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? Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 2 / 26
Honesty Mechanisms Reputation Gossip Language Outline 1 Honesty 2 Mechanisms 3 Reputation 4 Gossip 5 Language Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 3 / 26
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. Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 4 / 26
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. Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 5 / 26
Honesty Mechanisms Reputation Gossip Language Cooperation vs. Coordination A B Cooperate Defect A b , b 0, 0 Cooperate b − c , b − c − c , b B 0, 0 b , b Defect b , − c 0,0 Signals are credible in games of coordination, but not in games of cooperation. Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 6 / 26
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. Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 7 / 26
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. Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 8 / 26
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. Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 9 / 26
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. Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 10 / 26
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. Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 11 / 26
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. Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 12 / 26
Honesty Mechanisms Reputation Gossip Language In a population of size N How long does it take to encounter everyone? N − 1 N � E ( T ) = (1) N − i i =0 Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 13 / 26
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 ) ≤ 2 e − 2 nǫ 2 P ( | ˆ θ − θ ∗ | ≥ ǫ ) ≤ (1 − δ ) (2) 2 log (1 − δ ) n ≥ 2 ǫ 2 Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 14 / 26
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. Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 15 / 26
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. Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 16 / 26
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? Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 17 / 26
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” or “I don’t know.” Receiver’s trust in sender and gossiper adjusted based on outcome, and accuracy of advice. Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 18 / 26
Honesty Mechanisms Reputation Gossip Language Gossip 1.0 0.8 factor(conf) 1 0.6 50 avg_q factor(hon) 0.4 0.2 0.8 0.2 0.0 0 1000 2000 3000 4000 time Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 19 / 26
Honesty Mechanisms Reputation Gossip Language Gossip 1.0 0.8 factor(hon) 0.3 0.6 0.7 avg_q factor(conf) 0.4 1 50 0.2 0.0 0 1000 2000 3000 4000 time Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 20 / 26
Honesty Mechanisms Reputation Gossip Language Gossip 1.0 0.8 factor(hon) 0.4 0.6 0.6 avg_q factor(conf) 0.4 1 50 0.2 0.0 0 1000 2000 3000 4000 time 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. Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 22 / 26
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 of 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. Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 24 / 26
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. Ahern (UPENN) Honest Signaling and the Maxim of Quality April 13, 2013 25 / 26
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