Presentation by Guillaume Touya at GIScience conference 2012 of a method to assess the global legibility of a generalised map based on social welfare techniques.

1. SSSSOCIALOCIALOCIALOCIAL WWWWELFAREELFAREELFAREELFARE TOTOTOTO AAAASSESSSSESSSSESSSSESS
THETHETHETHE GGGGLOBALLOBALLOBALLOBAL LLLLEGIBILITYEGIBILITYEGIBILITYEGIBILITY OFOFOFOF AAAA
GGGGENERALIZEDENERALIZEDENERALIZEDENERALIZED MMMMAPAPAPAP
IGN France - COGIT
GISciences 2012
Guillaume Touya

2. PRESENTATION OUTLINE
The Global Legibility of Generalized Maps
Social Welfare Theories
Proposition to Apply Social Welfare to Map Legibility
Global Legibility Social Welfare Proposition Results Conclusion
Results
Conclusion and Future Work
12.09.12 2

3. MAP GENERALIZATION
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 3
Initial data
Symbolized for
1:50 000
Before
generalization

4. MAP GENERALIZATION
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 4
Initial data Map
Generalization
After
generalization
Symbolized for
1:50 000
Before
generalization

5. GLOBAL LEGIBILITY AND CONSTRAINTS
User map requirements
Cartographic rules
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 5

6. GLOBAL LEGIBILITY AND CONSTRAINTS
User map requirements
Cartographic rules
Generalization constraints
« Building area > 0.4 map mm² »
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 6
« Building area > 0.4 map mm² »
« Building granularity > 0.1 map mm »
« Building alignments should be preserved »
« Building/road distance > 0.1 map mm »

7. GLOBAL LEGIBILITY AND CONSTRAINTS
User map requirements
Cartographic rules
Constraints assessed by monitorsmonitors (additional map features)
(Ruas, 1999; Touya & Duchêne, 2011)
Generalization constraints
« Building area > 0.4 map mm² »
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 7
« Building area > 0.4 map mm² »
« Building granularity > 0.1 map mm »
« Building alignments should be preserved »
« Building/road distance > 0.1 map mm »

8. GLOBAL LEGIBILITY AND CONSTRAINTS
Map global legibility ⇔ monitors satisfaction distribution
60
80
monitors nb
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 8
0
20
40
1 2 3 4 5 6 7 8 satisfaction scale

9. USE CASES
Use Case 1: Final output
map generalization
initial data
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 9

10. USE CASES
Use Case 1: Final output
map generalization
initial data
evaluated map
Generalization 1 Generalization 2
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 10
Perfect (8) Medium (4) Unacceptable (1)
Generalization 1 Generalization 2

11. USE CASES
Use Case 1: Final output
map generalization
initial data
evaluated map
Generalization 1 Generalization 2
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 11
Perfect (8) Medium (4) Unacceptable (1)
Generalization 1 Generalization 2

12. USE CASES
Use Case 1: Final output
map generalization
initial data
evaluated map
Generalization 1 Generalization 2
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 12
Perfect (8) Medium (4) Unacceptable (1)
Generalization 1 Generalization 2
mean =
7.2
mean =
5.8

13. USE CASES
Use Case 2: Manual editing
map generalization
initial data
manual editing
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 13

14. USE CASES
Use Case 2: Manual editing
map generalization
initial data
manual editing
evaluated map
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 14

15. USE CASES
Use Case 2: Manual editing
map generalization
initial data
manual editing
evaluated map
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 15
perfect medium unacceptable
Generalization (1) Generalization (2)

16. USE CASES
Use Case 2: Manual editing
map generalization
initial data
manual editing
evaluated map
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 16
perfect medium unacceptable
Generalization (1) Generalization (2)
mean =
5.8
mean =
5.9

17. USE CASES
Use Case 3: Iterative comparison
map generalization
initial data
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 17

18. USE CASES
Use Case 3: Iterative comparison
map generalization
initial data
evaluated map
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 18
evaluated map

19. USE CASES
Use Case 3: Iterative comparison
map generalization
initial data
evaluated map
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 19
perfect medium unacceptable
State i+1State i

20. USE CASES
Use Case 3: Iterative comparison
map generalization
initial data
evaluated map
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 20
perfect medium unacceptable
State i+1State i
mean =
4.7
mean =
5.2

21. OBJECTIVES
The mean of satisfaction is not enough to accurately
assess global legibility
Previous research draw the same conclusion (Bard 2004,
Stöter et al 2010, Touya & Duchêne 2011)
Global Legibility Social Welfare Proposition Results Conclusion
Find more accurate methods
Try Social Welfare Theories?
12.09.12 21

