Presentation by Guillaume Touya at GIScience conference 2012

Transcript

1. S OCIAL W ELFARE TO A SSESS THE G LOBAL L EGIBILITY OF A G ENERALIZED M AP Guillaume Touya IGN France - COGIT GISciences 2012
2. P RESENTATION O UTLINE The Global Legibility of Generalized Maps Social Welfare Theories Proposition to Apply Social Welfare to Map Legibility Results Conclusion and Future Work 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 2
3. M AP G ENERALIZATION Symbolized for 1:50 000 Before generalization Initial data 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 3
4. M AP G ENERALIZATION Symbolized for 1:50 000 Before generalization After generalization Generalization Initial data 12.09.12 Global Legibility Social Welfare Map Proposition Results Conclusion 4
5. G LOBAL L EGIBILITY AND C ONSTRAINTS User map requirements Cartographic rules 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 5
6. G LOBAL L EGIBILITY AND C ONSTRAINTS User map requirements Generalization constraints Cartographic rules « Building area > 0.4 map mm² » « Building granularity > 0.1 map mm » « Building/road distance > 0.1 map mm » « Building alignments should be preserved » 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 6
7. G LOBAL L EGIBILITY AND C ONSTRAINTS User map requirements Generalization constraints Cartographic rules Constraints assessed by monitors (additional map features) (Ruas, 1999; Touya & Duchêne, 2011) « Building area > 0.4 map mm² » « Building granularity > 0.1 map mm » « Building/road distance > 0.1 map mm » « Building alignments should be preserved » 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 7
8. G LOBAL L EGIBILITY AND C ONSTRAINTS Map global legibility ⇔ monitors satisfaction distribution monitors nb 80 60 40 20 0 1 12.09.12 Global Legibility Social Welfare 2 Proposition 3 4 5 Results 6 7 8 satisfaction scale Conclusion 8
9. U SE C ASES Use Case 1: Final output map generalization initial data 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 9
10. U SE C ASES Use Case 1: Final output map generalization evaluated map initial data Generalization 1 Generalization 2 Perfect (8) 12.09.12 Global Legibility Medium (4) Social Welfare Unacceptable (1) Proposition Results Conclusion 10
11. U SE C ASES Use Case 1: Final output map generalization evaluated map initial data Generalization 1 Generalization 2 Perfect (8) 12.09.12 Global Legibility Medium (4) Social Welfare Unacceptable (1) Proposition Results Conclusion 11
12. U SE C ASES Use Case 1: Final output map generalization evaluated map initial data Generalization 1 Generalization 2 mean = 5.8 mean = 7.2 Perfect (8) 12.09.12 Global Legibility Medium (4) Social Welfare Unacceptable (1) Proposition Results Conclusion 12
13. U SE C ASES Use Case 2: Manual editing map generalization manual editing initial data 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 13
14. U SE C ASES Use Case 2: Manual editing map generalization manual editing initial data evaluated map 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 14
15. U SE C ASES Use Case 2: Manual editing map generalization manual editing initial data evaluated map Generalization (1) Generalization (2) perfect 12.09.12 Global Legibility Social Welfare medium unacceptable Proposition Results Conclusion 15
16. U SE C ASES Use Case 2: Manual editing map generalization manual editing initial data evaluated map Generalization (1) Generalization (2) mean = 5.9 mean = 5.8 perfect 12.09.12 Global Legibility Social Welfare medium unacceptable Proposition Results Conclusion 16
17. U SE C ASES Use Case 3: Iterative comparison map generalization initial data 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 17
