Unfortunately, unlike the unweighted cases, this reduction cannot be easily modified for the case of adding weighted voters of 3-veto elections or deleting weighted voters in 3-approval elections. This is because it is not possible to compute the final score of p **following the addition or deletion of voters in these cases. Recall**
that in unweighted cases, it can be assumed that without loss of generality we will alter as many voters as possible.

Theorem 27 k-approval elections for k ≥ 3 and k-veto for k ≥ 4 are computationally resistant to $**bribery.**
Proof: **This problem is a generalization of unpriced bribery for the same election systems, which is NPhard.** Theorem 28 Weighted 1-approval and 1**-veto elections are computationally vulnerable to constructive control by adding and deleting voters.**
Proof: **We consider the four cases separately. In 1-approval constructive control by adding voters, it**
is only relevant to add voters approving our distinguished candidate p**. We thus add the heaviest voters** approving p, up to our quota or until we are out of such voters. Control is possible iff p **wins in this case.**
In 1-veto constructive control by adding voters, for each candidate p
′ beating p**, we must eventually add**
votes vetoing p
′**. Without loss of generality we can add the heaviest vote. Our algorithm thus works as**
follows. Until p **is winning, for each candidate** p
′currently beating p**, we add the vote vetoing** p
′ **with the**
heaviest weight.

In 1-approval constructive control by deleting voters, we see that for each candidate p
′ beating p**, we**
must eventually delete a vote approving p
′**. Without loss of generality we can delete the heaviest vote. Our**
algorithm thus works as follows. Until p **is winning, for each candidate** p
′ beating p**, we delete the vote**
approving p
′ **with the heaviest weight.**
In 1-veto constructive control by deleting voters, we delete the **heaviest votes vetoing** p.

Theorem 29 Weighted k-approval elections for k ≥ 4 and k-veto elections for k ≥ 3 **are computationally** resistant to control by adding voters. Similarly, weighted k-approval elections for k ≥ 3 and k**-veto elections**
for k ≥ 4 **are computationally resistant to control by deleting voters.**
Proof: **These problems are generalizations of the corresponding unweighted problems for the same election** systems, which are NP-hard.