The Marschak Machina triangle is an aid to visualization of behaviors of utility functions.

It is defined over a triangle:
Start with X={x,y,z} with x">"y">"z

S2={x in R^3: x in R^3+, Sum(i=1,3,xi=1)}

Each point in the triangle is some mixture of x,y, and z. On this set, affine utility function should have parallel indifference lines. A steep slope => risk averse.

In reality, peoples indifference lines seem to fan out. This is supported by the common consequence effect and common ratio effect.