18. U SE C ASES Use Case 3: Iterative comparison map generalization initial data evaluated map 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 18
19. U SE C ASES Use Case 3: Iterative comparison map generalization initial data evaluated map State i State i+1 perfect 12.09.12 Global Legibility Social Welfare medium unacceptable Proposition Results Conclusion 19
20. U SE C ASES Use Case 3: Iterative comparison map generalization initial data evaluated map State i State i+1 mean = 5.2 mean = 4.7 perfect 12.09.12 Global Legibility Social Welfare medium unacceptable Proposition Results Conclusion 20
21. O BJECTIVES 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) Find more accurate methods Try Social Welfare Theories? 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 21
22. The Global Legibility of Generalized Maps Social Welfare Theories Proposition to Apply Social Welfare to Map Legibility Results Conclusion and Future Work 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 22
23. S OCIAL W ELFARE T HEORIES Economical theory to assess societies collective welfare Better? 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 23
24. S OCIAL W ELFARE T HEORIES Economical theory to assess societies collective welfare Better? Mathematical working out where (ui) = (u1, u2, …, un) 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 24
25. S OCIAL W ELFARE T HEORIES Economical theory to assess societies collective welfare Better? Mathematical working out where (ui) = (u1, u2, …, un) 3 main point of views Utilitarian (Bentham, 1789) Egalitarian (Rawls, 1971) Mixes of utilitarism and egalitarism 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 25
26. S OCIAL W ELFARE O RDERING Social Welfare Orderings (SWOs) order populations ( ) n n i =1 i =1 Proposition Results SWOutilitarism : (ui ) f u 'i ⇔ ∑ ui > ∑ u 'i 12.09.12 Global Legibility Social Welfare Conclusion 26
27. S OCIAL W ELFARE O RDERING Social Welfare Orderings (SWOs) order populations ( ) n n i =1 i =1 SWOutilitarism : (ui ) f u 'i ⇔ ∑ ui > ∑ u 'i Collective Utility Functions (CUFs): a single value to assess collective welfare n CUFutilitarism = ∑ ui n i =1 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 27
28. A L IBRARY OF SWO S mean--based mean Utilitarian Social Welfare Orderings (ui ) f (u i ) ⇔ ∑ ui > ∑ u i n Standard utilitarism : n ' ' i =1 i =1 (ui ) f (u 'i ) ⇔ (∑ ui ) p > (∑ u n Powered utilitarism : n 1 p i =1 ' p i 1 ) p i =1 Example with 5 elements populations u 1 2 3 12.09.12 4 w v 5 6 7 8 Global Legibility 1 2 3 4 5 6 Social Welfare 7 8 1 2 3 Proposition 4 5 6 7 ufvfw 8 Results Conclusion 28
29. A L IBRARY OF SWO S Egalitarian Social Welfare Orderings minimum--based minimum (ui ) f (u 'i ) ⇔ min(ui ) > min(ui' ) Leximin egalitarism: ∃i / ui < poverty _ line Leximin with poverty line: leximin if else utilitarian Example with 5 elements populations u 1 2 3 4 5 poverty line 12.09.12 w v 6 7 8 1 2 3 4 5 6 poverty line Global Legibility Social Welfare 7 8 1 2 3 4 5 6 7 wfvfu 8 poverty line Proposition Results Conclusion 29
30. A L IBRARY OF SWO S Mixed Social Welfare Orderings (ui ) f (u 'i ) ⇔ ∏ ui > ∏ u 'i Nash welfare: n n i =1 i =1 (ui ) f (u 'i ) ⇔ ∑ ( w(ui ).ui ) > ∑ (w(u 'i ).u 'i ) Owa welfare: n n i =1 i =1 for w( x) : [1,8] a ℜ Example with 5 elements populations u 1 2 3 12.09.12 4 w v 5 6 7 8 Global Legibility 1 2 3 4 5 6 Social Welfare 7 8 1 2 3 Proposition 4 5 6 7 vf wfu 8 Results Conclusion 30
31. The Global Legibility of Generalized Maps Social Welfare Theories Proposition to Apply Social Welfare to Map Legibility Results Conclusion and Future Work 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 31
