Honest Signaling and the Maxim of Quality Christopher Ahern - - PowerPoint PPT Presentation

Honesty Mechanisms Reputation Gossip Language

Honest Signaling and the Maxim of Quality

Christopher Ahern

University of Pennsylvania

April 13, 2013

Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 1 / 26

Honesty Mechanisms Reputation Gossip Language

What keeps language meaningful?

Why don’t we say things we know to be false? Why don’t we say things for which we lack evidence?

Why should we care?

Can we ground our assumptions? Can we integrate more aspects of meaning?

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Honesty Mechanisms Reputation Gossip Language

Outline

1 Honesty 2 Mechanisms 3 Reputation 4 Gossip 5 Language

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Honesty Mechanisms Reputation Gossip Language

Honesty as Cooperation

Cooperation

When a self-interested agent incurs a cost (c) to confer a benefit (b) on another agent.

Prisoner’s Dilemma

Cooperate Defect Cooperate b − c, b − c −c, b Defect b, −c 0,0 Where b > c > 0, defection is the dominant strategy, and mutual defection the only equilibrium.

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Honesty Mechanisms Reputation Gossip Language

Honesty in Signaling

Prisoner’s Dilemma

Cooperate Defect Cooperate b − c, b − c −c, b Defect b, −c 0,0 “I am going to cooperate!” Is the signal credible? If it is true you should defect. If it isn’t true you should still defect.

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Honesty Mechanisms Reputation Gossip Language

Cooperation vs. Coordination

A B A b, b 0, 0 B 0, 0 b, b Cooperate Defect Cooperate b − c, b − c −c, b Defect b, −c 0,0 Signals are credible in games of coordination, but not in games of cooperation.

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Honesty Mechanisms Reputation Gossip Language

Honest Signaling and Deception

Deception Undermines Signaling

Signals cease to reliably correlate with any aspect of the sender. Gullible receivers do worse than skeptics. Skeptical receivers do not attend to signals. Senders shouldn’t bother signaling if receivers don’t attend to signals.

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Honesty Mechanisms Reputation Gossip Language

General Classes of Mechanisms (Scot-Phillips 2010)

Indices

Signal form is tied to signal meaning.

Handicaps

Signal cost is tied to signal form. Cost is incurred by reliable/honest signalers.

Deterrents

Costs are incurred (at least partially) by dishonest senders.

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Honesty Mechanisms Reputation Gossip Language

General Classes of Mechanisms (Scot-Phillips 2010)

Indices

Language is arbitrary.

Handicaps

Lying and telling the truth require the same amount of effort.

Deterrents

Many possibilities.

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Honesty Mechanisms Reputation Gossip Language

Reputation

Three basic components (Trivers, 1971)

Ability to recognize individual agents Keep track of past interactions Condition future behavior on past interactions

Iterated Prisoner’s Dilemma with Choice and Refusal

Agents have propensity to interact with each other. Results of interactions change this over time. Agents can choose who to interact with (or not) over time.

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Honesty Mechanisms Reputation Gossip Language

Reputation: Cooperation to Coordination

Cooperate Defect Cooperate b − c, b − c −c, b − e Defect b − e, −c 0,0 Possibility of exclusion from group creates new equilibrium, when e > c. Result: You don’t say what you know to be false when the consequences are right.

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Honesty Mechanisms Reputation Gossip Language

Effectiveness of Reputation

How long to exclude the dishonest?

Depends on population size. Depends on behavior of agents. Depends on criteria for exclusion.

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Honesty Mechanisms Reputation Gossip Language

In a population of size N

How long does it take to encounter everyone?

E(T) =

N−1

• i=0

N N − i (1)

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Honesty Mechanisms Reputation Gossip Language

What about variable behavior?

