Oversimplifying a bit here but to put it bluntly, she's the eyecandy for the show. The main focus of that live broadcast was the talking heads and on-site reports of the elections after all ...
what a lovely candy she was though
Her being studious and smart enough to keep up and even participate a little bit in the discussion was just icing on the cake ... and idk about getting more young people interested in politics but it certainly get idol fans (mainly momusu, err ok... maybe just the Sayu-wotas ) to watch it judging from the rate the threads at 2ch were moving when it aired.
2012/12/16(日) 21:03:02 レス総数 : 1657res/分
#│ 局 │ レス数. │ 率 │ 番組
.━┿━━━━━┿━━━━━┿━━┿━━━━━━━━━━━━━━━━
1|.テレビ東京.|. 882res/分.|. 54%|池上彰の総選挙ライブ
2| NHK総合 . |. 328res/分.|. 20%|衆院選2012開票速報
In contrast the actual tv ratings during the hour Sayu was on is almost half the ratings of NHK's elections coverage at the same time although it's still pretty good
17.3% 19:55-21:00 NHK 衆院選2012開票速報
*8.6% 19:54-21:00 TX* 池上彰の総選挙ライブ・第1部
I'll refrain to comment on the elections itself since I know basically nothing about it

----
Sayu's comment from the latest J-Melo journal
Sayumi Michishige
(Morning Musume。)
Dec. 10, 2012
I have a new passion: making fruit juice. I put all kinds of fruit in my juicer: bananas, kiwis, blueberries, pears, and lots more. I love making banana-and-chocolate milkshake and fruity desserts too. You should try this! Yum-yum!