22. The Global Legibility of Generalized Maps
Social Welfare Theories
Proposition to Apply Social Welfare to Map Legibility
Global Legibility Social Welfare Proposition Results Conclusion
Results
Conclusion and Future Work
12.09.12 22

23. SOCIAL WELFARE THEORIES
Economical theory to assess societies collective welfare
Better?
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 23

24. SOCIAL WELFARE THEORIES
Economical theory to assess societies collective welfare
Better?
Mathematical working out
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 24
where (ui) = (u1, u2, …, un)
Mathematical working out

25. SOCIAL WELFARE THEORIES
Economical theory to assess societies collective welfare
Better?
Mathematical working out
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 25
where (ui) = (u1, u2, …, un)
Mathematical working out
3 main point of views
Utilitarian (Bentham, 1789)
Egalitarian (Rawls, 1971)
Mixes of utilitarism and egalitarism

26. SOCIAL WELFARE ORDERING
Social Welfare Orderings (SWOs) order populations
( ) ( ) ∑∑ ==
>⇔
n
i
i
n
i
iiimutilitaris uuuuSWO
1
'
1
'
: f
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 26

27. SOCIAL WELFARE ORDERING
Social Welfare Orderings (SWOs) order populations
( ) ( ) ∑∑ ==
>⇔
n
i
i
n
i
iiimutilitaris uuuuSWO
1
'
1
'
: f
Global Legibility Social Welfare Proposition Results Conclusion
Collective Utility Functions (CUFs):
a single value to assess collective welfare
12.09.12 27
nuCUF
n
i
imutilitaris ∑=
=
1

28. A LIBRARY OF SWOS
Utilitarian Social Welfare Orderings meanmean--basedbased
( ) ( ) ∑∑ ==
>⇔
n
i
i
n
i
iii uuuu
1
'
1
'
fStandard utilitarism :
( )
nn
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 28
1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
u v w
wvu ff
Powered utilitarism : ( ) ( ) ∑∑ ==
>⇔
n
i
pp
i
p
n
i
p
iii uuuu
1
1
'
1
1
'
)()(f
Example with 5 elements populations

29. A LIBRARY OF SWOS
Egalitarian Social Welfare Orderings minimumminimum--basedbased
Leximin egalitarism: ( ) ( ) )min()min( ''
iiii uuuu >⇔f
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 29
1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
u v w
uvw ff
Example with 5 elements populations
Leximin with poverty line: leximin if
else utilitarian
linepovertyui i _/ <∃
poverty line poverty line poverty line

30. A LIBRARY OF SWOS
Mixed Social Welfare Orderings
( ) ( ) ∏∏ ==
>⇔
n
i
i
n
i
iii uuuu
1
'
1
'
fNash welfare:
( ) ( ) >⇔ ∑∑f )).(()).(( '''
uuwuuwuu
n
ii
n
iiii
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 30
1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
u v w
uwv ff
Example with 5 elements populations
Owa welfare:
( ) ( )
][ ℜ
>⇔ ∑∑ ==
a
f
8,1:)(
)).(()).((
11
xwfor
uuwuuwuu
i
ii
i
iiii

31. The Global Legibility of Generalized Maps
Social Welfare Theories
Proposition to Apply Social Welfare to Map Legibility
Global Legibility Social Welfare Proposition Results Conclusion
Results
Conclusion and Future Work
12.09.12 31

32. SOCIAL WELFARE ANALOGY
Social welfare individual ⇔ Constraint monitor
Individual welfare ⇔ Constraint monitor satisfaction
SWOs order several generalized outputs
CUFs assess a generalized output legibility
Global Legibility Social Welfare Proposition Results Conclusion
CUFs assess a generalized output legibility
12.09.12 32

33. SOCIAL WELFARE ANALOGY
Social welfare individual ⇔ Constraint monitor
Individual welfare ⇔ Constraint monitor satisfaction
SWOs order several generalized outputs
CUFs assess a generalized output legibility
Global Legibility Social Welfare Proposition Results Conclusion
CUFs assess a generalized output legibility
Other SWOs better than utilitarian SWO for the use cases?
What is the best suited SWO for each use case?
12.09.12 33

34. PROPOSED METHODOLOGY
Nash
SWOutilitarian
SWOLeximin
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
Toy distributions (TD)
Build Toy Distributions1
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 34
SWOLeximin
SWO
SWOs library
Toy distributions (TD)
Use
case 3
Use
case 2
Use
case 1
Use cases

