Table 1.

Feature Likelihoods to Best Differentiate Competing Theoretical Models of the Value of Information

	Feature likelihoods					Model preferring F (m1)				Model preferring G (m2)
Condition	P(f1|a)	P(f1|b)	P(g1|a)	P(g1|b)	DStr	Model	PStrm1	eum1(F)	eum1(G)	Model	PStrm2	eum2(F)	eum2(G)
1	0	.24	.57	0	14.5	Probability gain	14.4	0.072	0.000	Information   gain (impact,   probability   certainty)	−14.5	0.135	0.280
2	0	.29	.57	0	20.2	Probability gain	17.4	0.087	0.000	Impact   (information   gain,   probability   certainty)	−23.5	0.122	0.239
3	0	.40	.73	.22	8.2	Information gain   (probability   gain, probability   certainty)	7.2	0.238	0.166	Impact	−9.2	0.168	0.214
4	.05	.95	.57	0	37.9	Probability gain,   information   gain, impact	36.0a	—	—	Probability   certainty	−39.9	0.000	0.399

Note: Subjects classified the species of simulated plankton specimens as species a or b, where the species was a probabilistic function of two two-valued features, F (with values f₁ and f₂) and G (with values g₁ and g₂). In all conditions, P(a) = .70 and P(b) = .30. F denotes the feature with higher probability gain, and G denotes the feature with lower probability gain. Disagreement strength (DStr) is the geometric mean of the opposed models’ respective absolute preference strengths; it scales between 0 (none) and 100 (maximal). PStr_m1 denotes Model 1’s preference strength between F and G. This is positive because Model 1 prefers F over G in each case. PStr_m2 denotes Model 2’s preference strength between F and G. This is negative because Model 2 prefers G over F in each case. PStr scales between −100 and 100. The expected utility (eu) of F according to Model 1 is denoted by eu_m1(F). Models in parentheses were not optimized in the condition per se, but also prefer the feature in their respective columns.

^aIn Condition 4, PStr_m1 is based on the geometric mean of the individual preference strengths of probability gain (50), information gain (34), and impact (28).