Alice can spend all her 100 tokens on A, and she gets 10 votes on A. Ditto Bob can spend all his 100 tokens on B, and he gets 10 votes on B.
But if each of them spends 50 on A and 50 on B, then A and B both get 2*sqrt(50) ~= 14 votes, so both Alice and Bob win by colluding.
What's to stop them doing this?
Bob can convince Alice to spend half her tokens on proposition B but then betray her and spend all his tokens on B, resulting in 17 votes for B and only 7 for A.
When voting is anonymous there is no way to detect if voters keep their pledge or not, so this should deter them from voting in any other way than in their own interest.
Unlike ordinary people, the legislators are working for their voters, who deserve to know if they got what they paid for. If I send Bob to the legislature, understanding that he plans to get rid of all the bloody clowns, I certainly want to know if he supported the Bill that gives every Clown $5000 of the city's tax revenue to buy more ludicrous shoes and lapel flowers. If Bob can promise he's anti-clown, then arrive in the legislature and vote a straight pro-clown slate knowing he'll face no consequences, that's no way to run a representative democracy!
Alice and Bob are making a good deal. Well working democracy should involve maximum amount of deliberation and deal making. It's a good thing. If you want more of that kind of deal making votes should be visible though (quadratic voting between representatives in parliament might work the way you suggest).