A Spatial (Geometric) Model of Roll Call Voting

  1. Each Legislator is represented by an ideal point and has a symmetric, single-peaked utility function centered at her ideal point over the policy space.

  2. Each Roll Call Vote is represented by Two points
    -- One Corresponding to the Yea Outcome -- Oy
    -- and One Corresponding to the Nay Outcome -- On.

  3. Legislators vote Probabilistically for the closest outcome:

    Probability of Yea = P[U(Oy) > U(On)]
    Probability of Nay = P[U(Oy) < U(On)]