A new method for enhancing collective intelligence using expert’s knowledge

Figures & data

Figure 1. A collective of 5 members.

Figure 2. Simulation procedure.

Table

Algorithm 1 Comparison of collective performance
1:	Input: Simulation settings
2:	Output: collective performance of collectives
3:	BEGIN
4:	Step 1: Generate collectives (reputation values, solutions)
5:	Step 2: Determine collective solution of each collective (based on criterion O2)
6:	Step 3: Compute collective performance (P1)
7:	Step 4: Provide expert’s knowledge
8:	Step 5: Modify collective solutions (Definition 3)
9:	Step 6: Determine collective solution of each collective (based on criterion O2)
10:	Step 7: Compute collective performance (P2)
11:	Step 8: Compare collective performance P1 and P2
12:	END

Figure 3. Collective 1.

Table 1. Updating individual solutions.

	$(x_1:1.0)$	$(x_2:0.6)$	$(x_3:0.2)$	$(x_4:1.0)$	$(x_5:0.3)$
$p_i$	100	200	300	200	100
$p_i^{\mathrm{\prime }}$	100	200	220	200	170

Table 2. Ranges of different reputation levels.

	Reputation	Solution range
L1	[0.0–0.4]	[0, 2000]
L2	[0.5–0.7]	[500, 1500]
L3	[0.8–1.0]	[750, 1250]

Table 3. Simulation results.

Size	Diff1	WR1	QIC1	Diff2	WR2	QIC2
9	0.8755	0.6689	0.8433	0.9564	0.6878	0.8554
109	0.9326	0.7078	0.9662	0.9816	0.8243	0.9750
209	0.9234	0.6875	0.9626	0.9796	0.8075	0.9732
309	0.9242	0.6817	0.9636	0.9798	0.8058	0.9737

Figure 4. Diff measure.

Figure 5. WR measure.

Figure 6. QIC measure.

Table 4. Kruskal–Wallis test results.

Measures	Cardinalities
	9	109	209	309
Diff	(58.49, <0.0001)	(104.31, <0.0001)	(138.22, <0.0001)	(135.07, <0.0001)
WR	(0.31, 0.58)	(56.12, <0.0001)	(89.27, <0.0001)	(101.68, <0.0001)
QIC	(0.0034, 0.95)	(4.36, 0.0367)	(11.78, 0.0005)	(11.62, 0.0006)

Note: All significance values are in bold.

Table 5. Diversity levels of collectives.

Cardinality	D1_1	D1_2	D2_1	D2_2
9	449.7790	152.7373	297.0780	99.6590
109	450.1480	145.7520	299.1790	97.9583
209	452.5390	148.2410	303.4780	100.2954
309	451.8010	147.1780	303.4030	99.7061

Figure 7. Diversity (D1) measure.

Figure 8. Diversity (D2) measure.