Parameter Estimation

Cooperation θ, Defection (1 − θ). True parameter θ∗. Goal is to approximate true parameter, with certain error (ǫ) and confidence (δ). P(|ˆ θ − θ∗| ≥ ǫ) ≤ 2e−2nǫ2 P(|ˆ θ − θ∗| ≥ ǫ) ≤ (1 − δ) n ≥ log

2 (1−δ)

2ǫ2 (2)

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Honesty Mechanisms Reputation Gossip Language

Evaluation

Best Case

Behavior is categorical and time to sort population is just the time to encounter each agent.

Worst Case

Behavior is probabilistic and threshold for confidence is high.

Overall

Time to encounter others grows linearithmically with size of

• population. Number of encounters required grows quadratically with

stricter error rate.

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Honesty Mechanisms Reputation Gossip Language

Gossip

Suppose...

...each agent gets additional information from others. The more you gossip, the less time you need to exclude dishonest agents. If you receive k additional pieces of information about interactions, then the number of interactions is n

k .

Essentially...

...counteracts the pressures of population size and confidence.

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Honesty Mechanisms Reputation Gossip Language

Problem

Doesn’t this just lead us back to the same question of why agents would be honest talking about others?

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Honesty Mechanisms Reputation Gossip Language

Simulation of IPD/CR

Parameters

Honesty: Agents propensity to be honest. Confidence: Amount of information needed to gossip.

Pairing, Interaction

Agents grouped randomly in each round (sender, receiver, gossiper). Sender asks receiver to play. Receiver agrees or declines. Receiver gets advice from gossiper: “Sender will cooperate/defect”

• r “I don’t know.”

Receiver’s trust in sender and gossiper adjusted based on outcome, and accuracy of advice.

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Honesty Mechanisms Reputation Gossip Language

Gossip

0.0 0.2 0.4 0.6 0.8 1.0 1000 2000 3000 4000

time avg_q

factor(conf) 1 50 factor(hon) 0.2 0.8 Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 19 / 26

Honesty Mechanisms Reputation Gossip Language

Gossip

0.0 0.2 0.4 0.6 0.8 1.0 1000 2000 3000 4000

time avg_q

factor(hon) 0.3 0.7 factor(conf) 1 50 Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 20 / 26

Honesty Mechanisms Reputation Gossip Language

Gossip

0.0 0.2 0.4 0.6 0.8 1.0 1000 2000 3000 4000

time avg_q

factor(hon) 0.4 0.6 factor(conf) 1 50 Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 21 / 26

Honesty Mechanisms Reputation Gossip Language

Evaluation

Speak

When you have sufficient evidence.

Don’t speak

When you don’t.

Overall

Best to condition advice on evidence.

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Honesty Mechanisms Reputation Gossip Language

Honest Signaling and the Maxim of Quality

Honest Signaling

Is possible when deterrents provide incentive to be honest. The threat

• f exclusion from interactions prompts behavior.

Maxim of Quality (Grice, 1975)

Try to make your contribution one that is true:

1 Do not say what you believe to be false 2 Do not say that for which you lack adequate evidence Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 23 / 26

Honesty Mechanisms Reputation Gossip Language

Conclusion

What keeps language meaningful?

We’re not honest because we’re benevolent creatures. Our cognitive capacities and social circumstances deter us from dishonesty. Even in the face of divergent preferences.

Why should we care?

Truth conditions, the Cooperative Principle, and the Maxim of Quality are eminently reasonable. We can consider language in cases where deterrents are effective or not.

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Honesty Mechanisms Reputation Gossip Language

Thanks!

To Robin Clark, Mark Liberman, Dave Embick, Jason Quinley, Jon Stevens, members of the third-year research seminar at Penn. To MACSIM organizers.

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Honesty Mechanisms Reputation Gossip Language

References

Grice (1975) Logic and Conversation Scott-Phillips (2010) Evolutionarily Stable Communication and Pragmatics Searcy & Nowicki (2005) The Evolution of Animal Communication Trivers (1971) The evolution of reciprocal altruism

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