A. There are manifest dangers in the persuasive aspect of leadership.

B. It is alarming, for example, to reflect how great a part the power to speak well has acquired in an age of broadcasting.

C. It is quite possible for men to feel that they are freely giving their allegiance to a leader, when actually they are simply slaves of his techniques of propaganda.

D. At its lowest, the technique of persuasion may involve all those devices of suggestion and propaganda that are so freely available to the unscrupulous in a scientific age.

A preliminary assessment of the given statements suggests that Sentence A would serve as an apt introduction. It sets the stage by alerting the reader to a significant issue - the inherent dangers involved in persuasive leadership. The remaining sentences seem to build on this theme. 

Sentence D is a viable follow-up to A. After establishing the concern in A, D delves deeper into what makes persuasive leadership dangerous. It explains the mechanics behind the danger by highlighting how persuasion can devolve into manipulative techniques ("suggestion and propaganda") that are especially accessible in modern, scientifically advanced times. 

We can further link B to D: B brings in a concrete 'example' that modern communication (broadcasting) has amplified the power of persuasive speech. The example reinforces the previous point by illustrating a specific arena where persuasive techniques are especially potent.

Finally, Sentence C ties the discussion together by demonstrating the consequence of the persuasive tactics outlined in the previous sentences. It warns that despite the appearance of free choice, people can be subtly manipulated - becoming unwitting subjects to propaganda. This conclusion leaves us with a clear understanding of the stakes involved, as initially introduced in A.

Thus, we obtain a coherent paragraph with the arrangement A-D-B-C (Option D).