Does having only one sharing button lead to content being shared more?
- Many buttons makes harder choice for user and make some distraction.
- With one social button, the user might not be prefer this social network.
The number of social share buttons that has the highest conversion rate depends on a number of factors, and so no single number answer can reasonably be given.
The general rule from my own experience is that it's best to keep it down to as few as possible. Often even just having a single option outperforms 3 or 5 options, but it depends on your site and your target audience.
That said, you should be looking at more than just the number of shares, but rather the quality and reach of those shares. For example, if I have a website targeting professional developers, then Facebook shares may not be nearly as important as Twitter shares. Also, generic shares tend to perform worse than shares with notes written by the person doing the sharing.
TL;DR: Try to keep the number as low as is reasonable, but there is no magic number to answer your question.
It depends a lot on what type of content it is, and what type of user/reader you are showing the content to.
I'd personally argue that having the top 3 (Twitter, Facebook, Google+) is often enough, anyone interested in posting to others will take the 3 seconds to copy/paste the url/details to the other social app to submit.