SLANGIntroduction 3

Roland MuhlenberndSeminar fur Sprachwissenschaft

University of Tubingen

Overview

Simulation on Social NetworksNaming GameSocial Impact TheoryThe Coevolution Model

Game Theory & LinguisticsEvolutionary Game TheoryRational Communication

Network Games: Simulating Linguistic Phenomena

Homework

Overview

Preliminary Schedule

Simulation on Social Networks: Network TheoryThe New Science of Networks (Watts, 2004)

I Small-World networksI high cluster coefficient CI low average shortest path length L

I cluster coefficient C =∑

i Ci

n

I individual cluster coefficient Ci = number of connections among N(i)(|N(i)|×|N(i)|−1)/2

I average shortest path length L =∑

i Lin

I individual average shortest path length Li =∑

j 6=i P(i ,j)

n−1

Simulation on Social Networks: Network TheoryThe New Science of Networks (Watts, 2004)

Simulation on Social Networks: Naming GameAgreement Dynamics on Interaction Networks (Barrat et al., 2007)

I agents play theNaming Game

I different networktopologies (complete,lattice, small-world)

I different strategies(play-last, play-first,play-smart)

Simulation on Social Networks: Social Impact TheoryUsing Social Impact Theory to simulate Language Change (Nettle, 1999)

Social Impact Theory (Latane 1981): The likelihood that a personwill respond to social influence will increase with:

I Strength: how important the influencing group of people areto you.

I Immediacy: how close the group are to you (in space andtime) at the time of the attempted influence.

I Number: How many people there are in the group.

Simulation on Social Networks: Social Impact TheoryUsing Social Impact Theory to simulate Language Change (Nettle, 1999)

I Idea: a speaker will adopt the variant with the greatest impacton him

I the impact of variant p is influenced by social and functionalparameters: Ip = bp × f (Sp,Dp,Np), whereby

I bp represents acquisitional bias for using pI Np is the number of individuals using p (number)I Sp is the status of a individual using p (strength)I Dp is the social distance to a individual using p (immediacy)

Simulation on Social Networks: Social Impact TheoryUsing Social Impact Theory to simulate Language Change (Nettle, 1999)

Nettle’s simulations on a social map:

5 4 3 2 1 1 2 3 4 5 5 4 3 2 1

5 4 3 2 1 1 2 3 4 5 5 4 3 2 1

5 4 3 2 1 1 2 3 4 5 5 4 3 2 1

I horizontal: familial social ties (parents, children...)

I vertical: horizontal social ties (own peer group like friends)I In each life stage (simulation step) a whole cohort along the

vertical goes through language acquisition at the same timeI age 1-3: for two possible variants p and q compute Ip and Iq

and acquire variant with higher impact value (mutation 5%)I age 1 has no influenceI age 4-5: stay at acquired variant

I After each life stage: increase ages by one and replace age 5by age 1 (replace dead by newborn agents)

Simulation on Social Networks: Social Impact TheoryUsing Social Impact Theory to simulate Language Change (Nettle, 1999)

Parameter: ∀i , j : si = sj , a = 1

Parameter: ∀i , j : si = sj , a = .5

Simulation on Social Networks: Social Impact TheoryUsing Social Impact Theory to simulate Language Change (Nettle, 1999)

Nettle’s conclusion:

I Emergence of separate dialects by decreasing the importancelearners give to conformity (decreasing parameter a)

I Changes are adopted if there are speakers which are muchmore influential than others (superinfluential agents)

I Functional biases determine the fate of competing linguisticvariants (bq >> 1)

”Functional biases may therefore affect the direction of languagechange rather than providing sufficient conditions for it to occur...The incessant change of languages on [these] items must be apurely social process.” (Nettle 1999)

Simulation on Social Networks: Social Impact TheoryLanguage Change and Social Networks (Ke, Gong & Wang, 2008)

Ke, Gong & Wang’s critique:

I Nettle’s population structure is a weighted regular network.Real world networks are neither regular nor random.

