Measuring the strength of trade unions and identifying the privileged groups: A two-dimensional approach and its implementation

Figures & data

Figure 1. Resilience of a group within trade unions and resilience of trade unions within a group.

Table 1. Symbols and annotations used in the text.

A: A set containing people belonging to a specific group

U: The set of all trade union members

W: The universal set containing the whole society

x: number of people belonging A but not affiliated with the trade union (see Equation 2)

y: number of trade union members who do not belong to A (see Equation 3)

z: number of trade union members who are belonging to A (see Equation 1)

r: number of people who neither belong to A nor affiliated with the trade union

P: relative power (see Equation 9)

R: relative representation (see Equation 10)

β: privilege condition (see Equation 28)

α: Attitude indicator showing(see Equation 25)

Figure 2. Set theoretical view of trade union representation. See also Table 1

A: a set containing people belonging to a specific group; U: the set of all trade union members; W: the universal set containing the whole society; x: number of people belonging A but not affiliated with the trade union (see equation 2); y: number of trade union members who do not belong to A (see equation 3); z: number of trade union members who are belonging to A (see equation 1); r: number of people who neither belong to A nor affiliated with the trade union.

Figure 3. Changes in attractiveness of trade union representation — dotted line — as response to population changes: logic of exclusiveness. See also Table 1.

x: number of people belonging to a group A but not affiliated with the trade union (see equation 2); y: number of trade union members who do not belong to A (see equation 3); z: number of trade union members who are belonging to A (see equation 1); r: number of people who neither belong to A nor affiliated with the trade union.

Figure 4. Visualization space.

Figure 5. Gradual recruitment of trade union members from a single group. See also Table 1.

x: number of people belonging to a group A but not affiliated with the trade union (see equation 2); y: number of trade union members who do not belong to A (see equation 3); z: number of trade union members who are belonging to A (see equation 1); r: number of people who neither belong to A nor affiliated with the trade union.

Figure 6. Four basic indicators of the model. See also Table 1.

x: number of people belonging to the designated educational group but not affiliated with trade unions (see equation 2); y: number of trade union members who do not belong to the designated educational group (see equation 3); z: number of trade union members who are belonging to the designated educational group (see equation 1); r: number of people who neither belong to the designated educational group nor affiliated with trade unions.

Figure 7. Privilege condition (β) and union membership (z). See also Table 1, and Equations 1 and 28.

Figure 8. Movement of the attitude indicator (α) across groups and countries. See also Table 1 and Equation 25.

Figure 9. Movements of educational groups in the visualization space.

Table

	Germany
	low education		secondary education		tertiary education		union members	sample size
	member	not a member	member	not a member	member	not a member
2002	25	163	215	998	116	351	357	1868
2004	12	150	168	992	95	377	274	1793
2006	7	168	175	1066	53	317	234	1785
2008	26	165	171	886	79	387	276	1715
2010	19	240	210	1081	62	295	291	1906
2012	15	213	181	1035	74	345	270	1863
2014	10	173	222	1035	85	394	317	1918
	United Kingdom
	low education		secondary education		tertiary education
	member	not a member	member	not a member	member	not a member	union members	sample size
2002	130	562	42	183	155	312	326	1385
2004	106	566	43	171	83	201	232	1170
2006	79	555	35	184	231	499	345	1583
2008	73	479	47	190	207	553	327	1549
2010	50	413	141	549	103	233	294	1489
2012	46	309	108	507	85	234	240	1290
2014	41	299	133	436	114	289	288	1312
	Norway
	low education		secondary education		tertiary education
	member	not a member	member	not a member	member	not a member	union members	sample size
2002	51	87	462	432	300	160	814	1492
2004	83	120	286	290	329	178	698	1286
2006	57	95	248	354	300	216	605	1270
2008	35	78	234	319	288	172	557	1126
2010	42	100	235	289	246	164	523	1075
2012	42	112	299	293	304	132	645	1182
2014	34	96	227	249	249	129	510	984
	Spain
	low education		secondary education		tertiary education
	member	not a member	member	not a member	member	not a member	union members	sample size
2002	36	365	43	266	32	151	112	894
2004	51	377	28	199	31	214	110	901
2006	41	449	46	286	55	207	142	1083
2008	54	606	47	418	58	271	159	1454
2010	63	453	44	240	53	243	160	1097
2014	56	430	57	266	53	232	166	1094

