#### Supplement to Bounded Rationality

## Long descriptions for figures in Bounded Rationality

### Figure 1 description

Two graphs labeled (a) and (b):

- Graph (a) is a four quadrant graph with an origin at (0,0). The
x-axis is labeled \(v(x)\) and goes from −100 to 100; the left
side is labeled ‘losses’ and the right side
‘gains’. The y-axis is labeled
*x*and goes from −30 to 30. A single curved line starts at the lower left (approx. (−100,−24)) at about a 30 degree angle, goes through the origin at almost a 90 degree angle then goes back to a 30 degree angle by the end (approx. (100,10)). - Graph (b) is a 10 by 10 layout with
*x*and*y*both going from 0 to 1. The y-axis is labeled \(w(p)\) and the x-x-axis*p*. A straight dashed line goes from (0,0) to (1,1). A solid curved line also goes between the same points. It is above the dashed line from (0,0) to about (.35,.35) and below the dashed line after that point.

### Figure 2 description

The center of the mostly symetrical diagram consists of four vertical boxes, the whole labeled above as ‘cues’ and individually inside from top to bottom as \(X_1\), \(X_i\), \(X_j\), \(X_n\). Cue \(X_i\) and \(X_j\) are connected by a line labeled \(\rho_{X_i, X_j}\).

To the left of the cues is a box labeled above in green as ‘criterion value’ and inside as \(Y_e\). Each of the four cues is connected to it with a line and each line labeled \(\rho_{Y_e, X_1}\) (with \(X_1\) replaced appropriately).

To the right of the cues is a box labeled above in blue as ‘subject response’ and inside as \(Y_s\). Each of the four cues is connected to it with a line and each line labeled \(\rho_{Y_s, X_1}\) (with \(X_1\) replaced appropriately).

Below the cues is an equation \(r_a = \rho_{Y_e,Y_s}\) and below that in red the label ‘achievement index’. Lines connect the equation to both \(Y_e\) and \(Y_s\).

Below this equation and label is another \(G= \rho_{\hat{Y}_e,
\hat{Y}_s}\) and below that a label in red ‘matching
index’. To the left a line goes to a box containing
\(\hat{Y}_e\) and labeled in green ‘*predicted* criterion
value’. A line from this box in turn goes to an equation \(R_e =
\rho_{Y_e,\hat{Y}_e}\) which is labeled in green ‘environmental
predictability’. A final line goes from this equation back to
the original green box that was labeled ‘criterion
value’

To the right of ‘matching index’ goes a line to a box
containing \(\hat{Y}_{s}\) and labeled in blue
‘*predicted* subject responses’. A line from this
box in turn goes to an equation \(R_s = \rho_{Y_s,\hat{Y}_s}\) which
is labeled in blue ‘response linearity’. A final line goes
from this equation back to the original blue box that was labeled
‘subject response’.

In the lower left is the equation

\[Y_e = \sum^{n}_{i=1} \beta_{e,j}X_j + \epsilon_e\]Under the right hand part of the equation but not including \({}+\epsilon_e\) is a horizontal brace labeled \(\hat{Y}_e\)

In the lower right is the equation

\[Y_s = \sum^{n}_{i=1} \beta_{s,j}X_j + \epsilon_s\]Under the right hand part of the equation but not including \({}+\epsilon_e\) is a horizontal brace labeled \(\hat{Y}_s\)

### Figure 3 description

A diagram of four targets in a two by two layout. Each of the four targets consists of five concentric rings with the innermost ring colored gray. From innermost to outermost the rings are numbered 0 through 4.

The top left target is labeled ‘(low bias & low variance)’. A cluster of black dots is in ring 0.

The top right target is labeled ‘(low bias & high variance)’. Black dots are scattered at all angles in rings 0 through 2.

The bottom left target is labeled ‘(high bias & low variance)’. Black dots are clustered in the upper right quadrant in rings 2 and 3.

The bottom right target is labeled ‘(high bias & high variance)’. Black dots are mostly in the bottom right quadrant though some in the top right quadrant in all rings.