  In the impartial selection problem, a subset of agents up to a fixed size $k$
among a group of $n$ is to be chosen based on votes cast by the agents
themselves. A selection mechanism is impartial if no agent can influence its
own chance of being selected by changing its vote. It is $\alpha$-optimal if,
for every instance, the ratio between the votes received by the selected subset
is at least a fraction of $\alpha$ of the votes received by the subset of size
$k$ with the highest number of votes. We study deterministic impartial
mechanisms in a more general setting with arbitrarily weighted votes and
provide the first approximation guarantee, roughly $1/\lceil 2n/k\rceil$. When
the number of agents to select is large enough compared to the total number of
agents, this yields an improvement on the previously best known approximation
ratio of $1/k$ for the unweighted setting. We further show that our mechanism
can be adapted to the impartial assignment problem, in which multiple sets of
up to $k$ agents are to be selected, with a loss in the approximation ratio of
$1/2$.
