Notebook

Notebook

EnglishEspañol

Why keep a promise that no longer pays?

An illustrated story about this question, and the research that grew out of it.

No promise

“Will you promise me you’ll roll the die?”

Choosing needs JavaScript. The story goes on as if you had promised.

And I promise you this is worth your next few minutes. Scroll down to see what happens.

cooperatesdefectscooperatedefect33both better off0550pays you more11where both end up

Before the promise, a famous game: the prisoner’s dilemma.

Two people in separate rooms. Each chooses to cooperate or to defect, without knowing what the other does and without being able to talk.

Play once.

If you both cooperate, you each get 3 coins. If you both defect, 1 each. If only one of you defects, that one takes 5 and the other gets 0.

Playing needs JavaScript. In the story the other always defects: if you cooperate, you get 0 and they get 5; if you defect, you both get 1.

Payoffs: yours first, the other's second
The other cooperatesThe other defects
You cooperate3, 30, 5
You defect5, 01, 1

Why defect? Think like the other.

Take the other’s two moves one at a time, and see what pays you more against each.

If the other cooperates, what pays you more?

Defecting pays you more in both columns: 5 against 3, and 1 against 0.

Whatever you do, defecting pays more.

And the other reasons just as you do. So both defect and end up with 1 each, when cooperating would have given them 3.

What if they played again and again? No one tells it better than The Evolution of Trust, by Case (2017).

The dilemma, in depth

cooperatesdefectscooperatedefect33both better off0550pays you more11where both end up

Now they can send each other a message before choosing.

Same rooms, same game. Pick what you would write to the other.

Hey… what are you going to do?

I’ll cooperate. I promise.

Me too. I promise.

Costs you nothing

Writing needs JavaScript. The story goes on as if you had promised, and the other had promised back.

Talk is cheap.

A message costs nothing and binds no one: economists call it cheap talk. Saying you will cooperate changes no payoff, and defecting still pays more. And yet people keep their word.

Another game, the same tension.

In the game of Vanberg (2008), only one person decides. The other chooses nothing and receives whatever the first decides. It is not the prisoner’s dilemma, but keeping your word costs you all the same.

Now you decide.

The other can only wait.

You promised the other you’d roll the die.

Deciding needs JavaScript. These are the payoffs of the decision.

Payoffs of the decision
DecisionYouThe other
Roll the die1012, or 0 if a 1 comes up
Keep the 14140

Why keep your word, then? Two voices answer.

One is what the other expects: letting them down hurts. It is called guilt aversion. The other is your word: breaking it hurts, whatever the other expects.

Guilt aversion: Charness and Dufwenberg (2006); Battigalli and Dufwenberg (2007).

Almost always, they say the same.

The other expects you to roll precisely because you promised. To tell the two apart, you need a case where the expectation stays and the promise goes.

The trick: change the person.

That is what Vanberg (2008) did: he switched partners. In his reading, each voice then predicts something else.

  • What the other expects “Roll just the same: the new partner expects the same, and doesn’t know about the switch.”

  • My word “Roll less: you promised this person nothing.”

The lights go out.

When they come back, someone else is sitting in the other’s seat. Only you know: the one who decides sees the switch, and the one who receives never does.

A new partner, holding a promise of their own.

They were promised too, by someone else who decides, as you do. In the experiment the switch came at random; in this story it is always this case, a fixed example.

What the other expects is still there. Your word is not: you gave it to someone who left.

One person on each card.

Each one is someone different, who knows nothing of the others. Decide on each.

  1. A new partnerCard 1 of 6

    Someone else wrote to them:“Don’t worry. I’ll roll the die.”

Or swipe the card towards your choice.

Deciding needs JavaScript. A different person waits on each card: with 3 of them you chatted and promised; with the other 3, the lights went out, and a new partner sat down holding a promise from someone else.

Now you are the one who receives.

“I’ll roll the die. I promise.”

Betting needs JavaScript. The recipients in the experiment answered on a scale from “certainly rolls” to “certainly doesn’t roll”.

The lights went out on the other side.

The one who promised you now decides for someone else, and a new partner decides for you: the same fixed case, seen from the other side. In the experiment of Vanberg (2008), recipients could not see it either. Those who held a promise bet almost the same with a switch as without one:

  • No switch: 70
  • With a switch: 68
Same partner73%70New partner54%68

And the real people?

