  We introduce a new opinion dynamics model where a group of agents holds two
kinds of opinions: inherent and declared. Each agent's inherent opinion is
fixed and unobservable by the other agents. At each time step, agents broadcast
their declared opinions on a social network, which are governed by the agents'
inherent opinions and social pressure. In particular, we assume that agents may
declare opinions that are not aligned with their inherent opinions to conform
with their neighbors. This raises the natural question: Can we estimate the
agents' inherent opinions from observations of declared opinions? For example,
agents' inherent opinions may represent their true political alliances
(Democrat or Republican), while their declared opinions may model the political
inclinations of tweets on social media. In this context, we may seek to predict
the election results by observing voters' tweets, which do not necessarily
reflect their political support due to social pressure. We analyze this
question in the special case where the underlying social network is a complete
graph. We prove that, as long as the population does not include large
majorities, estimation of aggregate and individual inherent opinions is
possible. On the other hand, large majorities force minorities to lie over
time, which makes asymptotic estimation impossible.
