Economic agents make decisions in particular models. These models do not need to be related to financial contexts, and economics can be used to describe how agents will act in any other field in which humans act.
As an example, how would economic principles be applied to the process of a democratic election?
Long story short: Preferences orderings are over more abstract outcomes instead of money. It's still a story of maximizing expected utility.
Agents are usually assumed to have preferences over outcomes. This is assuming something like consequentialism. In financial models, the outcomes are dollar amounts and so there is a natural preference ordering. In something like a political model, outcomes are policies. So, people have indirect preferences over political candidates based on beliefs and seek to influence the outcome by voting. This is probably a bad model of voting, as most people don't honestly believe their vote matters I'm guessing.
Beyond voting to influence current decision-making, here is a good paper about voting as communicating: Piketty (2000)
I think what you're looking for is the field of "political economy." According to the Wikipedia article, this term can relate to several different things. You'll want to look at "public choice theory." As its wikipedia article says,
Public choice or public choice theory refers to "the use of economic tools to deal with traditional problems of political science". Its content includes the study of political behavior. In political science, it is the subset of positive political theory that studies self-interested agents (voters, politicians, bureaucrats) and their interactions, which can be represented in a number of ways, such as standard constrained utility maximization, game theory, or decision theory.
