Court - to try to attract something or someone, seduce, tempt, to invite, try to achieve something 

-To court the top players
-without research doing  business is Courting a failure 

Sway- Influence, power, rule, 
v- to influence , bend to one's will 
That being said, an experienced politician knows how to sway his electorate with the help of medias 

Gauge: Measure, get a sense, 
 A good teacher will somehow gauge his students' comprehension fo the class material before having them sit for a formal test.