Joe Arpaio’s tenure as Sheriff was characterized by gratuitous cruelty, racism, incompetence, and systematic violations of constitutional rights. 

So Donald Trump’s pardon of him was overdetermined:

It is highly relevant that Trump and Arpaio first became allies while Trump was rising to prominence within the Republican Party by pushing the racist conspiracy theory that Barack Obama was not born in the United States. 

The Arizona sheriff actually launched a farcical investigation into Obama’s birth certificate, wasting taxpayer money to build his cred with his resentful white supporters. 

That Arpaio and Trump would become mutual admirers was inevitable.

They are both racist buffoons.