Vermont District Races (00031)

This dataset contains votes for 15 different races for various public offices held in Vermont in 2014. This data was collected and donated by Jeremy A Hansen. There are 3 to 6 candidates and 532 to 1960 voters in these data files. Not all races were competitive so not every race is reported for every district.

Required citations: Jeremy A. Hansen. Ballot-Level Observations About Vermont's 2014 General Election. New England Journal of Political Science 8 (2): 185-217, 2016 (Bibtex).

Download the dataset [zip, 7.2 KB]

Details

Election Politics

Number of files: 15
Total size: 9.2 KB
Data types: toc.
Publication date: April 13, 2017
Last modification: July 4, 2023

East Montpelier Vermont Assistant Judge — 00031-00000001.toc

1094 Voters, 3 Alternatives

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General Properties
Number of alternatives	3
Number of voters	1094
Number of unique preferences	7
Ballot Structure
Size of the smallest ballot	3
Size of the largest ballot	3
Minimum number of indifferences	1
Maximum number of indifferences	1
Size of the smallest indifference	1
Size of the largest indifference	3
Preference Structure
Strict orders	✗
Complete orders	✓
Approval profile	✓
Aggregtated Structure
Condorcet winner	✓

Preview of the File
1	# FILE NAME: 00031-00000001.toc
2	# TITLE: East Montpelier Vermont Assistant Judge
3	# DESCRIPTION:
4	# DATA TYPE: toc
5	# MODIFICATION TYPE: original
6	# RELATES TO:
7	# RELATED FILES:
8	# PUBLICATION DATE: 2017-04-13
9	# MODIFICATION DATE: 2022-09-16
10	# NUMBER ALTERNATIVES: 3
11	# NUMBER VOTERS: 1094
12	# NUMBER UNIQUE ORDERS: 7
13	# ALTERNATIVE NAME 1: Conlon
14	# ALTERNATIVE NAME 2: Kinzel
15	# ALTERNATIVE NAME 3: Lolli
16	331: {1, 3}, 2
17	270: 2, {1, 3}
18	139: 1, {2, 3}
19	128: {1, 2}, 3
20	116: {1, 2, 3}
21	66: {2, 3}, 1
22	44: 3, {1, 2}

East Montpelier Vermont Senate — 00031-00000002.toc

1094 Voters, 6 Alternatives

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General Properties
Number of alternatives	6
Number of voters	1094
Number of unique preferences	38
Ballot Structure
Size of the smallest ballot	6
Size of the largest ballot	6
Minimum number of indifferences	1
Maximum number of indifferences	2
Size of the smallest indifference	1
Size of the largest indifference	6
Preference Structure
Strict orders	✗
Complete orders	✓
Approval profile	✓
Aggregtated Structure
Condorcet winner	✓

Preview of the File
1	# FILE NAME: 00031-00000002.toc
2	# TITLE: East Montpelier Vermont Senate
3	# DESCRIPTION:
4	# DATA TYPE: toc
5	# MODIFICATION TYPE: original
6	# RELATES TO:
7	# RELATED FILES:
8	# PUBLICATION DATE: 2017-04-13
9	# MODIFICATION DATE: 2022-09-16
10	# NUMBER ALTERNATIVES: 6
11	# NUMBER VOTERS: 1094
12	# NUMBER UNIQUE ORDERS: 38
13	# ALTERNATIVE NAME 1: Cummings
14	# ALTERNATIVE NAME 2: Doyle
15	# ALTERNATIVE NAME 3: Gaffney
...	...
19	236: {1, 3, 6}, {2, 4, 5}
20	191: {2, 4, 5}, {1, 3, 6}
21	153: {1, 2, 6}, {3, 4, 5}
22	62: {1, 2, 5}, {3, 4, 6}
23	48: 6, {1, 2, 3, 4, 5}
24	40: {1, 6}, {2, 3, 4, 5}
25	38: 2, {1, 3, 4, 5, 6}
26	31: 1, {2, 3, 4, 5, 6}
27	30: {1, 5, 6}, {2, 3, 4}
28	25: 5, {1, 2, 3, 4, 6}
...	...

