Are there election systems where voters cast a vote on the final composition of the legislature, rather than individual parties or candidates?

Question

As an example, Germany is well known for having the problem of forming a coalition due to a large number of parties being elected to their legislative body. I imagine this can be frustrating to some voters who might prefer a stable coalition, even if it means their favorite party can no longer participate. One way to achieve this is to have people vote on the final composition of the parliament, rather than individual parties. This would be highly convoluted, but same can be told of many theoretical voting systems.

Does such a system exist, at least in voting theory?

Answer 1

In some regional elections in Germany, the voters can cast multiple (usually three) votes for different lists or candidates (Panachage). This allows them to give 1/3 and 2/3 of their vote to different parties, or even discard one and split the remainder 1/2 to 1/2. There are some wrinkles how the party list interact with individual votes, but the voter can cast votes for up to three parties.

Answer 2

Does such a system exist, at least in voting theory?

No.

While some systems allow voters to cast multiple votes that can be split between candidates or parties, no system allows one to vote on the total composition of the body elected. It isn't even clear what such a system would look like.

Perhaps the closest analogy would be voting systems within legislative bodies regarding an overall budget for a governmental entity, in which one could have each member allocate the available governmental funds as they see fit and aggregate the preferences of individual legislators.

But, no system in existence or seriously proposed does that for a legislature. There is really no good reason that it should, as it would be very confusing and the vast majority of voters simply want to maximize the power of their favorite parties or candidates, rather than having some particular balance of parties.