ictsa programming contest 2009 legal cheating in elections

ICTSA Programming Contest 2009Legal Cheating in Elections

Gordon Pace

Claudia Borg

Chris Porter

Legal Cheating

District boundary manipulation to give an unfair advantage, or gerrymandering has a long history… 1812: Governor Elbridge Gerry in Massachusetts drew up a

district so distorted geographically, that it was likened to a salamander – ‘better call it a gerrymander’ someone commented!

Legal Cheating

Legal Cheating

Gerrymandering works through the wasted vote effect. Why do we not use a more effective electoral system?

Arrow’s impossibility theorem from 1951 demonstrates that no voting system can convert individual rankings into a global one – there can be no fair election system.

An Example

An ExampleWest Gozo

PX=80PY=100

East GozoPX=120PY=190

CirkewwaPX=60PY=50

St Paul’sPX=70PY=90

MostaPX=100PY=150

RabatPX=120PY=140

VallettaPX=240PY=100

MarsaxlokkPX=100PY=50

ZurrieqPX=210PY=100

An ExamplePX elects 7

Variance = 255


Variance = 147


Variance = 141

The Programming Task

Given: A set of villages Connections between villages Expected voting preferences in each village for

the two parties PX and PY Number of districts to have

To return in less than 5 minutes: A district partitioning such that districts are

connected components

The Programming Task

A good partition is one which: Maximises the number of seats il-Partit tax-

Xurbana (PX) elects; and Minimises the differences in populations across

districts. Ideally there would have been:

A bound on the difference between district populations;

A bound on the distance between villages in a single district.

How to Solve It

The problem can be shown to be NP-complete (eg via the Knapsack problem).

A brute-force solution will only work for small instances.

Larger problems require the use of some search heuristic.

The Teams

5. Eat Your Apple! • David Bailey • Andrew Calleja • Alan Cassar • Stephen Fenech

6. dot • Marco Muscat • Joseph Borg

7. HND4 • Norbert DeBono • Matthew Xuereb • Andrew Vella

8. CG • Andrew Said

9. Village People • Darren Demicoli

1. Beeef • Alessio Magro • Reuben Bartolo • Jonathan Caruana

2. Unicus • Gianluca Valentino

3. WM • James Scicluna • Kevin Falzon • Ingram Bondin • Andrew Gauci

4. iLike • Andrew Borg Cardona • Michael Debono

The Teams Solutions: Beeef

Genetic Algorithm: using only selection and mutation (cross-over did not give better results).

Chromosome representation: consist of a list of districts, which in turn are composed of a list of villages.

Creation: ensures that: All the villages in a district must belong to the same `island'. Districts must be connected.

Mutation: works by selecting two districts at random and swapping two villages across: The two districts must belong to the same `island'. Check that connectivity is not lost by the addition or the removal.

Fitness function: Number of PX members elected, variance. Termination: upon convergence.

The Teams Solutions: Unicus

Heuristic based: The generator worked as follows, repeating as necessary. Repeat a number of times:

Identified the village where PX has the largest majority and population and place in District 1.

Identified the village with the largest PY majority and second largest population, and the village with the second largest PX majority and 3rd largest population, both of which had to be connected to each other, and placed them in District 2.

Create a district with the villages with the largest PX and PY majority, and repeat to use up the remaining villages. Repeat this process for all permutations.

Programmed in C using .NET 2.0

The Teams Solutions: WM

Special case scenarios, a brute-force search and a Montecarlo method were implemented one of which is chosen depending on the problem given.

For non-special cases, a measure of the complexity of the graph is estimated and depending on this one of the solutions is chosen based on benchmarking. Approach 1: Fully enumerative approach, resembling

brute force, but with immediate pruning of some impossible candidate solutions

Approach 2: An adaptive Montecarlo based approach with generation of results through analysis of the given accident space and appropriate ranking of resulting candidate solutions

A timer ensures a solution in the allotted 5 minutes.

The Teams Solutions: iLike

Random search: A modified Monte Carlo method, taking features from genetic algorithms

Chromosome: District configurations Random generation: Generates random distribution

of villages (randomising villages, and placing random separators), and checked for validity

Selection: Fitness: More elected PX MPs or better variance is preferred. Validity: Checked later for performance reasons

Stopping criteria: 100 generations or reaching a long enough plateau (dependant on size of the problem)

The Teams Solutions: Eat Your Apple! Preprocessing:

Split the country into separate islands Each island (based on its population) is assigned a number of

districts to be allocated within it. Phase 1: Clustering Algorithm

On each island a clustering algorithm groups villages into districts such that the number of elected PX candidates is maximized.

Starts off a random village, and adds others clustered around the initial village.

