Here are two examples that illustrate the potential difference to me:
Example 1: You are a general and 200 of your troops are being held captive by an enemy. All friendly soldiers are equally valued by the general and all deaths below are friendly deaths. The general is indifferent about enemy deaths. He must pick one of the two options:
- Attack the enemy, resulting in 200 deaths with certainty.
- Do nothing, in which case the enemy will kill the 200 captured soldiers.
Omission bias might lead the general to prefer option 2. The fuzzy human reasoning might be that in choosing the first option, the general somehow causes 200 deaths, while in choosing the second option, it is the enemy that causes the deaths, so the general may prefer the second option even though he should be indifferent between them. This example can not be applied for Action Bias because there is no ambiguity, uncertainty or risk in the example.
Example 2: There is an urn with 1 red ball and 1 blue ball inside. A ball is drawn randomly from the urn, and, if it matches your color, you win $100. Your options are as follows:
- Choose red as your color
- Choose blue as your color
- Do nothing and be randomly assigned a color
Note that Omission bias is inapplicable here as there are no harmful actions, and there are really no morality issues at play. On the other hand, Action bias might imply that agents are more likely to pick the first or second options here than they are to choose the third option, even though homo economicus would be indifferent across the three.
To conclude, the key difference, as I see it, is that Action bias is really only relevant in situations with risk or ambiguity. I think technically speaking there is no ambiguity here, since the rules of the game and the balls in the urn are known to the player, but you could easily transform it into a game with ambiguity by saying the player doesn't know the contents of the urn and instead has some belief. Omission bias, on the other hand, is more related to morality. If a bad thing is going to happen, we'd rather it happen because of something that we didn't do than something that we did.