Choice Probabilities

Equal Probabilities (Line of Indifference)

Suppose there is a point X_i,


such that the probabilities of both choices are 1/2. That is:

Doing a bit of algebra we can get the following expression:

General Expression for the Line/Plane of Indifference

The expression:

is the same as the general equation for a plane in s-dimensional space. To see this, let Z be any point such that the following is true:

then all the points, Z, that satisfy the equation form a plane through the s-dimensional space and is the normal vector (that is, it is perpendicular) to the plane. For example, suppose that:

This produces the equation .6Z₁ + .8Z₂ = .4. All the points that satisfy this equation, for example, (1, -.25), (.5, .125), (0, .5), (-.5, .875), etc. -- line on a line. Graphically.....