When bad things happen to bad people

Sometimes when bad things happen to bad people, we feel like they deserve them. Suppose Alice has broken into Bob’s house to poison his beloved dog, and on her way out she trips and breaks her leg. It sure seems that she got what she deserved.

But the bad that a bad person deserves is punishment: an intentional harsh treatment by a punisher. Our feeling that Alice got what she deserved can only be right if there is some supernatural judge—for clearly no natural judge is behind this—who as a punishment has either caused her to break her leg or at least intentionally failed to prevent the leg-breaking.

I think this provides us with a little bit of evidence that God exists. For a feeling that p is some evidence that p. So, the feeling that Alice got what she deserved is some evidence that she got what she deserved.

Moral risk

Say that an action is deontologically doubtful (DD) provided that the probability of the action being forbidden by the correct deontology is significant but less than 1/2.

There are cases where we clearly should not risk performing a DD action. A clear example is when you’re hunting and you see a shape that has a 40% chance of being human: you should not shoot. But notice that in this case, deontology need play no role: expected-utility reasoning tells you that you shouldn’t shoot.

There are, on the other hand, cases where you should take a significant risk of performing a DD action.

Beast Case: The shape in the distance has a 30% chance of being human and a 70% chance of being a beast that is going to devour a dozen people in your village if not shot by you right now. In that case, it seems it might well be permissible to shoot.

This suggests this principle:

1. If a DD action has significantly higher expected utility than refraining from the action, it is permissible to perform it.

But this is false. I will assume here the standard deontological claim that it is wrong to shoot one innocent to save two.

Villain Case: You are hunting and you see a dark shape in the woods. The shape has a 40% chance of being an innocent human and a 60% chance of being a log. A villain who is with you has just instructed a minion to go and check in a minute on the identity of the shape. If the shape turns out to be a human, the minion is to murder two innocents. You can’t kill the villain or the minion, as they have bulletproof jackets.

The expected utility of shooting is significantly higher than of refraining from the action. If you shoot, the expected lives lost are (0.4)(1)=0.4, and if you don’t shoot the expected lives lost are (0.4)(2)=0.8. So shooting has an expected utility that’s 0.4 lives better than not shooting. But it is also clear, assuming the deontological claim that it is wrong to kill one to save two, that it is wrong to shoot in this case.

What is different from the villain case and the dangerous beast case is that in the Villain Case, the difference in expected utilities comes precisely from the scenario where the shape is human. Intuition suggests we should tweak (1) to evaluate expected utilities in a way that ignores the good effects of deontologically forbidden things. This tweak does not affect the Beast Case, but it does affect the Villain Case, where the difference in utilities came precisely from counting the life-saving benefits of killing the human.

I don’t know how to precisely formulate the tweaked version of (1), and I don’t know if it is sufficiently strong to covere all cases.

Defining killing

My presentation on killing for the Bios Centre is now on YouTube.

Canadian doubles

Since the shutdowns of the spring, I’ve been playing more tennis, with my son and with graduate students. Sometimes you end up having three people wanting to play tennis, though, and what do you do?

The canned solution is Canadian doubles where you have two people on one side and one on the other, you get two points for winning on the singles side and one for winning on doubles, you rotate the players counterclockwise between games, and you end at some fixed number of points, say 11, by a lead of two. And the singles court is used on the singles side while the doubles court is used on the doubles side.

This is a good game: alternating between being a single playing facing off against two and playing as part of a team is fun. However, we noticed two difficulties. First, the standard rotation scheme has the result that each time one serves, one faces the same person. That reduces the variation. A fix of this is to depart from the counterclockwise rotation. A more serious problem is that towards the end of a match, when playing on the double side, one can have a perverse desire to lose the game. For imagine that your partner has 10 points, you have 8, and the third player has less than 8. Then if your side wins, your partner reaches 11 and wins the match. But if your side loses, you may still have a chance to win the match later. This can sap motivation.

Also missing from the standard Canadian doubles is that in the interest of trying all combinations, it would be nice to have the chance to be a singles server and a singles receiver in the same match.

So, after a number of iterations, here is improved Canadian doubles (I am Canadian, by the way). Instead of playing to a fixed score, you play three rounds of six games. Highest score wins. Ties are possible. You can end early if you can see that the number of games left is insufficient to change the ranking between the players.

The first and third rounds have serving from the doubles side. The second round has serving from the singles side. In each round, positions rotate in such a way that each of the six arrangements occurs once. Moreover, the positions are so arranged as to minimize the same player “being on the spot” too many times in a row. Thus, no one serves twice in a row or is in singles twice in a row, and we rule out the tiring sequence of singles, then serving, then singles again. I generated the sequences with a brute force python script.

Round 1: Service from doubles side

Server	Partner	Receiver
B	C	A
C	A	B
A	B	C
C	B	A
A	C	B
B	A	A

Round 2: Service from singles side

Server	Receiver-Deuce	Receiver-Ad
A	C	B
C	A	B
A	B	C
B	A	C
C	B	A
B	C	A

Round 3: Service from doubles side

Server	Partner	Receiver
C	B	A
B	A	C
A	C	B
B	C	A
A	B	C
C	A	B

Loving excessively and the existence of God

1. Francis of Assisi did not love nature excessively and Mother Teresa did not love the needy too much.

2. Francis loved nature as reflecting God and Mother Teresa loved the needy as images of God.

3. If God does not exist, then to love nature as reflecting God or to love someone as an image of God is to love something as better than it is.

4. To love something as better than it is is to love it excessively.

5. So, if God does not exist, Francis of Assisi loved nature excessively and Mother Teresa loved the needy too much. (2–4)

6. So, God exists. (1 and 5)

Nonadditive scoring rules and domination

I wrote a rough draft of a paper proving geometrically that any strictly proper scoring rule continuous on the probabilities has every score of a non-probability dominated by a score of a probability, without assuming additivity of score. My proof is very much geometric.

Notes: Richard Pettigrew first announced this result in a forthcoming paper, but his proof is flawed. Then Michael Nielsen found a proof in the special case of bounded scoring rules. Finally, Nielsen and I approximately simultaneously (within hours of each other) found quite different proofs without the assumption of boundedness (though there could still be problems in one or the other proof). Research continues regarding how far the condition of continuity can be weakened.