I’d say a lottery based on merit would be appropriate to choose leadership in certain areas for a reasonable duration. Determining merit could be a sticky issue if misapplied though, and could lead to some of the issues we deal with now.

Perhaps people could vote on a pool of experts for the final decision, with each expert advertising the solutions or progress they hope to achieve during the term of their leadership. It could just amount to people voting on the methods each expert chooses to accomplish their goals, depending on how specialized the office is.

As for leading the country, I am unsure if such an office is necessary. I am personally not a fan of the centralization of power when society is this profoundly sick. We need to patch the leaks in our ship before we can worry about captaining it.