Introduction to higher order knowledge: The Omission/Commission Distinction

1. Introduction to higher order knowledge: The Omission/Commission Distinction

2. We will explain a hand full of puzzles using one simple model: -symbolic gestures -omission commission -chemical norms -innuendos All using the concepts of “higher order beliefs” and “common knowledge”

3. Let’s start with the omission commission distinction.

4. First, let’s remember what the omission/commission distinction is Recall Batman…

5. “I won’t kill you…but I don’t have to save you”

6. Batman commits an act of omission because doesn’t save bad guy when he has the chance. If Batman would have killed him, this would have been an act of commission Notice: Batman’s intention is the same (to kill bad guy) The outcome is the same (bad guy dies) But Batman (and presumably the viewer) thinks omission less bad

7. Not just fiction. Let’s look at some evidence hat we all make this distinction

8. Subjects brought into the lab and shown two scenarios that differ only in whether someone commits act of omission or commission In both cases intentions and consequences are clear Here is the setup of one such scenario…

11. Act of omission…

12. Notice, you know David’s intentions

14. Versus an act of commission…

15. Notice David’s intentions are held constant

16. Subjects consistently rate acts of omission as less bad E.g., Spranca, Minsk, and Baron (1991) find that approximately 2/3 of subjects rate omission as less bad, and almost no one rates commission as less bad

17. Not just fiction or the lab. We distinguish between omission and commission in law…

18. It is illegal for a physician to assist a patient in committing suicide

19. On September 17, 1998, Dr. Kevorkian administered Thomas Youk a lethal injection Youk's family described the lethal injection as humane, not murder But… On March 26, 1999, Kevorkian was charged with second-degree murder and found guilty Source: http://en.wikipedia.org/wiki/Jack_Kevorkian#Trials

20. But it isn’t illegal for a physician to turn off life support…

22. Again, same outcome, but act of omission is treated as (much) less bad than act of commission

23. The omission / commission distinction shows up in important historical/political events, too…

24. The Struma, 1941

25. Decrepit ship with over 700 Jewish refugees, en route to British controlled Palestine, where Jewish migration was restricted. Had to make an emergency stop in Turkey The British pressured the Turks not to let the Jews go ashore … after 10 weeks of negotiating between the Brits and Turks … the (non-functioning) boat was towed to sea and (to no one’s surprise)…

27. Survivors: 1

28. Would the British have torpedoed the ship themselves?

29. Another historical example…

30. Many argue Sharon “allowed” the massacre. Would he have ordered his troops to commit the massacre? Was he judged as severely as if he had?

31. In short, the omission/commission distinction is ubiquitous And plays significant role in decisions as serious as those that affect life and death

32. Whyis omission viewed differently from commission? When is omission viewed differently from commission? Is this distinction something we should legally respect or overcome?

33. To answer this question, let’s consider the following simple game theory model:

34. First, David chooses whether to switch the track to save his car and hurt construction worker (i.e. transgression of commission). You and Mark can easily see if the tracks are switched

36. Then David, Mark, and you play a variation of the indirect reciprocity game, e.g.: • Each period, players are randomly matched. • When matched, can pay cost c to help by b • Discount rate δ

37. Consider the following “ethical system”: David should not switch the tracks. Start by thinking of everyone as “good” If observe David switching the tracks, consider him “bad” If observe anyone defecting against anyone good, consider him “bad.” Cooperate against everyone who is good. Notice that this “ethical system” is a Nash Equilibrium (for sufficiently high delta and b>c) I.e. if you think others abide by this ethical system, so should you

38. What if we change this from commission to omission? How should we model this? First, we want to make sure that you are still aware the intentions were bad (i.e. you see David looking back and forth at his keys). But…and this is the crucial assumption…let’s assume that Mark is unlikely to observe this. (that is we presume that acts of omission, EVEN IF the intentions are obvious to you, that’s only because you know some key contextual information like seeing him look back and forth, but its safe to assume that others probably are not always privy to such information).

39. What if we don’t have “perfect information” about others’ past actions? For example, if Mark can’t see that David was there…

40. δ

41. Let’s model this…

42. First, David chooses whether to keep the track to save his car and hurt construction worker (i.e. transgression of commission). Let’s assume that 90% of the time David is not paying attention. If the train comes and David does nothing, you can see whether David intended to do nothing after hesitating or was just not paying attention, but Mark cannot distinguish. (Notice that when the tracks are switched, both you and Mark can perfectly tell the intention, since the track cannot be unintentionally switched)

43. Now is there a Nash Equilibrium where you defect against David if he (intentionally) doesn’t flip the switch (i.e. transgresses by omission)? No! (provided 90% is sufficiently high relative relative to b,c,δ) Because Mark will presume that David was likely asleep and you are just defecting to save c…

44. I.e. knowing that David’s intention were bad isn’t sufficient to cause punishment in repeated games…rather, you must also know that Mark knows David’s intentions were bad. This is called a second order knowledge

45. In fact one can show that second order knowledge aren’t all that matter…third order knowledge matter too…and fourth order and fifth order and… This is called common knowledge

46. Notice our logic depended on: -High prior probability of “paying attention” -Punishment is caused by repeated game -The fact that omission requires contextual information to know intentions (You will show all this more rigorously in homework!)

47. Alright, let’s show the evidence…

48. First study… Showed M-Turkers the trolley scenario (for now just the omission scenario) Varied whether Mark could see David as well as you (i.e. manipulated “second order knowledge”)

50. δ