The main aim of a persuasive speech is to convince or motivate an audience to do something. You are essentially trying to command the audience to adopt your own point of view. The best persuasive speech topics are thought-provoking, daring and have a clear opinion.
Due to the fact that the main purpose of the persuasive speech is to convince but at the same time to be provoking for the audience, I would say that the best type of reasoning is the deductive reasoning.
Deductive reasoning is when you go from the general to the particular. In other words, you present a series of ideas and you reach a conclusion or rule.
This kind of reasoning is better to convince or persuade people because you select what particular pieces of information present them, but you make them reach the conclusion. In that way, you let them think that they are deciding the outcome of the reasoning without realizing that you manipulated them by presenting the options that would cause that outcome.
On the other hand, using inductive reasoning is no as effective since you have to present them the final reasoning or golden idea to the audience and try to make them apply it in their particular situations. By doing such a thing you overtly give them no choice to make rather than accept or not your idea, which is ultimately a dangerous bargain to make.
So, to give a final and concrete answer, the best type of reasoning in a persuasive speech is:
Deductive reasoning