I Superinfluential speakers are necessary to overcome thethreshold, facing a challenge in explaining ”changes frombelow” (Labov 2001)

Simulation on Social Networks: Social Impact TheoryLanguage Change and Social Networks (Ke, Gong & Wang, 2008)

Ke, Gong & Wang’s account:I Adopting Nettle’s age structure:

I ages 1-5, learner 1-2, teachers 2-5I increasing age by one in each simulation stepI replacing dead agents (> 5) by newborn (1)

I Replacing Nettle’s social map by different network types:I regular, small-world, random, scale-freeI agents of different ages are randomly distributedI agents can only communicate with direct neighboursI no value of social distance

I all agents have the same statusI Learners adopt variant of highest fitness as a product of a

functional and a frequency value 1:

F (U) = fu × qu

1This is just a simplification of Nettle’s formula: impact is called fitness, fu represents the functional bias and

qu represents the residue of the social impact (number) by excluding status (strength) and immediacy (distance)

Simulation on Social Networks: Social Impact TheoryLanguage Change and Social Networks (Ke, Gong & Wang, 2008)

Results:

I regular and small-world network: high success probability, butslow diffusion rate

I random and scale free network: fast diffusion rate, but lowersuccess probability

I probabilistic learners drastically increase the probability oflanguage change

Simulation on Social Networks: Coevolution ModelExploring social structure effect... (Gong, Minett & Wang, 2008)

I Coevolution model: more complex mental model for agentsI different network structures (star, scale-free, 2 populations)

Game Theory & Linguistics: Evolutionary Game TheoryThe Evolution of Communication (Wiley, 1983)

The evolution of communication depends on the changes in fitnessof sender and receiver:

I what strategies for signaling are most effective in evokingresponses from a potential receiver?

I how can a signaler (or receiver) manipulate the behavior ofthe other individual to its own advantage?

I how should animals communicate with each other in thecourse of conflicts?

Game Theory & Linguistics: Evolutionary Game TheoryThe Evolution of Communication (Wiley, 1983)

Cooperate Defect

Cooperate R;R S;TDefect T;S P;P

Tabelle : Prisoner’s Dilemma

I R: RewardP: PunishmentT: TemptationS: Sucker

I T > R > P > S

Trusting Devaluing

Honest R;R’ S;T’Bluffing T;S’ P;P’

Tabelle : Sender-Receiver Game

I T > R > P > S

I R ′ = P ′ > S ′,T ′

Game Theory & Linguistics: Evolutionary Game TheoryEvolutionary Game Theory for Linguistics (Jager, 2004)

Important concepts:

I Nash Equilibrium

I EvolutionaryStable Strategy

I ReplicatorDynamics

A B

A 1 1B 1 0

Tabelle : Pigeonorientation game

Game Theory & Linguistics: Evolutionary Game TheoryEvolutionary Game Theory for Linguistics (Jager, 2004)

Important concepts:

I Nash Equilibrium

I EvolutionaryStable Strategy

I ReplicatorDynamics

H D

H 1,1 7,2D 2,7 3,3

Tabelle : Hawks andDoves

Game Theory & Linguistics: Evolutionary Game TheoryEvolutionary Game Theory for Linguistics (Jager, 2004)

The ”Division of Pragmatic Labor”

”The simpler of two competing expressions is assigned tothe prototypical meaning, while the more complexexpression is reserved for the less prototypical situation.”

