Mechanisms for Enforcing Honest Signaling Christopher Ahern cahern @ - - PowerPoint PPT Presentation

Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion

Mechanisms for Enforcing Honest Signaling

Christopher Ahern cahern@ling.upenn.edu

University of Pennsylvania, Department of Linguistics and Institute for Research in Cognitive Science

August 8, 2012

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion

Goals

Explore mechanisms that might keep human signaling honest. What is honesty? Should honesty in signaling evolve? persist? What, if anything, makes humans honest? What does this have to say about the study of communication and meaning?

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion

Talk Outline

1

Honest Signaling

2

Signaling with Partial Common Interest

3

Possible Mechanisms

4

Conclusion

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion

Section Outline

Questions to answer

• 1. What is the relevant notion of honesty?
• 2. How does it relate to the study of meaning?

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Honesty

What is Honesty?

Honesty (Searcy & Nowicki, 2005)

Honesty is the absence of deception. Deception occurs when a Sender sends a signal to a Receiver and:

• 1. the Receiver responds in a way that benefits the Sender
• 2. the response is appropriate if the signal reliably indicates a situation, X,

and

• 3. it is not the case that X obtains

Relationship to Cooperation

Requires cooperation on the part of senders. Senders must forgo some benefit to use signals honestly.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Honesty

When is Cooperation/Honesty Possible?

A B A 1,1 0,0 B 0,0 1,1 Work Shirk Work 3,3 0,4 Shirk 4,0 2,2 Cooperation is possible in Work-Shirk (Right), but not in Pure Coordination Game (Left). Would an A-player say, “I am going to play B!”? Would anyone believe, “I am going to Work!”?

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Deception

Deception and the Evolution of “Meaning”

Deception Undermines “Meaning”

Assuming that deception involves a loss on the part of the receiver, if individuals have incentive to deceive each other then conventional signaling is counter-selected for (Zahavi, 1993). Signals cease to reliably correlate with any aspects of the sender or the environment. Credulous receivers do worse than skeptical ones. Skeptical receivers do not attend to signals. Senders should not signal if receivers do not attend to signals. Signaling should disappear under the effects of deception.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Deception

How do we get to where we are?

Grice’s (1975) Maxim of Quality

Try to make your contribution one that is true. (1) Do not say what you believe is false. (2) Do not say that for which you lack adequate evidence.

More generally

Words are meaningful. We might ask what sorts of social and cognitive mechanisms allow them to be so.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion

Section Outline

Questions to answer

• 1. What is the formal apparatus we are using?
• 2. What is a reasonable game structure?
• 3. What are the results?

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Signaling Games

Signaling Games

Signaling Game: {S,R},T,δ,M,A,US,UR

S is the sender, and R is the receiver. T is a set of states δ is a probability distribution over those states M is a set of messages A is a set of actions US and UR are the utility functions of S and R

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Signaling Games

Signaling Games

Structure of play

Sender observes a state t ∈ T, determined by δ. Sender chooses a message m ∈ M based on a strategy s ∈ [T → M] which is transmitted to the receiver. Receiver takes an action a ∈ A based on the message received and a strategy r ∈ [M → A]. Payoffs for S and R are determined by the type t, message sent s(t), and action taken r(s(t)).

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Signaling Games

Signaling Games in Extensive Form

δ S R a1 a2 m1 R a1 a2 m2 t1 S R a1 a2 m1 R a1 a2 m2 t2

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Example

Ralph

Likes: tasty fruit, going for long swings on the vine Dislikes: non-tasty fruit, being lied to

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Example

Sally

Likes: tasty fruit, going for long swings on the vine Dislikes: non-tasty fruit, being lied to

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Example

A match made in heaven?

Sally approaches Ralph and suggests...

He forage in the bushes with her for fruit. He lift her up into a tree to get tasty fruit for both of them.

Ralph can...

Ignore Sally entirely Forage in the bushes Lift her into the tree

Sally responds to..

being ignored by moving on. an agreement to forage by foraging. being lifted up into the tree by...

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Example

Take another look

Sally

Is Sally a cute clapping chimpanzee? Or is she scheming on some darker purpose?

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Example

Suppose there are two kinds of Sally

Honest Sally

Will gather as much fruit as possible and drop it down for both to share.

Dishonest Sally

Will eat as much fruit as possible without dropping any down for Ralph.

A problem for Ralph

How much effort should he put into cooperating with Sally based on the signal sent? Does it reveal whether she will actually get fruit for both?

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Example

Preferences for Sally

Honest Sally

Prefers that Ralph lift her into the tree to anything else. Prefers foraging in the bushes with Ralph to being ignored.

Dishonest Sally

Prefers foraging in the bushes to being lifted into the tree. She cannot eat that much before being found out by Ralph and the risk of being hurt when he finds out is sufficient to outweigh most of the benefit of the tasty fruit. Being ignored is least preferable.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Example

Preferences for Ralph

For Honest Sally

Exact same preferences as Honest Sally. Lifting her up into the tree is better than foraging is better than ignoring.