Fayston Vermont Assistant Judge — 00031-00000003.toc

532 Voters, 3 Alternatives

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General Properties
Number of alternatives	3
Number of voters	532
Number of unique preferences	7
Ballot Structure
Size of the smallest ballot	3
Size of the largest ballot	3
Minimum number of indifferences	1
Maximum number of indifferences	1
Size of the smallest indifference	1
Size of the largest indifference	3
Preference Structure
Strict orders	✗
Complete orders	✓
Approval profile	✓
Aggregtated Structure
Condorcet winner	✓

Preview of the File
1	# FILE NAME: 00031-00000003.toc
2	# TITLE: Fayston Vermont Assistant Judge
3	# DESCRIPTION:
4	# DATA TYPE: toc
5	# MODIFICATION TYPE: original
6	# RELATES TO:
7	# RELATED FILES:
8	# PUBLICATION DATE: 2017-04-13
9	# MODIFICATION DATE: 2022-09-16
10	# NUMBER ALTERNATIVES: 3
11	# NUMBER VOTERS: 532
12	# NUMBER UNIQUE ORDERS: 7
13	# ALTERNATIVE NAME 1: Conlon
14	# ALTERNATIVE NAME 2: Kinzel
15	# ALTERNATIVE NAME 3: Lolli
16	147: {1, 3}, 2
17	133: 2, {1, 3}
18	82: {1, 2, 3}
19	72: 1, {2, 3}
20	58: {1, 2}, 3
21	25: {2, 3}, 1
22	15: 3, {1, 2}

Fayston Vermont House — 00031-00000004.toc

532 Voters, 4 Alternatives

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General Properties
Number of alternatives	4
Number of voters	532
Number of unique preferences	11
Ballot Structure
Size of the smallest ballot	4
Size of the largest ballot	4
Minimum number of indifferences	1
Maximum number of indifferences	2
Size of the smallest indifference	1
Size of the largest indifference	4
Preference Structure
Strict orders	✗
Complete orders	✓
Approval profile	✓
Aggregtated Structure
Condorcet winner	✓

Preview of the File
1	# FILE NAME: 00031-00000004.toc
2	# TITLE: Fayston Vermont House
3	# DESCRIPTION:
4	# DATA TYPE: toc
5	# MODIFICATION TYPE: original
6	# RELATES TO:
7	# RELATED FILES:
8	# PUBLICATION DATE: 2017-04-13
9	# MODIFICATION DATE: 2022-09-16
10	# NUMBER ALTERNATIVES: 4
11	# NUMBER VOTERS: 532
12	# NUMBER UNIQUE ORDERS: 11
13	# ALTERNATIVE NAME 1: Grad
14	# ALTERNATIVE NAME 2: Greshin
15	# ALTERNATIVE NAME 3: Read
...	...
17	105: {2, 3}, {1, 4}
18	90: {1, 2}, {3, 4}
19	79: {3, 4}, {1, 2}
20	59: {1, 4}, {2, 3}
21	52: {2, 4}, {1, 3}
22	46: {1, 3}, {2, 4}
23	36: 3, {1, 2, 4}
24	24: 2, {1, 3, 4}
25	19: 4, {1, 2, 3}
26	18: 1, {2, 3, 4}
...	...

Fayston Vermont Senate — 00031-00000005.toc

532 Voters, 6 Alternatives

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General Properties
Number of alternatives	6
Number of voters	532
Number of unique preferences	34
Ballot Structure
Size of the smallest ballot	6
Size of the largest ballot	6
Minimum number of indifferences	1
Maximum number of indifferences	2
Size of the smallest indifference	1
Size of the largest indifference	6
Preference Structure
Strict orders	✗
Complete orders	✓
Approval profile	✓
Aggregtated Structure
Condorcet winner	✓

Preview of the File
1	# FILE NAME: 00031-00000005.toc
2	# TITLE: Fayston Vermont Senate
3	# DESCRIPTION:
4	# DATA TYPE: toc
5	# MODIFICATION TYPE: original
6	# RELATES TO:
7	# RELATED FILES:
8	# PUBLICATION DATE: 2017-04-13
9	# MODIFICATION DATE: 2022-09-16
10	# NUMBER ALTERNATIVES: 6
11	# NUMBER VOTERS: 532
12	# NUMBER UNIQUE ORDERS: 34
13	# ALTERNATIVE NAME 1: Cummings
14	# ALTERNATIVE NAME 2: Doyle
15	# ALTERNATIVE NAME 3: Gaffney
...	...
19	109: {1, 3, 6}, {2, 4, 5}
20	77: {2, 4, 5}, {1, 3, 6}
21	69: {1, 2, 6}, {3, 4, 5}
22	34: 2, {1, 3, 4, 5, 6}
23	27: {1, 2, 5}, {3, 4, 6}
24	21: 1, {2, 3, 4, 5, 6}
25	21: {1, 2, 3, 4, 5, 6}
26	18: {1, 6}, {2, 3, 4, 5}
27	15: {2, 5, 6}, {1, 3, 4}
28	15: 6, {1, 2, 3, 4, 5}
...	...

