Indirect reciprocity · image scoring

Word getsaround

Reciprocity needs you to meet the same person twice. Most of the people you deal with you will never see again, and they get helped anyway. The missing mechanism is that somebody is watching. I help you, it is noticed, and later somebody else helps me.

The rules

Helping someone who can never repay you

Everyone carries a score. Helping raises it, refusing lowers it. When you are asked for help you can see the other person's score, most of the time, and you decide on that. You will never meet them again.

A strategy here is one number: the score you insist on before you will help. Set it below the bottom and you help everybody. Set it above the top and you help nobody. In between you are choosing, and the choosing is what turns out to matter.

Alexander (1987) argued that this is where moral systems come from. Nowak and Sigmund (1998) made the claim precise enough to test, and found that it holds only above an exact line.

Start from
Generation
0
not started
Requests met
—
between strangers
Choosing who
—
rather than always or never
The line
—
word must travel above this
Whether word travels far enough
How choosy the population is
Over time drag or arrow keys to replay
Requests met Donors who choose who to help
Across many populations
Things worth trying

Four runs that each show something

Press Word travels
Nearly every request is met, between people who will never meet again. Most of the population is choosing who to help rather than helping everyone.
Press Nobody hears anything
Nothing. Not reduced helping, none. A reputation you cannot build is worth nothing to have.
Slide word-travels slowly upward from 20%
The switch is very sharp, but it does not sit exactly on the predicted line. The algebra says a quarter; this population needs closer to two fifths. Refusing to help someone with a bad score lowers your own, so discriminating costs more here than the clean calculation allows for.
Raise the cost of helping to near the benefit
It stops, even with word travelling perfectly. The prediction is about the ratio, not about either number.
Watch the unconditional helpers
They never carry this. Help that survives is help that checks first, which is a distinctly unsentimental thing for a model of morality to say.
The argument

Why anyone cares

Alexander's claim was not modest. He argued that moral systems are indirect reciprocity: that what we call conscience is a mechanism for maintaining a reputation worth having.

What the mechanism buys you

Direct reciprocity, the kind Second Guess models, only works between people who meet repeatedly. That covers a village and not a city. Indirect reciprocity lifts the restriction: the person I help need never help me, provided somebody notices and the noticing spreads. It is the only well-understood mechanism that scales cooperation past the people you know.

The line, and why it is exact

Helping costs you something and is worth more to them. Nowak and Sigmund's result is that helping evolves only when the chance of your reputation being known exceeds that cost-to-benefit ratio. Below the line, building a reputation does not pay for itself and nothing gets started.

The switch above is sharp, and it sits a little higher than the algebra says: with a ratio of a quarter the population needs word to travel closer to two fifths of the time. That gap is not noise. Refusing to help someone with a bad score lowers your own score too, so a discriminator pays for discriminating, and the clean condition does not account for it. That is the same moral hazard discussed below, showing up as a number.

What survives is not generosity. It is generosity that checks first.

What it does not settle

Watch which strategies carry the cooperation and they are the discriminators, not the unconditional helpers. That is worth sitting with if the model is being offered as an account of morality: the thing that evolves is conditional, calculating, and indifferent to whether the person in front of it deserves anything in any sense other than the score.

There is a second problem the model makes visible only if you look for it. Refusing to help someone with a bad score lowers your own, so a discriminator is punished for discriminating. Brandt and Sigmund called this the moral hazard in image scoring, and it is why later work replaced bare scores with standing rules that distinguish justified refusals from unjustified ones. Those rules need considerably more cognitive machinery, which weakens the claim that this is where morality came from.

What this model is not

Scores here are accurate, public, and free. Nobody lies about anyone, nobody has to spend anything to find out a score, and there is no gossip in the ordinary sense — no rumour, no motive, no reason to shade the truth about a rival. Every one of those is where the interesting difficulty in real reputation lives.

References

Sources

  1. Alexander, R. D. (1987). The biology of moral systems. Aldine de Gruyter.
  2. Brandt, H., & Sigmund, K. (2005). Indirect reciprocity, image scoring, and moral hazard. Proceedings of the National Academy of Sciences, 102(7), 2666–2670.
  3. Leimar, O., & Hammerstein, P. (2001). Evolution of cooperation through indirect reciprocity. Proceedings of the Royal Society B, 268(1468), 745–753.
  4. Milinski, M., Semmann, D., & Krambeck, H.-J. (2002). Reputation helps solve the tragedy of the commons. Nature, 415(6870), 424–426.
  5. Nowak, M. A., & Sigmund, K. (1998). Evolution of indirect reciprocity by image scoring. Nature, 393(6685), 573–577.
  6. Nowak, M. A., & Sigmund, K. (2005). Evolution of indirect reciprocity. Nature, 437(7063), 1291–1298.
  7. Panchanathan, K., & Boyd, R. (2003). A tale of two defectors: The importance of standing for evolution of indirect reciprocity. Journal of Theoretical Biology, 224(1), 115–126.
  8. Wedekind, C., & Milinski, M. (2000). Cooperation through image scoring in humans. Science, 288(5467), 850–852.