For Dishonest Sally

Ignoring is best as it leaves Ralph in a position to listen to or interact with honest senders. Foraging is better than lifting because it results in something rather than nothing.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Example

A stand-in payoff structure

Payoffs

a0 ape ae th 0,3 5,5 8,8 td 0,6 5,5 3,0 T = {th,td} (honest, dishonest sender) A = {a0,ape,ae} (expend no effort and ignore, expend some proportion

• f effort p to forage in the bushes, expend all energy to lift)

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Example

Bad news

Payoffs

a0 ape ae th 0,3 5,5 8,8 td 0,6 5,5 3,0

The only equilibria of the game are pooling

If types send different messages, td can benefit by sending the same signal as

• th. In response to this, receivers should play ape. Honest senders cannot

unilaterally change strategy to benefit.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Example

Doom and Gloom?

Short Answer: No, language does exist. Interesting Answer: No, language exists, and here are some ways to keep signaling honest.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion

Section Outline

Questions to answer

• 1. What general sorts of mechanisms are available?
• 2. Which ones should we consider for human language?
• 3. What are the results? How well do they do?

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Mechanisms

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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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Mechanisms

General Classes of Mechanisms (Scot-Phillips 2010)

Indices

Red deer roar formant dispersion is (negatively) correlated with size of vocal tract, and thus size overall. Can’t be faked.

Handicaps

Peacock’s tail requires more energy, makes it more likely to be caught by

• predator. Only fit peacock could support these demands and survive.

Deterrents

Punishment for lying. This could be physical or social (e.g. ostracization). Note, often requires effort on the part of those enacting punishment.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Mechanisms

General Classes of Mechanisms (Scot-Phillips 2010)

Indices

Language is arbitrary, diverse.

Handicaps

Not clear how to work the notion of cost into language. Especially problematic for combinatorial language (Lachmann et al. 2001).

Deterrents

Lots to explore!

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Mechanisms

Possible Deterrents

We consider

• 1. Neologisms: What does the introduction of new signals do?
• 2. Punishment: Does punishment solve the problem?
• 3. Memory: When does remembering foster honesty?
• 4. Gossip: Does gossip extend memory to a community?

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Neologisms

What are neologisms and what do they do?

Can be thought of in terms of...

Expanding M to include new messages Reusing unused messages in M

Destabilize the pooling equilibria

The pooling equilibria are not neologism-proof (Farrell, 1993)

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Neologisms

Neologism-Proof (Farrell, 1993)

Definition

For a given equilibrium for a game, suppose that there is an unused signal – a neologism – in the equilibrium that agents of a particular type t could use to unambiguously identify themselves. That is, there is a signal, that if taken as indicative of type t would benefit that type as well as the receiver, but no other type of sender t . If these conditions are met, then the equilibrium is not neologism proof.

Pooling equilibria are not neologism proof

a0 ape ae th 0,3 5,5 8,8 td 0,6 5,5 3,0 Honest types can employ unused signal to identify themselves.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Neologisms

Dynamics of neologisms

Markov Process

Sender strategies can be grouped into two sets: separating states where the types send different messages (Ss) and pooling states where the send the same message (Ps). Receiver strategies into those that take unique actions for each message used in a separating state (Sr) and those that take the identical action for two or more distinct messages (Pr). Define the states of the Markov process as combinations of the different sender and receiver strategies. Let q be the probability that an honest type will employ a neologism when in the pooling state.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Neologisms

Dynamics of neologisms

SsSr PsSr PsPr SsPr q 1−q

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Neologisms

What to expect?

Payoffs by role and state

SsSr PsSr PsPr SsPr th 8 8 5 5 td 3 5 5 R 8×δ(th)+6×δ(td) 8×δ(th) 5 5

Amount of time spent in each state

As q approaches 1, amount of time spent in each state approaches 1

4.

Note:Payoffs in SsSr reflect result of honest signaling. Payoffs in PsPr reflect result of dishonest signaling.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Neologisms

What to expect?

Expected utility by role

EUth = 1 4(8+8+5+5) = 6.5 EUtd = 1 4(0+3+5+5) = 3.25 EUR = 1 4(16×δ(th)+6×δ(td)+5+5) = 2.5×δ(th)+4 (1)

Comparisons

Honest Dishonest-Pooling Neologisms th 8 5 6.5 td 5 3.25 R 8×δ(th)+6×δ(td) 5 2.5×δ(th)+4

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Neologisms

Results: Neologisms

“Best case” scenario (q = 1)

Honest signalers do better with neologisms than they would with dishonest signaling, but not as well as with honest signaling. Dishonest signalers do best with dishonest signaling, better with neolgisms, and worst with honest signaling. Receivers do best with honest signaling, and better with neologisms if the proportion of honest signalers in the population exceeds a certain threshold, δ(th) > .4.

Main result

Neologisms allow for honest signaling by some agents some of the time, but are far from guaranteeing honest signaling by all agents all the time. It takes quite a bit of running to stay in place.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Punishment

What about punishment?

