group might make for more democratic decisions
by taking control away from an opinionated minority. \({ }^{36}\) In the
experiment with fish, golden shiners (small freshwater fish who have a very
strong tendency to stick together in schools) were trained to swim toward
either yellow or blue marks to receive a treat. Those swimming toward the
yellow mark were trained more to develop stronger preferences and became the
fish version of individuals with strong opinions. When a minority of five
opinionated fish (wanting to aim for the yellow mark) were mixed with a
majority of six less opinionated fish (wanting to aim for the blue mark), the
group swam toward the minority yellow mark almost all the time. When some
untrained fish with no prior preferences were added, however, the majority
opinion prevailed most of the time. \({ }^{37}\) Exercises 3.71 to 3.73
elaborate on this study.
What Is the Effect of Including Some Indifferent Fish? In the experiment
described above under Fish Democracies, the schools of fish in the study with
an opinionated minority and a less passionate majority picked the majority
option only about \(17 \%\) of the time. However, when groups also included 10
fish with no opinion, the schools of fish picked the majority option \(61 \%\)
of the time. We want to estimate the effect of adding the fish with no opinion
to the group, which means we want to estimate the difference in the two
proportions. We learn from the study that the standard error for estimating
this difference is about \(0.14 .\) Define the parameter we are estimating, give
the best point estimate, and find and interpret a \(95 \%\) confidence interval.
Is it plausible that adding indifferent fish really has no effect on the
outcome?
