Statistics should be used at first to see (most) shared posts rates. Other reasons could be considered probably, like which share option is most used… see your competition to discover more. An additional appreciated feature related to this topic could be to give a widget & shortcode to display most shared posts.
Also, something that converts better is offering the ability to display number of shares for all AND/OR single social network … but with a MINIMUM amount before displaying them. I’m more likely to use only total shares.
Optionally for later, you could implement a popup option to ask to “share the post if you like it” with options like : display after delay, % of page … max once every X times … option to “dont show again”. Plus an option to force sharing content or wait X seconds, also displayed after a delay… but that could be set for all OR only particular pages by ID.