Examples:”John went to church/jail.” vs. John went to the church/jail.”driller/cooker vs. drill/cook

Game Theory & Linguistics: Evolutionary Game TheoryEvolutionary Game Theory for Linguistics (Jager, 2004)

Game Theory & Linguistics: Evolutionary Game TheoryApplications of Game Theory in Linguistics (Jager, 2008)

Vowel categorizing game:I sender picks category vI sender chooses signal f1 ∈ F (v) randomlyI noise changes it to f2I receiver searches for perception event 〈f ′, v ′〉, minimizing

distance between f ′ and f2I if v ′ = v , the pair 〈f2, v〉 is added to the memory of perception

Game Theory & Linguistics: Evolutionary Game TheoryApplications of Game Theory in Linguistics (Jager, 2008)

Game Theory & Linguistics: Rational CommunicationGame Dynamics connects Semantics & Pragmatics (Jager, 2006)

Scalar Implicature:”Some boys came to the Party”→ 〈 some but not all boys came to the party 〉Model:Set of alternative excluding worlds:

I w1 : ∀x ∈ B : P(x)

I w2 : ∃x ∈ B : P(x) ∧ ∃x ∈ B : ¬P(x)

I w3 : ∀x ∈ B : ¬P(x)

Set of alternative expressions:

I f1 : ”all boys came to the party”

I f2 : ”some boys came to the party”

I f3 : ”some but not all boys came to the party”

I f4 : ”none of the boys came to the party”

Literal: f2 → {w1,w2} vs. Pragmatic: f2 → {w2}

Game Theory & Linguistics: Rational CommunicationThe Logic of indirect Speech (Pinker, Nowak, Lee, 2006)

I Would you like to come up and see my etchings? [sexualcome-on]

I If you could pass the guacamole, that would be awesome.[polite request]

I Nice store you got here. Would be a real shame if somethinghappened to it. [a threat]

I Gee, officer, is there some way we could take care of the tickethere? [a bribe]

Dishonest Officer Honest Officer

Don’t bribe Ticket TicketBribe Go Free Arrest for BriberyImplicate Bribe Go Free Ticket

Tabelle : Bribe Game

Network Games and Language: Language RegionsTalking to Neighbors (Zollman, 2004)

I agents are placed on a toroid latticeI agents play signaling game (stag hunt) rep. with neighborsI agents copy most successful strategy among the neighbors

Abbildung : from Zollmann, K. (2005), Talking to neighbors

Network Games and Language: Language RegionsSimu. the Emergence of Conventions in SW Netw. (Muhlenbernd, Franke, 2012)

I agents are placed on a small-world networkI agents play signaling game repeatedly with neighborsI agents learn strategy by learning dynamicsI analyze global/local properties vs emergence of convention

Network Games and Language: Language ContactConquest, Contact & Convention (Quinley, Muhlenbernd, 2012)

personal abstract

freedom libertyknowledge sciencebelief faithbrotherly fraternal

animal meat

swine porkcow beefsheep muttondeer venison

Tabelle : Systematic division of meaning space between words ofGermanic and French origin, possibly a result of lifestyle and educationdifferences. The left table shows the division between personal (Germanicorigin) and abstract (French origin) concepts. The right table shows thedivision betweens words for animals and their meat.

S1:’meat’ ”pork”

’animal’ ”swine”S2:

’meat’

”swine”’animal’

”pork”

Abbildung : The two strategies S1 and S2, whose emergence could beequiprobable without social influence.

Network Games and Language: Language ContactConquest, Contact & Convention (Quinley, Muhlenbernd, 2012)

Abbildung : Experiment 1: replaceagents agents randomly

Abbildung : Experiment 2: replaceagents with a high social status

Abbildung : Experiment 3: replacecentral agents with high status

per

c.S

1-t

rial

s

20%

40%

60%

80%

100%

1 2 3 4 5 6 7 8 9 β

Abbildung : Result Experiment 2

Homework

Watch the TED-talk:http://www.ted.com/talks/wade davis on endangered cultures.html

1. Summarize the talk (half a page)

2. How does the talk relate to class?

3. Try to find intersections to your presentation topic.

4. Unlike many of the TED presenters, not many of us in theroom are professional speakers. What areas do you feelconfident about in your presentation? What areas will youhave to work on?