Phase 2: Genetic Algorithm A genetic algorithm is applied on the output of the clustering

algorithm to generate fitter solutions Fitness function was global maximization of PX candidate count

and a globally minimized PY candidate count. Assigning more weight to the PX count gave better results.

The Teams Solutions: . (dot, tikka) Preprocessing: Splits the problem into

'islands' to support disconnected nodes.

Genetic algorithm Generation: using random starting village and

generate a connected district with a modified BFS search.

Fitness function: Number of PX members elected and variance

The Teams Solutions: HND4

Developed using C# on .NET framework 2.0 Preprocessing: Separate into different

islands. Heuristic search:

Grouping villages where PY dominates and group them in one district if possible

If more districts are still required PX dominant districts are divided into smaller ones.

The Teams Solutions: CG

Calculate all possible district sizes For each possible combination of sizes:

A district is created starting from a village and proceeding in a BFS manner.

Try to create the remaining districts ensuring no overlap. Remember the best solution found.

Would have liked to add: Heuristics to merge villages in a pre-analysis phase eg PY-

strong villages close to each other. Use a timer to ensure giving results on time.

The Teams Solutions: Village People Genetic algorithm coded in C Chromosome representation: partitions with

connected villages Crossover: injects a district into the chromosone Mutation: randomly assigns a village to a district Genetic repair: is used to ensure that the partitions

are still valid Fitness function: Sum of the ratio of members

elected of party X against party Y, and the inverse of the variance.

The Test Problems

Set of properties specified for 17 fictitious countries.

Each village has: 300 ≤ Voters ≤ 500

Generated randomly before the contest The ratio between the votes for the parties PX:PY was

allowed to could range between 20:80 and 80:20 Generated randomly before the contest

A number of regular map layouts were used.

The number of district was chosen so as to ensure an average of 4 villages per district.

The Test Problems

8 grid countries: 3x3 to 10x10

Asgvvjfcne Szoxxldneo Lltrdabguo

Lczktvafoj Moawloiblf Tgxgmzcaqw

Ciioesvamf Kazucjrgqf Hmxfstqddp

198,264 175,144 220,91

129,187 267,144 218,179

187,120 232,232 354,106

The Test Problems

3 full-mesh grid countries: 3x3, 7x7, 10x10

Asgvvjfcne Szoxxldneo Lltrdabguo

Lczktvafoj Moawloiblf Tgxgmzcaqw

Ciioesvamf Kazucjrgqf Hmxfstqddp

198,264 175,144 220,91

129,187 267,144 218,179

187,120 232,232 354,106

The Test Problems

3 circular countries with 10, 20 and 50 villages

AsgvvjfcneSzoxxldneo

Lczktvafoj

Ciioesvamf

198,264175,144

129,187

187,120

Lvjanqoway

Vvjzivqcmq

Xasfeuqsyp

165,309

Yisfhxnfvz

Imutautvmw

168,156

84,266

Wdyvaxlzyb

214,285

200,227

174,190

The Test Problems

3 circular countries with a hub sizes 10, 20 and 50

AsgvvjfcneSzoxxldneo

Lczktvafoj

Ciioesvamf

198,264175,144

129,187

187,120

Lvjanqoway

Vvjzivqcmq

Xasfeuqsyp

165,309

Yisfhxnfvz

Imutautvmw

168,156

84,266

Wdyvaxlzyb

214,285

200,227

174,190

Dastautvmw

74,263

The Test Problem

The biggest problem of them all

The Test Problem

The biggest problem of them all

Malta

The Test Problem: Malta

The Test Problem: Malta

An example from real-life: Malta 69 villages Connectivity based on geographical proximity Vote distribution based on the results of the last

local elections (2006 – 2008)1

13 districts

1taken from http://www.maltadata.com/tr-count1.htm

The Results: Grids [3x3]

Beeef Unicus WM iLikeEat

Your Apple!

Dot HND4 CGVillage People

3x311

829.54

N/A 11

829.54

11

1081.46

11

1081.46

11

829.54

8

860.24

11

829.54

11

829.54



Your Apple!


3x311

829.54

N/A 11

829.54

11

1081.46

11

1081.46

11

826.54

8

860.24

11

829.54

11

829.54

4x413

743.72

N/A 15

2126.26

14

2045.46

14

1855.38

14

1201.70

10

1246.64

14

1385.91

14

1557.84



Your Apple!


3x311

829.54

N/A 11

829.54

11

1081.46

11

1081.46

11

826.54

8

860.24

11

829.54

11

829.54

4x413

743.72

N/A 15

2126.26

14

2045.46

14

1855.38

14

1201.70

10

1246.64

14

1385.91

14

1557.84

5x520

628.31

N/A 24

2462.99

23

2346.45

21

1759.58

21

488.39

22

1644.56

TIME-OUT

22

2086.26



Your Apple!


