what makes an authors argument compeling

Answer 1

I find an argument compelling when --

* the author is an expert on this subject (or at least has thoroughly researched the subject)
* she uses logic
* he communicates clearly
* the arguments are well-organized

This site has additional ideas.

http://sourcesofinsight.com/2008/01/24/framing-compelling-arguments/

Answer 2

Compelling arguments are those that influence others. Here are some methods to help you influence others:

http://www.members.cox.net/dagershaw/lol/InfluenceAntecedents.html
http://www.members.cox.net/dagershaw/lol/InfluenceMorePrinciples.html
http://www.members.cox.net/dagershaw/lol/InfluenceStillMore.html
http://www.members.cox.net/dagershaw/lol/Persuasion.html

I hope this helps a little more. Thanks for asking.