yes

I would recommend starting with a research question that does not begin with an assumption that can hardly be generalized. There is definitely a connection between dynamics of power within police and military corps and patterns of behavior that can be associated with arrogance, but to do proper research your question should be phrased more like "Is there a higher percentage of attitudes and behaviors that can be considered arrogant (define arrogant) among military and police corps? And if yes, what might be the cause?" As you can see this is a very broad question, so you might have to reduce it further by defining your demographic sample, and performing a variety of tests to assess how you would measure arrogant behaviors/thought patterns. Also, in research you should avoid making statements about the being of others, as in "police officers and military officials are X", but more as in "70% of police officers and military officers behave/think in a way consistent with this definition of X". Words like disgusting don't have a place in research, while you might have all the reasons to use it in your personal life.

I would recommend reading Foucault and Elias Canetti as a starting point.

The effectiveness of police work depends (among other important factors), on the authority he or she can transmit. From my point of view, the essential question is to identify how many ways you can transmit authority but waiving arrogance.

I think you would be amazed at how arrogance disappears when a policeman comes home and takes off his uniform.

I think that you begin with a conclusion that it is not confirmed. I work as a Police and the arrogance that you commented is not a element that we need in our work as authority. We need to be serious and correct with citizend to trasmit authority, but I will not use the word arrogance.