3x311

829.54

N/A 11

829.54

11

1081.46

11

1081.46

11

826.54

8

860.24

11

829.54

11

829.54

4x413

743.72

N/A 15

2126.26

14

2045.46

14

1855.38

14

1201.70

10

1246.64

14

1385.91

14

1557.84

5x520

628.31

N/A 24

2462.99

23

2346.45

21

1759.58

21

488.39

22

1644.56

TIME-OUT

22

2086.26

6x6IN-VALID

N/A 33

3182.35

TIME-OUT

32

2932.91

30

545.97

23

3596.41

TIME-OUT

29

1583.77



Your Apple!


3x311

829.54

N/A 11

829.54

11

1081.46

11

1081.46

11

826.54

8

860.24

11

829.54

11

829.54

4x413

743.72

N/A 15

2126.26

14

2045.46

14

1855.38

14

1201.70

10

1246.64

14

1385.91

14

1557.84

5x520

628.31

N/A 24

2462.99

23

2346.45

21

1759.58

21

488.39

22

1644.56

TIME-OUT

22

2086.26

6x6IN-VALID

N/A 33

3182.35

TIME-OUT

32

2932.91

30

545.97

23

3596.41

TIME-OUT

29

1583.77

7x7IN-VALID

N/A 43

1670.34

TIME-OUT

TIME-OUT

42

1158.84

30

2862.67

TIME-OUT

39

2655.99



Your Apple!


3x311

829.54

N/A 11

829.54

11

1081.46

11

1081.46

11

826.54

8

860.24

11

829.54

11

829.54

4x413

743.72

N/A 15

2126.26

14

2045.46

14

1855.38

14

1201.70

10

1246.64

14

1385.91

14

1557.84

5x520

628.31

N/A 24

2462.99

23

2346.45

21

1759.58

21

488.39

22

1644.56

TIME-OUT

22

2086.26

6x6IN-VALID

N/A 33

3182.35

TIME-OUT

32

2932.91

30

545.97

23

3596.41

TIME-OUT

29

1583.77

7x7IN-VALID

N/A 43

1670.34

TIME-OUT

TIME-OUT

42

1158.84

30

2862.67

TIME-OUT

39

2655.99

8x845

1286.76

N/A 51

3200.13

TIME-OUT

TIME-OUT

47

759.37

41

3921.77

TIME-OUT

IN-VALID



Your Apple!


3x311

829.54

N/A 11

829.54

11

1081.46

11

1081.46

11

826.54

8

860.24

11

829.54

11

829.54

4x413

743.72

N/A 15

2126.26

14

2045.46

14

1855.38

14

1201.70

10

1246.64

14

1385.91

14

1557.84

5x520

628.31

N/A 24

2462.99

23

2346.45

21

1759.58

21

488.39

22

1644.56

TIME-OUT

22

2086.26

6x6IN-VALID

N/A 33

3182.35

TIME-OUT

32

2932.91

30

545.97

23

3596.41

TIME-OUT

29

1583.77

7x7IN-VALID

N/A 43

1670.34

TIME-OUT

TIME-OUT

42

1158.84

30

2862.67

TIME-OUT

39

2655.99

8x845

1286.76

N/A 51

3200.13

TIME-OUT

TIME-OUT

47

759.37

41

3921.77

TIME-OUT

IN-VALID

9x958

921.59

N/A 64

2627.06

TIME-OUT

TIME-OUT

61

647.30

51

3848.34

TIME-OUT

IN-VALID



Your Apple!


3x311

829.54

N/A 11

829.54

11

1081.46

11

1081.46

11

826.54

8

860.24

11

829.54

11

829.54

4x413

743.72

N/A 15

2126.26

14

2045.46

14

1855.38

14

1201.70

10

1246.64

14

1385.91

14

1557.84

5x520

628.31

N/A 24

2462.99

23

2346.45

21

1759.58

21

488.39

22

1644.56

TIME-OUT

22

2086.26

6x6IN-VALID

N/A 33

3182.35

TIME-OUT

32

2932.91

30

545.97

23

3596.41

TIME-OUT

29

1583.77

7x7IN-VALID

N/A 43

1670.34

TIME-OUT

TIME-OUT

42

1158.84

30

2862.67

TIME-OUT

39

2655.99

8x845

1286.76

N/A 51

3200.13

TIME-OUT

TIME-OUT

47

759.37

41

3921.77

TIME-OUT

IN-VALID

9x958

921.59

N/A 64

2627.06

TIME-OUT

TIME-OUT

61

647.30

51

3848.34

TIME-OUT

IN-VALID

10x1071

1477.11

N/A 77

3028.64

TIME-OUT

TIME-OUT

77

884.98

74

4552.36

TIME-OUT

73

2022.64

The Results: Grids+Diagonal [3x3]


Your Apple!


