What else must you accept?
A gamble gives a payoff for each possible outcome. Choose two gambles you accept, then explore the consequences of positive scaling, addition, and accepting every nonnegative, nonzero gamble.
Your accepted gambles
Payoffs are net gains. Negative means you pay.
The shaded region is the positive hull of your gambles and the two unit gains (1, 0) and (0, 1), clipped to this window.
Test a gamble h
Click the plot or use the sliders.
The acceptance cone
Horizontal: payoff if A. Vertical: payoff if B.
Arrows are accepted generators. The origin is excluded exactly when the assessments are coherent.
A free gain is desirable
Accept any gamble that never loses and wins in at least one outcome. This includes both positive axes, excluding the origin.
Scale it. Add it.
If two gambles are desirable, every positive combination is desirable too. These implications generate the cone.
Keep acceptance coherent
Zero must not be desirable. Together with accepting gains and combining gambles, this also excludes every nonpositive gamble.
Finite assessment model: D = posi({g₁, g₂} ∪ {g ≥ 0 : g ≠ 0}). When coherent, this is the smallest coherent extension. Displayed values are rounded to two decimals. Probabilities shown in the bar form its closed dual; boundary probabilities can assign expectation zero to accepted gambles.