Benchmarking what we’d do, I came across Democracy 3. It’s a semi-veteran government simulation game, published already in 2005 by Positech Games.
The player takes either the role of president or prime minister of a democratic government, and rules his country. He’s in charge of (almost?) an innumerable amount of things: from the big picture, including budget and tax policy, to very detailed ‘yes-no’ decisions on specific questions.
Also, arbitrary challenges take place, e.g. criminality, demonstrations and environmental problems.
The game requires a decent understanding of the government – thus, the target audience may be people of age +15, who are somehow into somewhat analytic and strategic, semi-realistic games.
The game also yielded a spin-off version in 2016, Democracy 3: Africa, with its own twist: when you’re ruling your country, either you’re to solve the difficult problems (such as forced marriages, poverty, children’s malnutrition), or to go deeper into fierce dictatorship.
This is democracy gamified – it concretizes that the decisions they’re making there aren’t light nor easy to make. Maybe there’s some kind of educational aspect to the game, too; assuming you’re a US citizen or that at least you know their governmental system quite well.
There are some controversial things in the game, regarding real-life: as an example, it’s possibile to adjust death penalty, legalize drugs etc.