3x37

645.46

N/A 7

643.58

7

646.30

7

1258.76

6

36.40

5

1163.59

7

719.40

7

645.46



Your Apple!


3x37

645.46

N/A 7

643.58

7

646.30

7

1258.76

6

36.40

5

1163.59

7

719.40

7

645.46

7x735

895.96

N/A 42

2153.71

TIME-OUT

TIME-OUT

40

1111.75

45

3749.09

TIME-OUT

39

2693.27



Your Apple!


3x37

645.46

N/A 7

643.58

7

646.30

7

1258.76

6

36.40

5

1163.59

7

719.40

7

645.46

7x735

895.96

N/A 42

2153.71

TIME-OUT

TIME-OUT

40

1111.75

45

3749.09

TIME-OUT

39

2693.27

10x1070

1352.75

N/A 75

4132.35

TIME-OUT

TIME-OUT

72

477.99

82

5560.82

TIME-OUT

69

1917.86

The Results: Wheels – 10 Villages


Your Apple!


108

235.65

N/A 8

235.65

8

235.65

8

1084.11

8

235.65

7

1071.86

8

235.65

8

235.65



Your Apple!


108

235.65

N/A 8

235.65

8

235.65

8

1084.11

8

235.65

7

1071.86

8

235.65

8

235.65

2015

1042.78

N/A 16

2066.65

TIME-OUT

14

1972.18

15

983.30

13

898.80

16

1336.61

15

1164.74



Your Apple!


108

235.65

N/A 8

235.65

8

235.65

8

1084.11

8

235.65

7

1071.86

8

235.65

8

235.65

2015

1042.78

N/A 16

2066.65

TIME-OUT

14

1972.18

15

983.30

13

898.80

16

1336.61

15

1164.74

5037

1021.30

N/A 39

1876.99

TIME-OUT

TIME-OUT

39

703.74

35

2748.83

TIME-OUT

IN-VALID

The Results: Wheels+Hub: 10 Villages


Your Apple!


109

1323.17

N/A 9

839.56

9

1086.27

9

1347.51

8

261.67

9

1323.17

9

839.56

9

1323.17



Your Apple!


109

1323.17

N/A 9

839.56

9

1086.27

9

1347.51

8

261.67

9

1323.17

9

839.56

9

1323.17

2015

2000.66

N/A 16

2475.86

14

2404.72

14

2064.76

15

938.33

11

1826.32

16

1519.45

15

2213.36



Your Apple!


109

1323.17

N/A 9

839.56

9

1086.27

9

1347.51

8

261.67

9

1323.17

9

839.56

9

1323.17

2015

2000.66

N/A 16

2475.86

14

2404.72

14

2064.76

15

938.33

11

1826.32

16

1519.45

15

2213.36

5036

3073.85

N/A 40

3716.95

TIME-OUT

TIME-OUT

37

1250.92

43

3851.62

TIME-OUT

37

2533.44

The Results: Malta

Beeef Unicus WM iLikeEat Your Apple!


Malta43

16553.87

N/A 35

35562.72

TIME-OUT

TIME-OUT

47

21847.33

28

53259.60

TIME-OUT

42

12016.04

The Scores

Team Score

Unicus No submission

The Scores

Team Score

Eat Your Apple 35


The Scores

Team Score

iLike 110

Eat Your Apple 35


The Scores

Team Score

Village People 205

iLike 110

Eat Your Apple 35


The Scores

Team Score

HND4 250

Village People 205

iLike 110

Eat Your Apple 35


The Scores

Team Score

Beeef 275

CG 275

HND4 250

Village People 205

iLike 110

Eat Your Apple 35


The Scores

Team Score

dot 495

Beeef 275

CG 275

HND4 250

Village People 205

iLike 110

Eat Your Apple 35


The Scores

Team ScoreWM 720

dot 495

Beeef 275

CG 275

HND4 250

Village People 205

iLike 110

Eat Your Apple 35


An Observation

Interesting result: One team managed to elect 47 members of parliament in

Malta out of 65! (PX=PL) Switching parties (not part of the contest) resulted in

another layout electing 43 members for the other party. (PX=PN)

In practice variance should be given more importance so as not to be accused of breach of the Constitution of Malta 61(4): “the number obtained by dividing the total electorate in the

division by the number of members to be returned to the House of Representatives from that division is as nearly equal to the electoral quota as is reasonably practicable”

Prosit tal-Programmi!

The password of the test suite was the first line of the Brikkuni song Il-Bar ta’ Taħt il-Knisja:

Fil-bar ta’ taħt il-knisja jonxru ħwejjeġ tal-mistħija u smajt li bintek tgħidx kemm tħobb tintelaq hemm

ictsa programming contest 2009 legal cheating in elections

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