  We discuss voting scenarios in which the set of voters (agents) and the set
of alternatives are the same; that is, voters select a single representative
from among themselves. Such a scenario happens, for instance, when a committee
selects a chairperson, or when peer researchers select a prize winner. Our
model assumes that each voter either renders worthy (confirms) or unworthy any
other agent. We further assume that the prime goal of each agent is to be
selected himself. Only if that is not feasible, will he try to get one of those
that he confirms selected. In this paper, we investigate the open-sequential
voting system in the above model. We consider both plurality (where each voter
has one vote) and approval (where a voter may vote for any subset). Our results
show that it is possible to find scenarios in which the selected agent is much
less popular than the optimal (most popular) agent. We prove, however, that in
the case of approval voting, the ratio between their popularity is always
bounded from above by 2. In the case of plurality voting, we show that there
are cases in which some of the equilibria give an unbounded ratio, but there
always exists at least one equilibrium with ratio 2 at most.