In the experiment of Vanberg (2008), 192 people played this game over 8 rounds, with someone new every round. In the rounds where the one deciding had promised the same partner, how often was the die rolled?

Guessing needs JavaScript. The figure: 73%.

And after a switch?

And in the rounds where the one deciding had promised, but faced a new partner promised by someone else?

Guessing needs JavaScript. The figure: 54%.

73% against 54%.

In the data of Vanberg (2008), after a switch the die was rolled far less often. And what the recipients expected barely moved: 70 against 68.

Vanberg's experiment, in depth

The word, in itself.

Vanberg (2008) concludes that the effect of promises is not explained by changes in what the other person expects, and that it suggests a preference for keeping one’s word in itself.

{ }

Why keep a promise that no longer pays?

I’m Montserrat Ximena Hernández Gallegos.

This is the question of my research, the one this whole page asks.

An engine, in TypeScript.

To work on it, I built a simulation engine, a program that works out what follows from a set of rules, written in TypeScript.

Working paper: Promises to whom: Identifying personal guilt and partner-specific commitment across populations (SSRN).

A third reason, in between.

Vanberg’s design separates what the other person expects from your word. But there is a third reason in between: it hurts you to let an expectation down, but only if you created it. This is personal guilt, from Kawagoe and Narita (2014).

A lab cannot tell it apart.

With a partner switch, you did not create your new partner’s expectation, so personal guilt also makes you roll less. And in any one-round experiment, personal guilt and partner-specific commitment, your word given to that person, predict the same thing. That is why Vanberg’s result fits both.

What separates them is background trust.

It is what people expect of someone before any promise is made. In the specification of Kawagoe and Narita (2014), personal guilt is the product of two amounts: the expectation that was already there, and what your promise added to it.

It weighs most in the middle.

If no one expected anything beforehand, the product is zero. If everyone already expected it, your promise added nothing, and the product is zero too. So it weighs most in the middle, at 38. Your word to that person weighs the same in any world.

One world for each value.

In a simulation, background trust was fixed at each value from 0 to 76 out of 100. The belief that a promise will be kept was held at 76: the mean second-order belief of dictators without a partner switch in Vanberg (2008, Table I). There, the other person sees which reason moves you before playing, and only joins if you will roll; if they don’t join, each keeps 5. That is why rolling pays 10 and not rolling pays 5.

What each reason earns.

Personal guilt earns 10 from 15 to 65 (measured in steps of 5), and 5 outside that window. Partner-specific commitment earns 10 across the whole range. General guilt, the voice of what the other expects, serves as a control and also earns 10: it is the same line as commitment.

051003876Personal guilt weighs mostPartner-specific commitmentGeneral guilt (control): same linePersonal guilt
Material payoff against background trust. Personal guilt pays inside an intermediate window. Partner-specific commitment pays the same amount throughout. The belief that a promise will be kept is held at 76.

A comparison across worlds.

Each world has its background trust held fixed: this is not a population moving along the curve. And in the middle, the two earn the same, so which of them ends up there is a matter of chance. A lab session sees a single point of the curve. Tracing it takes comparing populations with different background trust.

The engine’s code: github.com/Montse2308/promises-to-whom-engine (DOI 10.5281/zenodo.23222610).

The finding, in depth

Back at the first table.

The day is over, and the other asks you one last time. Whatever you answer, only you know why.

“You promised me you’d roll the die. Would you roll it now?”

Answering needs JavaScript. Whatever you would say, the story goes on.

And me?

At the start I promised you this was worth your next few minutes. Did I keep my promise?

Everything you chose stays in this tab: nothing is sent anywhere.

Answering needs JavaScript. Either way, thank you for staying to the end.

Why keep a promise that no longer pays?

Written, drawn and programmed by
Montserrat Ximena Hernández Gallegos
Starring
  • The circle, as you
  • The square, as the other
  • The triangle, as the new partner
  • The cloud, as what the other expects
  • The scroll, as my word
  • The golden thread, as your promise

Based on the experiment of Vanberg (2008).

Set in Fraunces and Nunito

The end

Watch again