Roy Wilson (2007)
Simulating the Effect of Social Influence on Decision-Making in Small, Task-Oriented, Groups
Journal of Artificial Societies and Social Simulation
vol. 10, no. 4 4
<https://www.jasss.org/10/4/4.html>
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Received: 24-Mar-2007 Accepted: 15-Jul-2007 Published: 31-Oct-2007
Observable |
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Unobservable (inferred) |
|
Unobservable (inferred) |
Communicative acts |
→ |
Social relations |
→ |
Expectation states |
↑ |
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|
↓ |
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← |
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← |
|
Figure 1. The social system |
these groups have a set of beliefs about 'human nature' and the organization of work and family that allow the participants to interpret the 'facts' in the human relations case. (Meeker 1994)Of course, not all such groups exhibit consensus regarding goals and values: EST is not applicable to these groups.
a |
→ |
X(+) |
→ |
Y(+) |
→ |
Z(+) |
→ |
T(+) |
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- |
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|
d |
→ |
X(-) |
→ |
Y(-) |
→ |
Z(-) |
→ |
Z(-) |
Figure 2. A social-psychological definition of the situation |
f(p(1) ∪ … ∪ p(n)) = 1 - [(1 - f(p(1))) × … × (1 - f(p(n)))] | (1.1) |
The value of e(x) is computed as the sign of the paths in the combination times the strength of combination of paths from x to the task outcomes. e(a) > 0, so (via equation (1.2)) the simple expectation state associated with a is (collective) task success. Similarly, because e(d) < 0, d is linked by the simple expectation state to (collective) task failure. Note that the prefixed sign in equations (1.2) and (1.3) is determined by the sign of the paths leading from the actor to the task outcome.
e(a) = +1 × (1 - [(1 - f(4) × (1 - f(5))]) = +0.1826 | (1.2) |
e(d) = -1 × (1 - [(1 -f(4)) × (1 - f(5))]) = -0.1826 | (1.3) |
ae(x) = 1 – 0.8174k | (1.4) |
ae(x-) = -(1 - 0.8174j) | (1.5) |
ae(x) = 0.8174j - 0.8174k | (1.6) |
a ↓ d → z ↑ w | |
Figure 3. Sample precedence graph |
ae(d) = 0.81742 - 0.81741 = -0.1493 | (1.7) |
Table 1: Initial aggregate expectation states derived from Figure 3 | |||
|
k pairs of positive paths |
j pairs of negative paths |
ae(x) |
|
(In degree of actor node) |
(Out degree of actor node) |
|
a |
1 |
0 |
+0.1826 |
w |
1 |
0 |
+0.1826 |
z |
0 |
1 |
-0.1826 |
d |
1 |
2 |
-0.1493 |
if ΣB(i, a, c)/5 < 0.5 then O(i, c) = 0 else O(i, c) = 1 | (1.8) |
δ = Δ(ae(x), ae(y)) | (1.9) |
num = e(0.472 + 0.632 × δ) | (1.10) |
p(y, S) = num / (num + 1) | (1.11) |
r = p(d, S) × B(i, d, c) | (1.12) |
s = [1 - p(d, S)] × B(i, a, c) | (1.13) |
B(u, d, c) = r + s | (1.14) |
if ΣB(f, a, c) / 5 < 0.5, then O(f, c) = 0 else O(f, c) = 1 | (1.15) |
/** * Each object of this class represents a Person. A Person is conceived as a * semi-autonomous entity and is represented by a CSProcess. CSProcesses * communicate over channels. * */ public class Person extends CommNode implements ISocialStructure { private SocialStructure _socialStructure; private Crew _socialStructureCrew; private TurnCrew _turnCrew; final CSTimer timer = new CSTimer(); /** * @param nodeId * @param simParameters * @param chanParameters * @param belief */ public Person( int nodeId, SimParameters simParameters, ChanParameters chanParameters, Belief belief) { super(nodeId, simParameters, chanParameters, belief); _socialStructure = _simParameters.get_socialStructure(); _socialStructureCrew = _simParameters.get_socialStructureCrew(); _turnCrew = _simParameters.get_turnCrew(); } // Each actor competes for a conversational turn private synchronized boolean is_my_turn() { boolean retval = false; _socialStructureCrew.startRead(); int current_x = _socialStructure.get_current_x(); int current_y = _socialStructure.get_current_y(); _socialStructureCrew.endRead(); if (current_x == _my_nodeId) { _tgt_nodeId = current_y; retval = _turnCrew.claim(_my_nodeId); } return retval; } // simulate processing of incoming message public void simulate_reader(int other_actor) { _turnCrew.release(); timer.sleep(_simParameters.get_worktime(_my_nodeId)); _socialStructureCrew.startRead(); double ps_focal = _socialStructure.compute_PS(other_actor, _my_nodeId); _socialStructureCrew.endRead(); _belief.update(_my_nodeId, other_actor, ps_focal); } // simulate formulation of outgoing message public void simulate_writer(String msg) { timer.sleep(_simParameters.get_worktime(_my_nodeId)); write_msg(update_msg(_normal_msg_out)); } // Each actor is modeled as a computational process public void run() { Message msg_in = null, msg_out = null; // Once initiated, run until 'poison' received from upstream while (!_poison_rcvd) { // If there is a message, read it and handle it if (_chanParameters.get_medium2person(_my_nodeId).pending()) { msg_in = read_msg(_simParameters.get_pkt_src_type()); _poison_rcvd = false; if (msg_in.is_Poison()) { // Forward the poison downstream msg_out = construct_msg_out(ICommNode.SEND_POISON); msg_out.set_content(_belief.get_datum_my_nodeId()); write_msg(msg_out); _poison_rcvd = true; } simulate_reader(msg_in.get_src_nodeId()); } if (!_poison_rcvd && is_my_turn()) { simulate_writer("Writer Cognition"); } } } } |
Figure 4. The Person class |
Table 2: Control variables and their values | |
Variable |
Value |
interactions |
375 per meeting |
lifeThinkTime |
6.4 seconds |
Table 3: Input variables and their values | |
Variable |
Value(s) |
η |
{0.625, 0.75} |
π |
{0.50} |
θ |
{0.25} |
B(i, x, c) |
For each x and each c, a fixed value in [0.0, 1.0] |
|
|
B(i, c) |
Vector of initial beliefs of group members regarding A(c) |
status |
{(H, M, M, L, M), (H, M, M, M), (M, M, M, L, M), (H, M, M, H, M)} |
Table 4: Correlations among the initial beliefs of actor types | |||||
|
Principal |
Social |
Nurse |
Teacher |
Counselor |
|
|
Worker |
|
|
|
Principal |
+1 |
|
|
|
|
Social Worker |
+0.124 |
+1 |
|
|
|
Nurse |
-0.153 |
-0.336 |
+1 |
|
|
Teacher |
-0.011 |
+0.082 |
-0.346 |
+1 |
|
Counselor |
+0.013 |
-0.012 |
-0.314 |
-0.389 |
+1 |
Table 5: Output variables | |
Variable |
Description |
B(f, c) |
Final belief of group members regarding A(c) |
O(i, c) |
A(c) under static model: 1 (true); 0 (false) |
O(f, c) |
A(c) under process model: 1 (true); 0 (false) |
steps2equilibrium |
# of interactions till the social network is complete |
participation(x) |
# of interactions in which x addresses some y |
Table 6: The static and process models on A(c) (over all c) | |||
Agree |
Disagree |
Total |
Proportion Agree |
2464 |
1087 |
3551 |
0.694 |
Table 7: The static and process models on A(c): More detail | |||
Decision |
Runs |
Runs |
Proportion |
model |
yielding 1 |
yielding 0 |
yielding 1 |
Static |
1760 |
1791 |
0.4956 |
Process |
2015 |
1536 |
0.5675 |
Table 8: Disagreement of the static and process decision models | |||
|
O(f, c) = 0 |
O(f, c) = 1 |
Static Total |
O(i, c) = 0 |
1120 |
671 |
1791 |
O(i, c) = 1 |
416 |
1344 |
1760 |
Process Total |
1536 |
2015 |
3551 |
Table 9: Static versus process outcomes (by status) | |||||
|
O(i, c) |
O(f, c) = 0 |
O(f, c) = 1 |
χ2 |
% |
|
|
|
|
for 2 × 2 |
0 → 1 |
(a) (H,M,M,L,M) |
0 |
296 |
152 |
|
60.3 |
|
1 |
100 |
340 |
|
|
|
|
|
|
0.0011 |
|
(b) (H,M,M,M,M) |
0 |
256 |
192 |
|
61.5 |
|
1 |
120 |
320 |
|
|
|
|
|
|
4.588e–05 |
|
(c) (M,M,M,L,M) |
0 |
264 |
183 |
|
67.5 |
|
1 |
88 |
352 |
|
|
|
|
|
|
7.888e–09 |
|
(d) (H,M,M,H,M) |
0 |
304 |
144 |
|
57.1 |
|
1 |
108 |
332 |
|
|
|
|
|
|
0.0234 |
|
Figure 5. Variation in mean participation frequency |
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