Manchester Vermont Assistant Judge — 00031-00000006.toc

1581 Voters, 4 Alternatives

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Check the following for more details.

General Properties
Number of alternatives	4
Number of voters	1581
Number of unique preferences	11
Ballot Structure
Size of the smallest ballot	4
Size of the largest ballot	4
Minimum number of indifferences	1
Maximum number of indifferences	2
Size of the smallest indifference	1
Size of the largest indifference	4
Preference Structure
Strict orders	✗
Complete orders	✓
Approval profile	✓
Aggregtated Structure
Condorcet winner	✓

Preview of the File
1	# FILE NAME: 00031-00000006.toc
2	# TITLE: Manchester Vermont Assistant Judge
3	# DESCRIPTION:
4	# DATA TYPE: toc
5	# MODIFICATION TYPE: original
6	# RELATES TO:
7	# RELATED FILES:
8	# PUBLICATION DATE: 2017-04-13
9	# MODIFICATION DATE: 2022-09-16
10	# NUMBER ALTERNATIVES: 4
11	# NUMBER VOTERS: 1581
12	# NUMBER UNIQUE ORDERS: 11
13	# ALTERNATIVE NAME 1: Colvin
14	# ALTERNATIVE NAME 2: Kokoras
15	# ALTERNATIVE NAME 3: Mook
...	...
17	435: {1, 3}, {2, 4}
18	319: {2, 4}, {1, 3}
19	276: {1, 2, 3, 4}
20	141: 1, {2, 3, 4}
21	113: 2, {1, 3, 4}
22	93: 4, {1, 2, 3}
23	90: 3, {1, 2, 4}
24	38: {3, 4}, {1, 2}
25	29: {1, 4}, {2, 3}
26	26: {1, 2}, {3, 4}
...	...

Manchester Vermont House — 00031-00000007.toc

1581 Voters, 4 Alternatives

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Check the following for more details.

General Properties
Number of alternatives	4
Number of voters	1581
Number of unique preferences	11
Ballot Structure
Size of the smallest ballot	4
Size of the largest ballot	4
Minimum number of indifferences	1
Maximum number of indifferences	2
Size of the smallest indifference	1
Size of the largest indifference	4
Preference Structure
Strict orders	✗
Complete orders	✓
Approval profile	✓
Aggregtated Structure
Condorcet winner	✓

Preview of the File
1	# FILE NAME: 00031-00000007.toc
2	# TITLE: Manchester Vermont House
3	# DESCRIPTION:
4	# DATA TYPE: toc
5	# MODIFICATION TYPE: original
6	# RELATES TO:
7	# RELATED FILES:
8	# PUBLICATION DATE: 2017-04-13
9	# MODIFICATION DATE: 2022-09-16
10	# NUMBER ALTERNATIVES: 4
11	# NUMBER VOTERS: 1581
12	# NUMBER UNIQUE ORDERS: 11
13	# ALTERNATIVE NAME 1: Berry
14	# ALTERNATIVE NAME 2: Browning
15	# ALTERNATIVE NAME 3: DuPont
...	...
17	381: {1, 2}, {3, 4}
18	268: {3, 4}, {1, 2}
19	210: 1, {2, 3, 4}
20	167: 4, {1, 2, 3}
21	153: {2, 4}, {1, 3}
22	129: {1, 4}, {2, 3}
23	68: 3, {1, 2, 4}
24	59: {2, 3}, {1, 4}
25	57: 2, {1, 3, 4}
26	53: {1, 2, 3, 4}
...	...

Manchester Vermont Senate — 00031-00000008.toc

1581 Voters, 3 Alternatives

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Check the following for more details.

