The Bradley effect concerns the discrepancy between opinion polls and actual election
outcomes that emerges when candidates do not exhibit mainstream ideological, sexual
or racial 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 tend to mask their true political preference and 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.
