The table below shows the total suffering given the four possibilities:

Your partner ----------------------- confess not confess Y confess: 10*2+10=30 0+20=20 o u not confess: 2*20+0=40 2*3+3=9So given the probability p of your partner confessing if you confess the expected, or average, amount of suffering would be 30p + 20(1-p)=10p+20. If you don't confess the expected amount of suffering would be 40p + 9(1-p)=31p+9. To find the indifference point equate the two expressions:

10p+20 = 31p+9

11 = 21p

p=11/21 =~ 52.4%.

Thus if you think your partner's probability of confessing is greater than 11/21 you should confess, otherwise you should keep your mouth shut.

What is a much more interesting question, with no answer that fits everybody, is what would you do if you assumed your partner had the same morals and priorities as you, and that he assumes the same thing of you.

Michael Shackleford, A.S.A.