32. S OCIAL W ELFARE A NALOGY Social welfare individual ⇔ Constraint monitor Individual welfare ⇔ Constraint monitor satisfaction SWOs order several generalized outputs CUFs assess a generalized output legibility 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 32
33. S OCIAL W ELFARE A NALOGY Social welfare individual ⇔ Constraint monitor Individual welfare ⇔ Constraint monitor satisfaction SWOs order several generalized outputs 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 Global Legibility Social Welfare Proposition Results Conclusion 33
34. P ROPOSED M ETHODOLOGY 1 Build Toy Distributions 1 2 3 4 5 6 7 8 12345678 12345678 Nash SWO utilitarian SWO Leximin SWO Toy distributions (TD) SWOs library Use Use Use case 3 case 2 case 1 Use cases 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 34
35. P ROPOSED M ETHODOLOGY 1 2 Build Toy Distributions Translate use cases into TD preferences 1 2 3 4 5 6 7 8 12345678 12345678 Nash SWO utilitarian SWO Leximin SWO Toy distributions (TD) penalizes favors SWOs library Use Use Use case 3 case 2 case 1 Use cases 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 35
36. P ROPOSED M ETHODOLOGY 1 2 Build Toy Distributions Translate use cases into TD preferences 1 2 3 4 5 6 7 8 12345678 12345678 Nash SWO utilitarian SWO Leximin SWO Toy distributions (TD) SWOs library 3 Analyse SWOs vs TD Use Use Use case 3 case 2 case 1 Use cases 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 36
37. P ROPOSED M ETHODOLOGY 1 2 Build Toy Distributions Translate use cases into TD preferences 1 2 3 4 5 6 7 8 12345678 12345678 Nash SWO utilitarian SWO Leximin SWO Toy distributions (TD) use SWOs library 4 3 use Associate adapted SWOs to each use case Analyse SWOs vs TD Use Use Use case 3 case 2 case 1 Use cases 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 37
38. P ROPOSED M ETHODOLOGY 1 2 Build Toy Distributions Translate use cases into TD preferences 1 2 3 4 5 6 7 8 12345678 12345678 Nash SWO utilitarian SWO Leximin SWO Toy distributions (TD) SWOs library 4 3 Associate adapted SWOs to each use case Analyse SWOs vs TD Use Use Use case 3 case 2 case 1 Use cases 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 38
39. T OY D ISTRIBUTION TO A NALYSE SWO S 80 Diffuse very good Diffuse good Fair 60 40 20 0 1 12.09.12 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 Good Extreme medium Diffuse medium Medium 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 Medium good Symmetrical Extreme good Extreme very good 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 Global Legibility Social Welfare Proposition Results Conclusion 39
40. P ROPOSED M ETHODOLOGY 1 2 Build Toy Distributions Translate use cases into TD preferences 1 2 3 4 5 6 7 8 12345678 12345678 Nash SWO utilitarian SWO Leximin SWO Toy distributions (TD) SWOs library 4 3 Associate adapted SWOs to each use case Analyse SWOs vs TD Use Use Use case 3 case 2 case 1 Use cases 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 40
41. U SE C ASES T O T OY D ISTRIBUTIONS Final Output Use Case Generalization 1 Generalization 2 favor rather than Perfect (8) 12.09.12 Global Legibility Medium (4) Social Welfare Proposition Unacceptable (1) Results Conclusion 41
42. U SE C ASES T O T OY D ISTRIBUTIONS Final Output Use Case Diffuse very good 1 2 3 4 Good 5 6 7 8 1 2 3 4 5 6 7 8 Favor rather than Extreme medium Fair 1 12.09.12 2 3 Global Legibility 4 5 6 7 1 2 3 4 5 6 7 8 8 Social Welfare Proposition Results Conclusion 42
43. U SE C ASES T O T OY D ISTRIBUTIONS Manual Editing Use Case Generalization (1) Generalization (2) penalize favor perfect 12.09.12 Global Legibility Social Welfare medium unacceptable Proposition Results Conclusion 43
