Do a quick Internet search for management styles, and you get articles that tell you about the six types, the 10 types or just three effective ones. Creating a taxonomy is a very effective way to get a teaching position or a consulting gig. But using a quick quiz will help you identify your style from the six as described by the consulting firm of Hay/McBer.
Now, a management style is a function of personality, in my opinion. An authoritative personality is going to tend to that kind of management style. Being a participatory manager is plain out of character for that kind of person. There are things you can do to move the needle a bit, but your style will reflect your personality and anything else will be inauthentic.
Once you know what kind of manager you are, you have to ask if that is appropriate for the organization in which you operate. For instance, a directive style is ideal in the military. That is exactly the wrong style if you are operating an academic research project composed of professors and post-doctoral researchers. A better approach there is a participatory one. An 18-year-old Marine recruit is just going to look for something different in a leader/manager than a 50-year-old theoretical physicist will.
And interestingly, there is a correlation between the organization's culture and retention based on management style. According to a comprehensive study of academic staff retention by a team of African professors: “When leadership style is unfavourable intention to leave increases and when it is favorable intention to leave decreases, hence enhancing staff retention.” Favorable here means suitable to the kind of individual employee the business or organization has attracted in the first place.
There is another factor, and that is business success itself. Simply put, people like to be on a winning team, and they will overlook the manager's style to a degree so long as the team is winning. This is as true in business as it is in baseball and basketball. Retaining talent that contributes to your success becomes a virtuous circle, and losing talent because of failures is a vicious one. Oddly, your staff may hate you but stick around because the business does well. And your staff may flee despite being enamored of you if the company is going down for the third time.
So, what is the ideal management style for retention? It is a style consistent with the manager's personality and corporate culture. And by retaining desired talent, the odds of success, and therefore even greater retention, increase.