35. 1 2 3 4 5 6 7 8
PROPOSED METHODOLOGY
Nash
SWOutilitarian
SWOLeximin
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
Toy distributions (TD)
Build Toy Distributions1
Translate use cases into TD preferences2
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 35
SWOLeximin
SWO
SWOs library
Toy distributions (TD)
Use
case 3
Use
case 2
Use
case 1
Use cases
favors
penalizes

36. 1 2 3 4 5 6 7 8
PROPOSED METHODOLOGY
Nash
SWOutilitarian
SWOLeximin
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
Toy distributions (TD)
Build Toy Distributions1
Translate use cases into TD preferences2
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 36
SWOLeximin
SWO
SWOs library
Toy distributions (TD)
Use
case 3
Use
case 2
Use
case 1
Use cases
Analyse SWOs vs TD3

37. 1 2 3 4 5 6 7 8
PROPOSED METHODOLOGY
Nash
SWOutilitarian
SWOLeximin
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
Toy distributions (TD)
Build Toy Distributions1
Translate use cases into TD preferences2
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 37
SWOLeximin
SWO
SWOs library
Toy distributions (TD)
Use
case 3
Use
case 2
Use
case 1
Use cases
Analyse SWOs vs TD3
Associate adapted SWOs to each use case4
use
use

38. 1 2 3 4 5 6 7 8
PROPOSED METHODOLOGY
Nash
SWOutilitarian
SWOLeximin
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
Toy distributions (TD)
Build Toy Distributions1
Translate use cases into TD preferences2
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 38
SWOLeximin
SWO
SWOs library
Toy distributions (TD)
Use
case 3
Use
case 2
Use
case 1
Use cases
Analyse SWOs vs TD3
Associate adapted SWOs to each use case4

39. TOY DISTRIBUTION TO ANALYSE SWOS
0
20
40
60
80
1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
Fair Diffuse
good
Diffuse very
good
Medium
Diffuse
medium
Extreme
medium
Good
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 39
1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
Extreme
very good
Extreme
good
SymmetricalMedium good
mediummedium

40. 1 2 3 4 5 6 7 8
PROPOSED METHODOLOGY
Nash
SWOutilitarian
SWOLeximin
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
Toy distributions (TD)
Build Toy Distributions1
Translate use cases into TD preferences2
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 40
SWOLeximin
SWO
SWOs library
Toy distributions (TD)
Use
case 3
Use
case 2
Use
case 1
Use cases
Analyse SWOs vs TD3
Associate adapted SWOs to each use case4

41. USE CASES TO TOY DISTRIBUTIONS
Final Output Use Case
Generalization 1 Generalization 2
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 41
Perfect (8) Medium (4) Unacceptable (1)
favor rather than

42. USE CASES TO TOY DISTRIBUTIONS
Final Output Use Case
Favor rather than
1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
Diffuse very
good Good
Global Legibility Social Welfare Proposition Results Conclusion
Favor rather than
12.09.12 42
1 2 3 4 5 6 7 8
Fair
1 2 3 4 5 6 7 8
Extreme
medium

43. USE CASES TO TOY DISTRIBUTIONS
Manual Editing Use Case
Generalization (1) Generalization (2)
favorpenalize
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 43
perfect medium unacceptable
favorpenalize

44. USE CASES TO TOY DISTRIBUTIONS
Manual Editing Use Case
penalize
1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
Medium
Diffuse
medium
Global Legibility Social Welfare Proposition Results Conclusion
favor
12.09.12 44
1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
Good

45. USE CASES TO TOY DISTRIBUTIONS
Iterative Generalization Use Case
State i+1State i
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 45
perfect medium unacceptable

46. USE CASES TO TOY DISTRIBUTIONS
Iterative Generalization Use Case
favor rather than
1 2 3 4 5 6 7 81 2 3 4 5 6 7 8
Diffuse
good
Good
Global Legibility Social Welfare Proposition Results Conclusion
favor rather than
12.09.12 46
1 2 3 4 5 6 7 81 2 3 4 5 6 7 8
Medium good Diffuse
medium

47. 1 2 3 4 5 6 7 8
PROPOSED METHODOLOGY
Nash
SWOutilitarian
SWOLeximin
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
Toy distributions (TD)
Build Toy Distributions1
Translate use cases into TD preferences2
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 47
SWOLeximin
SWO
SWOs library
Toy distributions (TD)
Use
case 3
Use
case 2
Use
case 1
Use cases
Analyse SWOs vs TD3
Associate adapted SWOs to each use case4

48. LIBRARY SWOS ANALYSIS
Variations in Toy Distributions ranking with Standard Utilitarism
SWO
utilitarian 0 8 9 10 1 2 3 5 4 6 7
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 48

