Welfare systems don't come with peoples names in the legislation, like "Bob always does the dishes". They are based on other properties which any citizen might

Welfare systems don't come with peoples names in the legislation, like "Bob always does the dishes". They are based on other properties which any citizen might sometime have. So they are more like, "the person who has least recently done the dishes (provided they are not now sick or injured) does the dishes." Welfare is not an example of the kind of democratic fairness dilemma that you raise with the Bob-always-does-the-dishes solution.