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In American society, romantic love is considered the main reason for people to marry. On the other hand, in some societies, romantic love is considered a form of obsession or madness. In fact, even in many societies where "true love" is not considered a form of insanity, arranged marriages are still the norm. For example, in many cultures it's believed that marriage is basically an economic arrangement. Thus, a farmer needs a wife both to bear children and to share the farm work while raising new "hands" as additional farm labor. In other societies, marriage is mainly about cementing connections between families. Indeed, most marriages between members of European royal or aristocratic lineages were primarily aimed at creating trust, loyalty, and mutual obligations between privileged and powerful families. Which phrase signals a contrast between ideals about marriage?

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The third sentence. Hope this helps.
The question is referring to a contrast so the proper phrase would be "on the other hand". 
This phrase means something along the lines of "looking at the other side" which refers to the other situation or event.
In fact means giving a true example
In other societies means examples of ideas from other places