44. U SE C ASES T O T OY D ISTRIBUTIONS Manual Editing Use Case penalize Diffuse medium Medium 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 Good favor 1 12.09.12 Global Legibility Social Welfare 2 3 4 5 6 Proposition 7 8 Results Conclusion 44
45. U SE C ASES T O T OY D ISTRIBUTIONS Iterative Generalization Use Case State i State i+1 perfect 12.09.12 Global Legibility Social Welfare medium unacceptable Proposition Results Conclusion 45
46. U SE C ASES T O T OY D ISTRIBUTIONS Iterative Generalization Use Case Diffuse good Good favor rather than 1 2 3 4 5 6 7 8 1 2 3 4 6 7 8 7 8 Diffuse medium Medium good favor rather than 1 12.09.12 5 2 Global Legibility 3 4 5 6 7 8 Social Welfare 1 Proposition Results 2 3 4 5 6 Conclusion 46
47. P ROPOSED M ETHODOLOGY 1 2 Build Toy Distributions Translate use cases into TD preferences 1 2 3 4 5 6 7 8 12345678 12345678 Nash SWO utilitarian SWO Leximin SWO Toy distributions (TD) SWOs library 4 3 Associate adapted SWOs to each use case Analyse SWOs vs TD Use Use Use case 3 case 2 case 1 Use cases 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 47
48. L IBRARY SWO S A NALYSIS Variations in Toy Distributions ranking with Standard Utilitarism SWO utilitarian 12.09.12 0 8 Global Legibility 9 10 Social Welfare 1 2 Proposition 3 5 Results 4 Conclusion 6 7 48
49. L IBRARY SWO S A NALYSIS 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 Leximin with poverty line SWO favors medium toy distributions Leximin with poverty line SWO penalizes diffuse toy distributions 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 49
50. L IBRARY SWO S A NALYSIS 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 3 0 1 -1 4 -1 -3 -3 0 0 0 4 -5 -3 -5 -1 6 7 4 3 -5 -5 4 -3 -1 -3 -1 4 6 5 -2 -5 -4 Owa (4, 3, 2, 1, 1, 2, 3, 4) Owa (1, 1, 1, 4, 4, 1, 1, 1) Owa (3, 3, 3, 2, 2, 1, 1, 1) Different parameters tested for parameterizable SWOs 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 50
51. P ROPOSED M ETHODOLOGY 1 2 Build Toy Distributions Translate use cases into TD preferences 1 2 3 4 5 6 7 8 12345678 12345678 Nash SWO utilitarian SWO Leximin SWO Toy distributions (TD) SWOs library 4 3 Associate adapted SWOs to each use case Analyse SWOs vs TD Use Use Use case 3 case 2 case 1 Use cases 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 51
52. F IND SWO S A DAPTED TO U SE C ASES Final Output Use Case Owa SWO 12.09.12 Global Legibility satisfaction 1 2 3 4 5 6 7 8 weight 4 3 2 1 1 2 3 4 Social Welfare Proposition Results Conclusion 52
53. F IND SWO S A DAPTED TO U SE C ASES Final Output Use Case Owa SWO satisfaction 1 2 3 4 5 6 7 8 weight 4 3 2 1 1 2 3 4 Manual Editing Use Case Powered utilitarian SWO (power = 5) 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 53
54. F IND SWO S A DAPTED TO U SE C ASES Final Output Use Case Owa SWO satisfaction 1 2 3 4 5 6 7 8 weight 4 3 2 1 1 2 3 4 Manual Editing Use Case Powered utilitarian SWO (power = 5) Iterative Generalization Use Case Leximin with poverty line SWO (satisfaction = 3) 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 54
55. The Global Legibility of Generalized Maps Social Welfare Theories Proposition to Apply Social Welfare to Map Legibility Results Conclusion and Future Work 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 55
56. R ESULTS FOR U SE C ASE 1 Final output: 25 constraints ≈ 6800 constraint monitors initial data 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 56
57. R ESULTS FOR U SE C ASE 1 Final output ≈ 6800 constraint monitors utilitarian welfare CUF = 5.72 12.09.12 Global Legibility Social Welfare Owa welfare CUF = 5.23 Proposition Results Conclusion 57
58. R ESULTS FOR U SE C ASE 1 Final output ≈ 6800 constraint monitors Damage 100 monitors from medium to low satisfactions 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 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 58
