  We introduce the confident voter model, in which each voter can be in one of
two opinions and can additionally have two levels of commitment to an opinion
--- confident and unsure. Upon interacting with an agent of a different
opinion, a confident voter becomes less committed, or unsure, but does not
change opinion. However, an unsure agent changes opinion by interacting with an
agent of a different opinion. In the mean-field limit, a population of size N
is quickly driven to a mixed state and remains close to this state before
consensus is eventually achieved in a time of the order of ln N. In two
dimensions, the distribution of consensus times is characterized by two
distinct times --- one that scales linearly with N and another that appears to
scale as N^{3/2}. The longer time arises from configurations that fall into
long-lived states that consist of two (or more) single-opinion stripes before
consensus is reached. These stripe states arise from an effective surface
tension between domains of different opinions.
