Given condition 4.2 Equal Treatment of Equals, from an Admissible Utility Function, where if agents have identical skills, then they must enjoy identical utility levels.
So lets take the example given in the book, where a society endowed with antibiotics in the amount just enough to treat only one patient. Now given this example we clearly see that when splitting the antibiotics equally and thereby treating no one, condition 4.2 will hold. But condition 4.1 Pareto efficiency will not.
This example will work with a treshold given, but what happens when there is monotonicity?
What then when instead of splitting the antibiotics equally, we treat them all equal and random? Then everyone will be treated “equally”.
As embedded in the 14th Amendment to the U.S. Constitution is the equal protection clause, which is the primary constitutional mechanism guaranteeing people equal treatment under the law. “The ideal in American law is that all people are treated equally under the law, and that the law should treat people based on their particular choices and actions, and never on legally irrelevant grounds like race,” Robin B. Kar said.
Thus, the equal protection clause as it’s currently interpreted “fails to guarantee people actual equal treatment under the law”.
Now as the criticisms stands, Would one be willing to sacrifice the sure rescue of Alice from near-certain death for the sake of an arbitrarily small chance of Bob’s survival?
Now, as Kar and Lindo say, they urge the Supreme Court to reinterpret the equal protection clause so that it safeguards not only against intentional discrimination but also “any disparate impact caused by racial beliefs that regularly function to produce inequality.”