  In many real world situations, collective decisions are made using voting
and, in scenarios such as committee or board elections, employing voting rules
that return multiple winners. In multi-winner approval voting (AV), an agent
submits a ballot consisting of approvals for as many candidates as they wish,
and winners are chosen by tallying up the votes and choosing the top-$k$
candidates receiving the most approvals. In many scenarios, an agent may
manipulate the ballot they submit in order to achieve a better outcome by
voting in a way that does not reflect their true preferences. In complex and
uncertain situations, agents may use heuristics instead of incurring the
additional effort required to compute the manipulation which most favors them.
In this paper, we examine voting behavior in single-winner and multi-winner
approval voting scenarios with varying degrees of uncertainty using behavioral
data obtained from Mechanical Turk. We find that people generally manipulate
their vote to obtain a better outcome, but often do not identify the optimal
manipulation. There are a number of predictive models of agent behavior in the
COMSOC and psychology literature that are based on cognitively plausible
heuristic strategies. We show that the existing approaches do not adequately
model real-world data. We propose a novel model that takes into account the
size of the winning set and human cognitive constraints, and demonstrate that
this model is more effective at capturing real-world behaviors in multi-winner
approval voting scenarios.
