Word choice between 推舉 , 推選 , 薦舉 How would one translate the 推舉 , 推選 , 薦舉? 

Im pretty sure they all mean something like electing or choosing. Among the three, 推選 is probably the most colloquial and conversational basic use, while 推舉 and 薦舉 are only seen in writing/more advanced level of use. 

When would you use 推舉 , 推選 , 薦舉? Please give examples in Chinese with basic English translation.
In 「推舉」,「推」means &quot;to push &quot;, and 「舉」 means &quot;to raise &quot;

「推舉」means to &quot;single out and elevate someone&quot; which means &quot; to recommend&quot;

In 「薦舉」,「薦」means &quot; to recommend&quot;

「薦舉」means &quot; to elevate and recommend someone&quot;

In「推選」, 「選」means &quot; to choose&quot;

「推選」means &quot;to single out and choose someone&quot; / &quot; to nominate and elect someone&quot;

Examples :

我推舉他為經理 ( I recommend him to be the manager)
我薦舉他為經理 ( I recommend him to be the manager)
眾人推舉之下，他成為了經理 ( After everybody recommended him, he became the manager)
眾人薦舉之下，他成為了經理 ( After everybody recommended him, he became the manager)
眾人推選他為經理 ( Everybody recommend and choose him to be the manager)

*「推舉」;「薦舉」;「推選」only apply to people
*「推薦」is the most common term for &quot;to recommend&quot;, followed by「推舉」and then「薦舉」
*「推薦」apply to either people or object
Example:
向日本人推薦美國牛肉 ( recommend American beef to Japanese)
我推薦他為經理 ( I recommend him to be the manager)
*「薦舉」is more commonly written as 「舉薦」
*「選舉」(election)