59. R ESULTS FOR U SE C ASE 1 Final output ≈ 6800 constraint monitors Damage 100 monitors from high to medium satisfactions 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 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 59
60. R ESULTS FOR U SE C ASE 1 Final output ≈ 6800 constraint monitors 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 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 60
61. R ESULTS FOR U SE C ASE 2 Manual editing x x x x 1 after alternative process 1 12.09.12 Global Legibility Social Welfare x 2 after alternative process 2 Proposition Results Conclusion 61
62. R ESULTS FOR U SE C ASE 2 Manual editing x x x x 1 utilitarian welfare CUF = 5.70 powered utilitarian CUF = 5.73 12.09.12 Global Legibility Social Welfare x 2 utilitarian welfare CUF = 5.70 > powered utilitarian CUF = 5.68 Proposition Results Conclusion 62
63. R ESULTS FOR U SE C ASE 2 Manual editing x x x x 1 utilitarian welfare CUF = 5.70 powered utilitarian CUF = 5.73 x 2 utilitarian welfare CUF = 5.70 > powered utilitarian CUF = 5.68 chosen SWO better than mean 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 63
64. R ESULTS FOR U SE C ASE 3 Iterative comparison: 25 constraints & 14.000 monitors initial data 12.09.12 Global Legibility after alternative process 2 Social Welfare Proposition Results Conclusion 64
65. R ESULTS FOR U SE C ASE 3 Iterative comparison initial data after alternative process 1 (D1) after alternative process 2 (D2) (D3) negligible improvement from D1 significant improvement from D1 Utilitarian welfare : D2 and D3 are equal improvements Leximin with poverty line SWO: D2 is negligible & D3 is significant 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 65
66. R ESULTS FOR U SE C ASE 3 Iterative comparison initial data after alternative process 1 (D1) after alternative process 2 (D2) (D3) negligible improvement from D1 significant improvement from D1 Utilitarian welfare : D2 and D3 are equal improvements Leximin with poverty line SWO: D2 is negligible & D3 is significant chosen SWO better than mean 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 66
67. C ONCLUSION AND F UTURE W ORK Analogy Social Welfare / Generalized Map Legibility Social Welfare Orderings chosen for specific use cases Results show improvements compared to mean 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 67
68. C ONCLUSION AND F UTURE W ORK Analogy Social Welfare / Generalized Map Legibility Social Welfare Orderings chosen for specific use cases Results show improvements compared to mean Test additional use cases Apply to other problems: Geoportal global legibility (Stigmar & Harrie, 2011) Mapped VGI (e.g. OpentStreetMap derived maps) 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 68
69. T HANKS FOR YOUR ATTENTION A NY QUESTIONS ? Social Welfare to Assess the Global Legibility of a Generalized Map
70. L IBRARY SWO S A NALYSIS Variations in Toy Distributions ranking with Standard Utilitarism Evaluation Method VERY GOOD GOOD DIFFUSE DIFFUSE GOOD FAIR MEDIUM EXTREME VERY GOOD EXTREME MEDIUM MEDIUM SYMMETRI GOOD DIFFUSE MEDIUM GOOD CAL 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 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 Global Legibility Social Welfare Proposition Results Conclusion 70
71. R ESULTS FOR U SE C ASE 3 Iterative comparison initial data after alternative process 1 (D1) after alternative process 2 (D2) (D3) negligible improvement from D1 significantimprovement from D1 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) 12.09.12 Global Legibility Social Welfare Proposition Results Conclusion 71