49. LIBRARY SWOS ANALYSIS
Variations in Toy Distributions ranking with Standard Utilitarism
SWO
utilitarian 0 8 9 10 1 2 3 5 4 6 7
leximin with
poverty line
4 -3 0 0 -1 4 4 3 -3 -3 -5
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 49
Leximin with poverty line SWO favors medium toy distributions
Leximin with poverty line SWO penalizes diffuse toy distributions

50. LIBRARY SWOS ANALYSIS
Variations in Toy Distributions ranking with Standard Utilitarism
SWO
utilitarian 0 8 9 10 1 2 3 5 4 6 7
leximin with
poverty line
4 -3 0 0 -1 4 4 3 -3 -3 -5
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 50
Owa
(4, 3, 2, 1, 1, 2, 3, 4)
3 0 1 -1 4 -1 -3 -3 0 0 0
Owa
(1, 1, 1, 4, 4, 1, 1, 1)
4 -5 -3 -5 -1 6 7 4 3 -5 -5
Owa
(3, 3, 3, 2, 2, 1, 1, 1)
4 -3 -1 -3 -1 4 6 5 -2 -5 -4
Different parameters tested for parameterizable SWOs

51. 1 2 3 4 5 6 7 8
PROPOSED METHODOLOGY
Nash
SWOutilitarian
SWOLeximin
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
Toy distributions (TD)
Build Toy Distributions1
Translate use cases into TD preferences2
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 51
SWOLeximin
SWO
SWOs library
Toy distributions (TD)
Use
case 3
Use
case 2
Use
case 1
Use cases
Analyse SWOs vs TD3
Associate adapted SWOs to each use case4

52. FIND SWOS ADAPTED TO USE CASES
Final Output Use Case
Owa SWO
satisfaction 1 2 3 4 5 6 7 8
weight 4 3 2 1 1 2 3 4
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 52

53. FIND SWOS ADAPTED TO USE CASES
Final Output Use Case
Owa SWO
Manual Editing Use Case
Powered utilitarian SWO (power = 5)
satisfaction 1 2 3 4 5 6 7 8
weight 4 3 2 1 1 2 3 4
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 53
Powered utilitarian SWO (power = 5)

54. FIND SWOS ADAPTED TO USE CASES
Final Output Use Case
Owa SWO
Manual Editing Use Case
Powered utilitarian SWO (power = 5)
satisfaction 1 2 3 4 5 6 7 8
weight 4 3 2 1 1 2 3 4
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 54
Powered utilitarian SWO (power = 5)
Iterative Generalization Use Case
Leximin with poverty line SWO (satisfaction = 3)

55. The Global Legibility of Generalized Maps
Social Welfare Theories
Proposition to Apply Social Welfare to Map Legibility
Global Legibility Social Welfare Proposition Results Conclusion
Results
Conclusion and Future Work
12.09.12 55

56. RESULTS FOR USE CASE 1
Final output: 25 constraints ≈ 6800 constraint monitors
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 56
initial data

57. RESULTS FOR USE CASE 1
Final output ≈ 6800 constraint monitors
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 57
utilitarian welfare CUF = 5.72 Owa welfare CUF = 5.23

58. RESULTS FOR USE CASE 1
Final output ≈ 6800 constraint monitors
Damage 100 monitors
from medium to low
satisfactions
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 58
utilitarian welfare CUF = 5.72 Owa welfare CUF = 5.23
utilitarian welfare CUF = 5.26 Owa welfare CUF = 5.11
Owa welfare is less sensitive to such variations

59. RESULTS FOR USE CASE 1
Final output ≈ 6800 constraint monitors
Damage 100 monitors
from high to medium
satisfactions
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 59
utilitarian welfare CUF = 5.72 Owa welfare CUF = 5.23
utilitarian welfare CUF = 5.26 Owa welfare CUF = 5.11
utilitarian welfare CUF = 5.35 Owa welfare CUF = 4.36
Owa welfare is more sensitive to such variations

60. RESULTS FOR USE CASE 1
Final output ≈ 6800 constraint monitors
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 60
utilitarian welfare CUF = 5.72 Owa welfare CUF = 5.23
utilitarian welfare CUF = 5.26 Owa welfare CUF = 5.11
utilitarian welfare CUF = 5.35 Owa welfare CUF = 4.36
chosen SWO better than mean

61. RESULTS FOR USE CASE 2
Manual editing
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 61
1 2
x
x
x
xx
after alternative process 2after alternative process 1

62. RESULTS FOR USE CASE 2
Manual editing
1 2
x
x
x
xx
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 62
1 2x
utilitarian welfare CUF = 5.70
powered utilitarian CUF = 5.73
utilitarian welfare CUF = 5.70
powered utilitarian CUF = 5.68>