Experimental results

Punishment supports the maintenance of cooperation in social dilemmas (Fehr and Gachter 2000, 2002; Fischbacher and Gachter 2010).

Problem

Punishment is costly. If it is possible to let others do the punishing and free-ride on their work, then everyone should opt out. This is, again, the problem of cooperation.

Signaling

Yelling, “I’ll help punish the miscreants!” is not credible. In the same way saying, “I’m going to work!” is not credible in the Work-Shirk game. Signaling pushes the problem of honesty to a higher level where meaning/honesty unravels yet again.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Memory

What to consider for memory?

Important Points

Learning process Population size and Expected Utility Costs Bounded memory

Intuitive Preliminaries

Memory should help keep signaling honest, but should be less effective in larger populations. If costs exceed benefits, it should not arise. Bounding memory lessens its effectiveness.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Memory

Learning process for memory

Imagine a receiver in a pooling equilibrium

Receiver decides to trust incoming signal with probability q. Totally skeptical receiver (q = 0), inqusitive receiver (q = 1) If receiver plays ae and gets a payoff of 8, then sender is honest. If receiver plays ae and gets a payoff of 0, then sender is dishonest. The next time a receiver encounters the sender, it can act accordingly.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Memory

Learning process for memory

How long does it take to discover all types?

E = 1 q

N−1

∑

i=0

N N −i (2) The ith agent will be discovered, on average, in this many interactions.The time to discover the type of agents increases quickly with the size of the

• population. How does this effect the viability of memory?

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Memory

Expected Utility with Memory

What’s what

Kt is the set of known senders at a given time t. K′

t the set of unknown receivers.

P(Kt) = |Kt|

N , where N is the size of the population.

If the sender is known, then the receiver is guaranteed the preferred payoff, which can be given as a = 8δ(th)+6δ(td) If the receiver is not known, then based on q, the receiver can expect to get a payoff of b = q[8δ(th)+0δ(td)]+(1−q)5.

Expected Utility of a receiver at a given time

EUt

R = P(Kt)(a)+P(K′ t)(b)

(3)

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Memory

When does memory payoff?

Relative to a baseline payoff B

Memory pays off in T interactions, when: T > (b−a) (b−B)

T

∑

i=0

P(Ki) (4)

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Memory

When does memory payoff?

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Memory

What about costs?

Possibilities

Fixed costs: having memory bears a constant cost Marginal costs: the amount remembered determines cost A bit of both

Limits

Maximum payoff is a = 8δ(th)+6δ(td). Relative to a baseline B, the cost of memory must be such that a−B > c for memory to confer any benefit.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Memory

What about limited memory?

Memory is not perfect

Let agents remember the past m reactions. Lessens the effectiveness of

• memory. Below example of utility averageed over 1000 agents in a population

N = 20 and various memory sizes. Costs not included.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Memory

Results: Memory

Memory works...

...well in a sufficently small population, or with long-lived agents, or with low marginal or fixed costs. If any, or a combination, of these hold, then we get agents who can’t help but tell the truth. This gets us the first submaxim of Quality.

Further considerations

Behaviors are not necessarily constant, and populations change over time.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Gossip

What is gossip?

Social Memory

Individual memory might be limited, but agents might signal information about other agents to other agents.

Benefits

If dishonest agents are allowed to move, or a population changes sufficiently quickly, the transmission of information through a network might allow receivers to better assess senders.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Gossip

Problems?

Solves an important one

Upon encountering an unknown sender a sender can ask a neighbor for advice. The neighbor must decide what information to send to the receiver: “Agent X is honest”, “Agent X is dishonest”, or “Agent X is honest or dishonest (I don’t know)”. There is no motivation for sender to be dishonest. Moreover, if he is wrong, then the receiver will likely mistrust the neighbor. This provides something like the second submaxim of Quality.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion

Main Points

Problem of honesty

Misaligned preferences select against the evolution of honest signaling.

Mechanisms

Deterrents are the most likely type of mechanism to solve this problem. Memory and gossip might serve to support honest signaling in general, and Grice’s Maxim of Quality in particular.

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion Ahern (IRCS) Mechanisms for Enforcing Honest Signaling August 8, 2012 48 / 50

Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion

Thanks!

To Jason for presenting. To everyone there for listening. To organizers for putting it all together.

Comments

Comments appreciated: cahern@ling.upenn.edu

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Honest Signaling Signaling with Partial Common Interest Possible Mechanisms Conclusion

References

1

Farrell (1993) Meaning and Credibility in Cheap-Talk Games

2

Fehr & Gachter (2000) Cooperation and Punishment

3

Fehr & Gachter (2002) Altruistic Punishment in Humans

4

Fischbacher & Gachter (2010) Social Preferences, Beliefs, and the Dynamics of Free-Riding in Public Good Experiments

5

Grice (1975) Logic and Conversation

6

Lewis (1969) Convention

7

Scott-Phillips (2010) Evolutionarily Stable Communication and Pragmatics

8

Searcy & Nowicki (2005) The Evolution of Animal Communication

9

Zahavi (1993) The Fallacy of Conventional Signalling

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