Singapore Politics: Representation

I'm a bit baffled by Members of Parliament (MPs) who are elected to represent constituencies they don't live in. This seems pretty common for the Parliamentary System, but it really doesn't make sense to me. Don't you want politicians to live in the same area they are representing? How else would they know or feel what their constituents feel? 

The US system is such that you can only represent the city/state that you live in. Of course, people have tried various ways around it, some have succeeded with convincing voters that they are similar to them like Hillary Clinton. Rudy Giuliani called Hillary Clinton a "carpetbagger" since she didn't actually lived in New York, only maintaining a NY address so as run for the US Senate. (1) Hillary won the race. Others aren't as successful as Hillary at convincing residents. 

Regardless, I thought this made a lot of sense. Why would I want someone from a different area to represent me? 

Granted, Singapore is only 277.3 square miles (718.3 km²) and so distance isn't too big of a problem, but it would still be nice to know that an MP lives in the same area and experiencing the same challenges as his/her constituents. 

After all, if he/she lives in a million dollar home in the secluded Sentosa Cove, would he/she really understand the lack of trash removal in a certain public housing block?

So I remain baffled by the Parliamentary System and how Members of Parliament (MPs) can come from any area, regardless of residence. What's to prevent candidates from selecting the constituency that they think they can win, rather than having to represent constituency that they live in? 

This idea of representation remains baffling to me.