They have a tendency to avoid taking responsibility the more powerful they become.
"They have a tendency to avoid taking responsibility"＝「彼らは責任から逃げる傾向がある」
"the more powerful they become"＝「偉くなればなるほど」
Sentence in context:
"Politicians and teachers, they both tend to flee from taking responsibility when they become more and more powerful."
アメリカ合衆国 
