 Indeed, the above principle follows from Independence and is in fact equivalent to Savage’s Eventwise Monotonicity condition, given the other conditions in place (Grant 1995). Therefore lotteries become increasingly preferred both as one moves north and as one moves west, since, in doing either, one shifts probability from a less to a more preferred outcome (from \(x_2\) to \(x_3\) when moving north and from \(x_1\) to \(x_2\) when moving west). The indifference curves are hence upward-sloping. Steeper slopes correspond to greater risk aversion, in the following sense: northeastern movements increase the spread of the distribution, i.e., the degree of risk involved, shifting probabilities from the middle outcome (\(x_2\)) to the extremal ones (\(x_1\) and \(x_3\)). The steeper the indifference curve, the greater an increase in probability of the best outcome is required in order to compensate for this increased risk. SEU clearly also requires that indifference curves be both linear and  parallel.[2]  To illustrate: