Question

argue something down†
1. Lit. to reduce something, such as a bill or a price, by arguing.
  I tried to argue the price down, but it did no good.
  Tom could not argue down the bill.
2. Fig. to urge the defeat of a proposal or a motion in a meeting through discussion.
  I am prepared to argue the proposal down in court.
  She will argue down the proposal in the council meeting.