  The Bradley effect concerns the discrepancy between opinion polls and actual
election outcomes that emerges when candidates do not exhibit ideological,
sexual or racial mainstream features. This effect was first observed during the
1982 election for the Governor of California that resulted in a significant
loss for the black Democratic candidate, Tom Bradley, despite him being ahead
in polls. It has been argued that poll respondents may tend to mask their true
political preference in favour of what is generally considered more socially
acceptable. We propose an exactly solvable statistical mechanical model, which
allows for a quantitative exploration of this phenomenon. The model includes
three main ingredients: (i) the tendency of individuals to align their real
preference to the declared (public) opinions of others, (ii) a term accounting
for an individual integrity factor, which induces voters to be consistent
between their public and private opinions, and (iii) a self-monitoring
component, which tunes the strength by which an individual is affected by and
wishes to publicly conform to social norms. We observe the emergence of order
in a wide range of parameters of the model and discuss the effect of noise on
the correlation between hidden and public preference. Finally, we present an
application of this model to the prediction of election outcomes.