General Properties
Number of alternatives	3
Number of voters	1581
Number of unique preferences	7
Ballot Structure
Size of the smallest ballot	3
Size of the largest ballot	3
Minimum number of indifferences	1
Maximum number of indifferences	1
Size of the smallest indifference	1
Size of the largest indifference	3
Preference Structure
Strict orders	✗
Complete orders	✓
Approval profile	✓
Aggregtated Structure
Condorcet winner	✓

Preview of the File
1	# FILE NAME: 00031-00000008.toc
2	# TITLE: Manchester Vermont Senate
3	# DESCRIPTION:
4	# DATA TYPE: toc
5	# MODIFICATION TYPE: original
6	# RELATES TO:
7	# RELATED FILES:
8	# PUBLICATION DATE: 2017-04-13
9	# MODIFICATION DATE: 2022-09-16
10	# NUMBER ALTERNATIVES: 3
11	# NUMBER VOTERS: 1581
12	# NUMBER UNIQUE ORDERS: 7
13	# ALTERNATIVE NAME 1: Campion
14	# ALTERNATIVE NAME 2: Roaf
15	# ALTERNATIVE NAME 3: Sears
16	535: {1, 3}, 2
17	391: 2, {1, 3}
18	246: 3, {1, 2}
19	146: {2, 3}, 1
20	108: {1, 2, 3}
21	96: 1, {2, 3}
22	59: {1, 2}, 3

St Johnsbury Vermont Assistant Judge — 00031-00000009.toc

1960 Voters, 3 Alternatives

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Check the following for more details.

General Properties
Number of alternatives	3
Number of voters	1960
Number of unique preferences	7
Ballot Structure
Size of the smallest ballot	3
Size of the largest ballot	3
Minimum number of indifferences	1
Maximum number of indifferences	1
Size of the smallest indifference	1
Size of the largest indifference	3
Preference Structure
Strict orders	✗
Complete orders	✓
Approval profile	✓
Aggregtated Structure
Condorcet winner	✓

Preview of the File
1	# FILE NAME: 00031-00000009.toc
2	# TITLE: St Johnsbury Vermont Assistant Judge
3	# DESCRIPTION:
4	# DATA TYPE: toc
5	# MODIFICATION TYPE: original
6	# RELATES TO:
7	# RELATED FILES:
8	# PUBLICATION DATE: 2017-04-13
9	# MODIFICATION DATE: 2022-09-16
10	# NUMBER ALTERNATIVES: 3
11	# NUMBER VOTERS: 1960
12	# NUMBER UNIQUE ORDERS: 7
13	# ALTERNATIVE NAME 1: Hall
14	# ALTERNATIVE NAME 2: Roosevelt
15	# ALTERNATIVE NAME 3: Vance
16	786: {1, 3}, 2
17	256: {1, 2}, 3
18	251: {2, 3}, 1
19	250: 1, {2, 3}
20	154: 3, {1, 2}
21	148: 2, {1, 3}
22	115: {1, 2, 3}

St Johnsbury Vermont House — 00031-00000010.toc

1960 Voters, 4 Alternatives

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Check the following for more details.

General Properties
Number of alternatives	4
Number of voters	1960
Number of unique preferences	11
Ballot Structure
Size of the smallest ballot	4
Size of the largest ballot	4
Minimum number of indifferences	1
Maximum number of indifferences	2
Size of the smallest indifference	1
Size of the largest indifference	4
Preference Structure
Strict orders	✗
Complete orders	✓
Approval profile	✓
Aggregtated Structure
Condorcet winner	✓

Preview of the File
1	# FILE NAME: 00031-00000010.toc
2	# TITLE: St Johnsbury Vermont House
3	# DESCRIPTION:
4	# DATA TYPE: toc
5	# MODIFICATION TYPE: original
6	# RELATES TO:
7	# RELATED FILES:
8	# PUBLICATION DATE: 2017-04-13
9	# MODIFICATION DATE: 2022-09-16
10	# NUMBER ALTERNATIVES: 4
11	# NUMBER VOTERS: 1960
12	# NUMBER UNIQUE ORDERS: 11
13	# ALTERNATIVE NAME 1: Beck
14	# ALTERNATIVE NAME 2: Fay
15	# ALTERNATIVE NAME 3: South
...	...
17	616: {1, 4}, {2, 3}
18	490: {2, 3}, {1, 4}
19	169: {1, 2}, {3, 4}
20	159: 1, {2, 3, 4}
21	133: {1, 3}, {2, 4}
22	93: 2, {1, 3, 4}
23	92: 4, {1, 2, 3}
24	69: {3, 4}, {1, 2}
25	61: 3, {1, 2, 4}
26	48: {2, 4}, {1, 3}
...	...

