Work and Play: Simulating Language Contact

(1)

Work and Play: Simulating Language Contact

Roland M ¨uhlenbernd

¹

& Jason Quinley

¹

1

Seminar f ür Sprachwissenschaft, Universit ät T übingen

Goals

I examine language contact on a social network

I what social factors are important?

I are conventions inevitable or contingent?

I extend signaling game accounts of language change

I investigate theories of social conditions and convention adoption

I how does context affect signaling strategies?

I does connectivity increase convention adoption?

Motivation: Systematic Divisions in English

I Q: Why are French cognates in English more prestigious?

I A: Historians cite social conditions after the Norman invasion personal abstract

freedom liberty knowledge science belief faith

brotherly fraternal

animal meat swine pork cow beef sheep mutton deer venison

Table: Systematic division of meaning space between words of Germanic and French origin.

Context Signaling Games: Structure

Q: How do conventions arise?

Informally:

I Senders and Receivers

I Nature chooses a context

I Context dictates possible topics

I Senders observe a topic

I Senders send a message

I Receivers interpret it with action

I Success upon coordination

I Failure otherwise

Formally:

I Sender S and Receiver R

I P_C(c) and P_T(t|c)

I C = {dinner, farm}

I T = {meat, animal}

I M = {swine, pork}

I A = {meat, animal}

I U(t_i, a_j) =

1 if i = j

0 else

Context Signaling Games: Extensive Form

N

S

R

1 0

R

1 0

S

R

0 1

R

0 1

N

S

R

1 0

R

1 0

S

R

0 1

R

0 1

.9 .1 .1 .9

dinner farm

’meat’ ’animal’ ’meat’ ’animal’

”swine” ”pork” ”swine” ”pork” ”swine” ”pork” ”swine” ”pork”

’m.’ ’a.’ ’m.’ ’a.’ ’m. ’a.’ ’m.’ ’a.’ ’m.’ ’a.’ ’m.’ ’a.’ ’m.’ ’a.’ ’m.’ ’a.’

Figure: (N.B. dashed lines connect situations the recipient cannot distinguish; leaves resulting in 1 depict successful communication.)

Social Network Structure

I Each node is an agent

I Each edge represents a CSG

I Size

represents social class

I Black dots represent invaders

Figure: Scale-free network with 300 agents.

Experimental Settings

I social network with scale-free properties

I 300 agents with a randomly chosen social status

I agents communicate with neighbors by CSG

I agents switch between sender and receiver

I agents learn by learning dynamics

belief learning + best response dynamics

I when all agents have learned the same strategy → Norman invasion by replacing 30 agents

Result 1: Context-Dependent Strategy

Dinner: ’meat’

’animal’ ”swine” Farm: ’meat’

’animal’ ”swine”

Result: Before the Norman Invasion, all agents learn this context-dependent strategy

The Norman Invasion: Different Settings

Experiment 1: Randomly chosen agents are replaced by Norman invaders

Experiment 2: Only agents with a social status higher than a given lower limit are candidates to be replaced

Experiment 3: Agents must have a high social status paired with a high degree of centrality to be candidates to be replaced

Result 2: Emergence of two Strategies

S₁: ’meat’ ”pork”

’animal’ ”swine” S₂: ’meat’

”swine”

’animal’

”pork”

Results:

I the whole society learns either S₁ or S₂

I both strategies are context-independent

I the emergence of each strategy is equiprobable in Experiment 1, but nor for Experiment 2 or 3

Result 3: Local properties

perc.S 1-trials

20%

40%

60%

80%

100%

1 2 3 4 5 6 7 8 9 β

perc.S1-trials

20%

40%

60%

80%

100%

1 2 3 4 5 6 7 8 9 β Results:

I by increasing the threshold β of the replaced agents, the probability for a society-wide spread of strategy S₁ raises (Experiment 2)

I if the social status σ is also correlated with a higher degree d and

therefore a higher local influence, the increasing of threshold β of the replaced agents leads to an accelerated raising of the probability for a society-wide spread of expected strategy S₁ (Experiment 3)

Conclusion & Outlook

I language conventions depend on social factors

I context and connectivity accelerate and ensure certain conventions emerging

I without uniform social factors, patterns like those seen in modern English are left to chance

I social networks are a promising ground for treatments of language variation and change

Jason Quinley & Roland M ühlenbernd Work and Play: Simulating Language Contact Universit ät T übingen