63. RESULTS FOR USE CASE 2
Manual editing
1 2
x
x
x
xx
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 63
1 2x
utilitarian welfare CUF = 5.70
powered utilitarian CUF = 5.73
utilitarian welfare CUF = 5.70
powered utilitarian CUF = 5.68>
chosen SWO better than mean

64. RESULTS FOR USE CASE 3
Iterative comparison: 25 constraints & 14.000 monitors
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 64
initial data after alternative process 2

65. RESULTS FOR USE CASE 3
Iterative comparison
(D1) (D2) (D3)
initial data after alternative process 2after alternative process 1
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 65
Utilitarian welfare : D2 and D3 are equal improvements
negligible improvement from D1 significant improvement from D1
Leximin with poverty line SWO: D2 is negligible & D3 is significant

66. RESULTS FOR USE CASE 3
Iterative comparison
(D1) (D2) (D3)
initial data after alternative process 2after alternative process 1
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 66
Utilitarian welfare : D2 and D3 are equal improvements
Leximin with poverty line SWO: D2 is negligible & D3 is significant
negligible improvement from D1 significant improvement from D1
chosen SWO better than mean

67. CONCLUSION AND FUTURE WORK
Analogy Social Welfare / Generalized Map Legibility
Social Welfare Orderings chosen for specific use cases
Results show improvements compared to mean
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 67

68. CONCLUSION AND FUTURE WORK
Analogy Social Welfare / Generalized Map Legibility
Social Welfare Orderings chosen for specific use cases
Results show improvements compared to mean
Test additional use cases
Global Legibility Social Welfare Proposition Results Conclusion
Test additional use cases
Apply to other problems:
Geoportal global legibility (Stigmar & Harrie, 2011)
Mapped VGI (e.g. OpentStreetMap derived maps)
12.09.12 68

69. THANKS FOR YOUR ATTENTION
A ?ANY QUESTIONS?
Social Welfare to Assess the Global
Legibility of a Generalized Map

70. LIBRARY SWOS ANALYSIS
Evaluation Method FAIR
GOOD
DIFFUSE
VERY
GOOD
DIFFUSE GOOD
MEDIUM
EXTREME
MEDIUM
DIFFUSE MEDIUM
MEDIUM
GOOD
SYMMETRI
CAL
GOOD
EXTREME
VERY
GOOD
EXTREME
StandardUtilitarianMethod 0 8 9 10 1 2 3 5 4 6 7
PoweredUtilitarianMethod (5.0) 2 0 1 -1 4 -1 -3 -2 0 0 0
LeximinPovertyLine (3.0) 4 -3 0 0 -1 4 4 3 -3 -3 -5
WeakPovertyMean (2.0, 6.0) 4 -3 0 0 -1 4 4 3 -3 -4 -4
Variations in Toy Distributions ranking with Standard Utilitarism
Global Legibility Social Welfare Proposition Results Conclusion
OwaWelfare (4, 3, 2, 1, 1, 2, 3, 4) 3 0 1 -1 4 -1 -3 -3 0 0 0
OwaWelfare (1, 1, 1, 4, 4, 1, 1, 1) 4 -5 -3 -5 -1 6 7 4 3 -5 -5
OwaWelfare (3, 3, 3, 2, 2, 1, 1, 1) 4 -3 -1 -3 -1 4 6 5 -2 -5 -4
IsoElasticMethod (30.0) 2 -3 0 0 -1 4 4 3 -3 -3 -3
IsoElasticMethod (0.5) 2 0 0 0 -1 2 3 2 -3 -3 -2
IsoElasticMethod (0.2) 2 0 0 0 -1 1 1 1 -3 -1 0
NashWelfare 2 0 0 0 -1 3 3 2 -3 -3 -3
BernoulliNashWelfare 4 0 0 0 -1 3 3 2 -3 -4 -4
AtkinsonWelfare (0.2) 4 0 0 0 -1 3 3 2 -3 -4 -4
AtkinsonWelfare (-10.0) 2 -3 0 0 -1 4 4 3 -3 -3 -3
12.09.12 70

71. RESULTS FOR USE CASE 3
Iterative comparison
(D1) (D2) (D3)
initial data after alternative process 2after alternative process 1
Global Legibility Social Welfare Proposition Results Conclusion12.09.12 71
utilitarian welfare : D2 and D3 are equal improvements (+0.6 to the mean)
Leximin with poverty line SWO: D2 is negligible (2.4% decrease of unsatisfied monitors)
D3 is significant (6.9% decrease)
negligible improvement from D1 significantimprovement from D1