St Johnsbury Vermont Senate — 00031-00000011.toc

1960 Voters, 3 Alternatives

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Check the following for more details.

General Properties
Number of alternatives	3
Number of voters	1960
Number of unique preferences	7
Ballot Structure
Size of the smallest ballot	3
Size of the largest ballot	3
Minimum number of indifferences	1
Maximum number of indifferences	1
Size of the smallest indifference	1
Size of the largest indifference	3
Preference Structure
Strict orders	✗
Complete orders	✓
Approval profile	✓
Aggregtated Structure
Condorcet winner	✓

Preview of the File
1	# FILE NAME: 00031-00000011.toc
2	# TITLE: St Johnsbury Vermont Senate
3	# DESCRIPTION:
4	# DATA TYPE: toc
5	# MODIFICATION TYPE: original
6	# RELATES TO:
7	# RELATED FILES:
8	# PUBLICATION DATE: 2017-04-13
9	# MODIFICATION DATE: 2022-09-16
10	# NUMBER ALTERNATIVES: 3
11	# NUMBER VOTERS: 1960
12	# NUMBER UNIQUE ORDERS: 7
13	# ALTERNATIVE NAME 1: Benning
14	# ALTERNATIVE NAME 2: Heath
15	# ALTERNATIVE NAME 3: Kitchel
16	738: {1, 3}, 2
17	445: {2, 3}, 1
18	334: 1, {2, 3}
19	226: 3, {1, 2}
20	95: 2, {1, 3}
21	89: {1, 2}, 3
22	33: {1, 2, 3}

Westminster Vermont Assistant Judge — 00031-00000012.toc

943 Voters, 4 Alternatives

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Check the following for more details.

General Properties
Number of alternatives	4
Number of voters	943
Number of unique preferences	11
Ballot Structure
Size of the smallest ballot	4
Size of the largest ballot	4
Minimum number of indifferences	1
Maximum number of indifferences	2
Size of the smallest indifference	1
Size of the largest indifference	4
Preference Structure
Strict orders	✗
Complete orders	✓
Approval profile	✓
Aggregtated Structure
Condorcet winner	✓

Preview of the File
1	# FILE NAME: 00031-00000012.toc
2	# TITLE: Westminster Vermont Assistant Judge
3	# DESCRIPTION:
4	# DATA TYPE: toc
5	# MODIFICATION TYPE: original
6	# RELATES TO:
7	# RELATED FILES:
8	# PUBLICATION DATE: 2017-04-13
9	# MODIFICATION DATE: 2022-09-16
10	# NUMBER ALTERNATIVES: 4
11	# NUMBER VOTERS: 943
12	# NUMBER UNIQUE ORDERS: 11
13	# ALTERNATIVE NAME 1: Duff
14	# ALTERNATIVE NAME 2: Kane
15	# ALTERNATIVE NAME 3: Landsman
...	...
17	486: {1, 2}, {3, 4}
18	171: 2, {1, 3, 4}
19	115: {1, 2, 3, 4}
20	39: 1, {2, 3, 4}
21	37: {3, 4}, {1, 2}
22	31: {2, 4}, {1, 3}
23	20: {2, 3}, {1, 4}
24	20: {1, 3}, {2, 4}
25	10: {1, 4}, {2, 3}
26	7: 3, {1, 2, 4}
...	...

Westminster Vermont Senate — 00031-00000013.toc

943 Voters, 5 Alternatives

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General Properties
Number of alternatives	5
Number of voters	943
Number of unique preferences	16
Ballot Structure
Size of the smallest ballot	5
Size of the largest ballot	5
Minimum number of indifferences	1
Maximum number of indifferences	2
Size of the smallest indifference	1
Size of the largest indifference	5
Preference Structure
Strict orders	✗
Complete orders	✓
Approval profile	✓
Aggregtated Structure
Condorcet winner	✓

