min(sum) vs min(max)

We tend to optimize by minimizing overall costs. In this case we do not care about individual costs - we care about sum of costs. Of course we can harness personal costs by constrains of optimization methods, but we still focus on sum of costs.

Personally I become angry if my costs are high, and not when overall sum of costs is high, and personally I do not really care if I pay average, a little more than average, or a little less than average. U just become angry when I pay a lot.

So how about if we start to minimize min(max) of our transport systems rather than sum of costs, we'd become happier (even though overall costs will be greater)

PS. The problem was discussed extensively on exemple of network versus user optimum equilibrium assignment method, but I'm not sure if this criteria is considered in policriteria traffic management (apart from implicite constraining parameters inside optimization problem definition)