  We study the election control problem with multi-votes, where each voter can
present a single vote according different views (or layers, we use "layer" to
represent "view"). For example, according to the attributes of candidates, such
as: education, hobby or the relationship of candidates, a voter may present
different preferences for the same candidate set. Here, we consider a new model
of election control that by assigning different rules to the votes from
different layers, makes the special candidate p being the winner of the
election (a rule can be assigned to different layers). Assuming a set of
candidates C among a special candidate "p", a set of voters V, and t layers,
each voter gives t votes over all candidates, one for each layer, a set of
voting rules R, the task is to find an assignment of rules to each layer that p
is acceptable for voters (possible winner of the election). Three models are
considered (denoted as sum-model, max-model, and min-model) to measure the
satisfaction of each voter. In this paper, we analyze the computational
complexity of finding such a rule assignment, including classical complexity
and parameterized complexity. It is interesting to find out that 1) it is
NP-hard even if there are only two voters in the sum-model, or there are only
two rules in sum-model and max-model; 2) it is intractable with the number of
layers as parameter for all of three models; 3) even the satisfaction of each
vote is set as dichotomous, 1 or 0, it remains hard to find out an acceptable
rule assignment. Furthermore, we also get some other intractable and tractable
results.

Computational Complexity;Computer Science and Game Theory