Preview of the File
1	# FILE NAME: 00031-00000013.toc
2	# TITLE: Westminster Vermont Senate
3	# DESCRIPTION:
4	# DATA TYPE: toc
5	# MODIFICATION TYPE: original
6	# RELATES TO:
7	# RELATED FILES:
8	# PUBLICATION DATE: 2017-04-13
9	# MODIFICATION DATE: 2022-09-16
10	# NUMBER ALTERNATIVES: 5
11	# NUMBER VOTERS: 943
12	# NUMBER UNIQUE ORDERS: 16
13	# ALTERNATIVE NAME 1: Balint
14	# ALTERNATIVE NAME 2: Diamondstone
15	# ALTERNATIVE NAME 3: Hasson
...	...
18	447: {1, 5}, {2, 3, 4}
19	141: 5, {1, 2, 3, 4}
20	78: {1, 2, 3, 4, 5}
21	72: {3, 5}, {1, 2, 4}
22	44: 3, {1, 2, 4, 5}
23	25: 1, {2, 3, 4, 5}
24	25: {1, 3}, {2, 4, 5}
25	21: {2, 4}, {1, 3, 5}
26	21: {4, 5}, {1, 2, 3}
27	19: {2, 5}, {1, 3, 4}
...	...

Wolcott Vermont House — 00031-00000014.toc

559 Voters, 4 Alternatives

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Check the following for more details.

General Properties
Number of alternatives	4
Number of voters	559
Number of unique preferences	11
Ballot Structure
Size of the smallest ballot	4
Size of the largest ballot	4
Minimum number of indifferences	1
Maximum number of indifferences	2
Size of the smallest indifference	1
Size of the largest indifference	4
Preference Structure
Strict orders	✗
Complete orders	✓
Approval profile	✓
Aggregtated Structure
Condorcet winner	✓

Preview of the File
1	# FILE NAME: 00031-00000014.toc
2	# TITLE: Wolcott Vermont House
3	# DESCRIPTION:
4	# DATA TYPE: toc
5	# MODIFICATION TYPE: original
6	# RELATES TO:
7	# RELATED FILES:
8	# PUBLICATION DATE: 2017-04-13
9	# MODIFICATION DATE: 2022-09-16
10	# NUMBER ALTERNATIVES: 4
11	# NUMBER VOTERS: 559
12	# NUMBER UNIQUE ORDERS: 11
13	# ALTERNATIVE NAME 1: Bouthillette
14	# ALTERNATIVE NAME 2: Gravel
15	# ALTERNATIVE NAME 3: Martin
...	...
17	220: {3, 4}, {1, 2}
18	144: {1, 2}, {3, 4}
19	61: 2, {1, 3, 4}
20	54: 3, {1, 2, 4}
21	34: {2, 3}, {1, 4}
22	10: 1, {2, 3, 4}
23	9: {2, 4}, {1, 3}
24	9: 4, {1, 2, 3}
25	9: {1, 2, 3, 4}
26	6: {1, 3}, {2, 4}
...	...

Wolcott Vermont Senate — 00031-00000015.toc

559 Voters, 3 Alternatives

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Check the following for more details.

General Properties
Number of alternatives	3
Number of voters	559
Number of unique preferences	7
Ballot Structure
Size of the smallest ballot	3
Size of the largest ballot	3
Minimum number of indifferences	1
Maximum number of indifferences	1
Size of the smallest indifference	1
Size of the largest indifference	3
Preference Structure
Strict orders	✗
Complete orders	✓
Approval profile	✓
Aggregtated Structure
Condorcet winner	✓

Preview of the File
1	# FILE NAME: 00031-00000015.toc
2	# TITLE: Wolcott Vermont Senate
3	# DESCRIPTION:
4	# DATA TYPE: toc
5	# MODIFICATION TYPE: original
6	# RELATES TO:
7	# RELATED FILES:
8	# PUBLICATION DATE: 2017-04-13
9	# MODIFICATION DATE: 2022-09-16
10	# NUMBER ALTERNATIVES: 3
11	# NUMBER VOTERS: 559
12	# NUMBER UNIQUE ORDERS: 7
13	# ALTERNATIVE NAME 1: Horne
14	# ALTERNATIVE NAME 2: Rodgers
15	# ALTERNATIVE NAME 3: Starr
16	131: 2, {1, 3}
17	127: {2, 3}, 1
18	100: {1, 3}, 2
19	81: 1, {2, 3}
20	54: {1, 2, 3}
21	48: 3, {1, 2}
22	18: {1, 2}, 3