Table

	Germany
	low education				secondary education				tertiary education
	z	x	y	r	z	x	y	r	z	x	y	r
2002	1.36	8.71	17.73	72.20	11.52	53.43	7.57	27.48	6.21	18.77	12.88	62.14
2004	0.66	8.38	14.64	76.32	9.36	55.29	5.94	29.41	5.28	21.03	10.02	63.67
2006	0.38	9.41	12.74	77.47	9.79	59.73	3.33	27.15	2.96	17.74	10.16	69.14
2008	1.52	9.60	14.60	74.28	9.99	51.69	6.13	32.19	4.60	22.59	11.52	61.29
2010	1.00	12.57	14.27	72.16	10.99	56.72	4.28	28.01	3.28	15.45	11.99	69.28
2012	0.82	11.45	13.66	74.07	9.70	55.54	4.78	29.98	3.97	18.53	10.51	66.99
2014	0.54	9.04	15.97	74.45	11.55	53.94	4.96	29.55	4.41	20.52	12.10	62.97
	United Kingdom
	low education				secondary education				tertiary education
	z	x	y	r	z	x	y	r	z	x	y	r
2002	9.38	40.62	14.19	35.81	3.02	13.24	20.55	63.19	11.17	22.57	12.40	53.86
2004	9.03	48.35	10.82	31.80	3.71	14.62	16.14	65.53	7.10	17.18	12.75	62.97
2006	4.99	35.08	16.82	43.11	2.24	11.62	19.57	66.57	14.58	31.49	7.23	46.70
2008	4.72	30.91	16.42	47.95	3.05	12.25	18.09	66.61	13.38	35.70	7.76	43.16
2010	3.34	27.72	16.38	52.56	9.45	36.89	10.27	43.39	6.93	15.67	12.79	64.61
2012	3.60	23.98	14.97	57.45	8.34	39.30	10.23	42.13	6.62	18.15	11.95	63.28
2014	3.13	22.82	18.82	55.23	10.12	33.21	11.83	44.84	8.70	22.01	13.25	56.04
	Norway
	low education				secondary education				tertiary education
	z	x	y	r	z	x	y	r	z	x	y	r
2002	3.45	5.80	51.09	39.66	30.99	28.95	23.55	16.51	20.11	10.70	34.43	34.76
2004	6.45	9.33	47.83	36.39	22.24	22.55	32.04	23.17	25.58	13.84	28.70	31.88
2006	4.49	7.48	43.15	44.88	19.53	27.87	28.11	24.49	23.62	17.01	24.02	35.35
2008	3.11	6.93	46.36	43.60	20.78	28.33	28.69	22.20	25.58	15.28	23.89	35.25
2010	3.95	9.30	44.66	42.09	21.82	26.83	26.79	24.56	22.85	15.26	25.76	36.13
2012	3.55	9.48	51.02	35.95	25.30	24.79	29.27	20.64	25.72	11.17	28.85	34.26
2014	3.46	9.76	48.37	38.41	23.07	25.31	28.76	22.86	25.31	13.11	26.52	35.06
	Spain
	low education				secondary education				tertiary education
	z	x	y	r	z	x	y	r	z	x	y	r
2002	4.07	40.81	8.41	46.71	4.87	29.80	7.61	57.72	3.54	16.92	8.94	70.60
2004	5.67	41.84	6.56	45.93	3.11	22.12	9.12	65.65	3.45	23.81	8.78	63.96
2006	3.78	41.45	9.29	45.48	4.25	26.40	8.82	60.53	5.04	19.07	8.03	67.86
2008	3.73	41.65	7.22	47.40	3.21	28.77	7.74	60.28	4.00	18.64	6.95	70.41
2010	5.76	41.29	8.84	44.11	4.02	21.91	10.58	63.49	4.82	22.20	9.78	63.20
2014	5.12	39.31	10.05	45.52	5.21	24.31	9.96	60.52	4.84	21.21	10.33	63.62